ALBERT

Description: 〈div data-abstract-type="normal"〉〈p〉The effectiveness of streak modes in controlling the oblique-type breakdown in a supersonic boundary-layer at Mach 2.0 is investigated using direct numerical simulations. Investigations in the literature have shown the effectiveness of streak modes in delaying the onset of transition dominated by two-dimensional waves, but in oblique breakdown, three-dimensional waves and a strong streak mode dominate the transition process. Paredes 〈span〉et al.〈/span〉 (〈span〉J. Fluid Mech.〈/span〉, vol. 831, 2017, pp. 524–553) discussed the possible stabilization of supersonic boundary layers by optimally growing streaks using parabolized stability equations. However, no study has as yet been reported regarding direct nonlinear control of oblique breakdown. This study deals with the effects of large-amplitude decaying streak modes generated by a blowing–suction strip at the wall to control full breakdown in a reference case. Modes with four to five times the fundamental wavenumber are found to be beneficial for controlling the transition. In the first region after the control-mode forcing, the beneficial mean-flow distortion (MFD), generated by inducing the control mode, is solely responsible for hampering the growth of the fundamental-mode. On the whole, the MFD and the three-dimensional part of the control contribute equally towards controlling the oblique breakdown. The results show significant suppression of transition, and substantial improvements have been observed in the levels of the skin-friction coefficient and wall-temperature in comparison to the uncontrolled case. Moreover, refreshing the control using an additional downstream control strip increases the gain. However, the forcing amplitude must be carefully chosen in order not to introduce a generalized inflection point in the spanwise averaged mean flow invoking enhanced disturbance growth.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The problem of interaction between disturbances and shock waves was solved by a theoretical approach called linear interaction analysis in the mid-twentieth century. More recently, great progress has been made in analysing shock–turbulence interactions by direct numerical simulation. However, an unsolved theoretical problem remains: What happens when no acoustic waves are stimulated behind the shock wave? The concept of a damped wave is introduced, which is a type of excited plane wave. Based on this, the dispersion and amplitude relationships between any incident plane wave and resulting stimulated waves are constructed analytically, systematically and comprehensively. The physical essence of damped waves and the existence of critical angles are clarified. It is demonstrated that a damped wave is a complex number space solution to the acoustic dispersion relationship under certain conditions. It acts as a bridge connecting fast and slow acoustic waves at the position where the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628130807083-0762:S0022112019004385:S0022112019004385_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 component of the group velocity is zero. There are two critical angles that can excite fast and slow acoustic waves, which determine the conditions that stimulate a damped wave. Our results show good agreement with theoretical and simulation results. The contribution of each excited wave to the transmission coefficient is evaluated, the distribution of the transmission coefficient is analysed and application to an engineering wedge model is performed.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The onset of thermal convection in a rapidly rotating spherical shell is studied by linear stability analysis based on the fully compressible Navier–Stokes equations. Compressibility is quantified by the number of density scale heights 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, which measures the intensity of density stratification of the motionless, polytropic base state. The nearly adiabatic flow with polytropic index 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is considered, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the adiabatic polytropic index. By investigating the stability of the base state with respect to the disturbance of specified wavenumber, the instability process is found to be sensitive to the Prandtl number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. For large 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the quasi-geostrophic columnar mode loses stability first; while for relatively small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 a new quasi-geostrophic compressible mode is identified, which becomes unstable first under strong density stratification. The inertial mode can also occur first for relatively small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and a certain intensity of density stratification in the parameter range considered. Although the Rayleigh numbers 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for the onsets of the quasi-geostrophic compressible mode and columnar mode are different by several orders of magnitude, we find that they follow very similar scaling laws with the Taylor number. The critical 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for convection onset is found to be always positive, in contrast with previous results based on the widely used anelastic model that convection can occur at negative 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. By evaluating the relative magnitude of the time derivative of density perturbation in the continuity equation, we show that the anelastic approximation in the present system cannot be applied in the small-〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and large-〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628092857401-0357:S0022112019004361:S0022112019004361_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 regime.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We study the breakup of confined fluid threads at low flow rates to understand instability mechanisms. To determine the critical conditions between the earlier quasi-stable necking stage and the later unstable collapse stage, simulations and experiments are designed to operate at an extremely low flow rate. The critical mean radii at the neck centres are identified by the stop-flow method for elementary microfluidic configurations. Two distinct origins of capillary instabilities are revealed for different confinement situations. One is the gradient of capillary pressure induced by the confinements of geometry and external flow, whereas the other is the competition between the capillary pressure and internal pressure determined by the confinements.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We report on a combined experimental and numerical study of convective heat transfer along ratchet surfaces in vertical natural convection (VC). Due to the asymmetry of the convection system caused by the asymmetric ratchet-like wall roughness, two distinct states exist, with markedly different orientations of the large-scale circulation roll (LSCR) and different heat transport efficiencies. Statistical analysis shows that the heat transport efficiency depends on the strength of the LSCR. When a large-scale wind flows along the ratchets in the direction of their smaller slopes, the convection roll is stronger and the heat transport is larger than the case in which the large-scale wind is directed towards the steeper slope side of the ratchets. Further analysis of the time-averaged temperature profiles indicates that the stronger LSCR in the former case triggers the formation of a secondary vortex inside the roughness cavity, which promotes fluid mixing and results in a higher heat transport efficiency. Remarkably, this result differs from classical Rayleigh–Bénard convection (RBC) with asymmetric ratchets (Jiang 〈span〉et al.〈/span〉, 〈span〉Phys. Rev. Lett.〈/span〉, vol. 120, 2018, 044501), wherein the heat transfer is stronger when the large-scale wind faces the steeper side of the ratchets. We reveal that the reason for the reversed trend for VC as compared to RBC is that the flow is less turbulent in VC at the same 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628072522266-0966:S0022112019004464:S0022112019004464_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Thus, in VC the heat transport is driven primarily by the coherent LSCR, while in RBC the ejected thermal plumes aided by gravity are the essential carrier of heat. The present work provides opportunities for control of heat transport in engineering and geophysical flows.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We explore the dynamics of inclined temporal gravity currents using direct numerical simulation, and find that the current creates an environment in which the flux Richardson number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, gradient Richardson number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and turbulent flux coefficient 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 are constant across a large portion of the depth. Changing the slope angle 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 modifies these mixing parameters, and the flow approaches a maximum Richardson number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 as 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 at which the entrainment coefficient 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The turbulent Prandtl number remains 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for all slope angles, demonstrating that 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is not caused by a switch-off of the turbulent buoyancy flux as conjectured by Ellison (〈span〉J. Fluid Mech.〈/span〉, vol. 2, 1957, pp. 456–466). Instead, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 occurs as the result of the turbulence intensity going to zero as 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, due to the flow requiring larger and larger shear to maintain the same level of turbulence. We develop an approximate model valid for small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 which is able to predict accurately 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 as a function of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and their maximum attainable values. The model predicts an entrainment law of the form 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627132031350-0413:S0022112019004300:S0022112019004300_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, which is in good agreement with the simulation data. The simulations and model presented here contribute to a growing body of evidence that an approach to a marginally or critically stable, relatively weakly stratified equilibrium for stratified shear flows may well be a generic property of turbulent stratified flows.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Ice scallops are a small-scale (5–20 cm) quasi-periodic ripple pattern that occurs at the ice–water interface. Previous work has suggested that scallops form due to a self-reinforcing interaction between an evolving ice-surface geometry, an adjacent turbulent flow field and the resulting differential melt rates that occur along the interface. In this study, we perform a series of laboratory experiments in a refrigerated flume to quantitatively investigate the mechanisms of scallop formation and evolution in high resolution. Using particle image velocimetry, we probe an evolving ice–water boundary layer at sub-millimetre scales and 15 Hz frequency. Our data reveal three distinct regimes of ice–water interface evolution: a transition from flat to scalloped ice; an equilibrium scallop geometry; and an adjusting scallop interface. We find that scalloped-ice geometry produces a clear modification to the ice–water boundary layer, characterized by a time-mean recirculating eddy feature that forms in the scallop trough. Our primary finding is that scallops form due to a self-reinforcing feedback between the ice-interface geometry and shear production of turbulent kinetic energy in the flow interior. The length of this shear production zone is therefore hypothesized to set the scallop wavelength.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Direct numerical simulation (DNS) is performed for two wall-bounded flow configurations: laminar Couette flow at 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and turbulent channel flow at 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the shear stress at the wall. The top wall is smooth and the bottom wall is a realistically rough superhydrophobic surface (SHS), generated from a three-dimensional surface profile measurement. The air–water interface, which is assumed to be flat, is simulated using the volume-of-fluid (VOF) approach. The two flow cases are studied with varying interface heights 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to understand its effect on slip and drag reduction (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉). For the laminar Couette flow case, the presence of the surface roughness is felt up to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the channel height in the wall-normal direction. Nonlinear dependence of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 on 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is observed with three distinct regions. A nonlinear curve fit is obtained for gas fraction 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 as a function of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 determines the amount of slip area exposed to the flow. A power law fit is obtained from the data for the effective slip length as a function of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and is compared to those derived for structured geometry. For the turbulent channel flow, statistics of the flow field are compared to that of a smooth wall to understand the effects of roughness and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Four cases are simulated ranging from fully wetted to fully covered and two intermediate regions in between. Scaling laws for slip length, slip velocity, roughness function and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 are obtained for different penetration depths and are compared to past work for structured geometry. 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190628070320625-0031:S0022112019004191:S0022112019004191_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is shown to depend on a competing effect between slip velocity and turbulent losses due to the Reynolds shear stress contribution. Presence of trapped air in the cavities significantly alters near-wall flow physics where we examine near-wall structures and propose a physical mechanism for their behaviour. The fully wetted roughness increases the peak value of turbulent intensities, whereas the presence of the interface suppresses them. The pressure fluctuations have competing contributions between turbulent pressure fluctuations and stagnation due to asperities, the near-wall structure is altered and breaks down with increasing slip. Overall, there exists a competing effect between the interface and the asperities, the interface suppresses turbulence whereas the asperities enhance them. The present work demonstrates DNS over a realistic multiphase SHS for the first time, to the best of our knowledge.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We developed a numerical method for the set of equations governing fully compressible convection in the limit of infinite Prandtl numbers. Reduced models have also been analysed, such as the anelastic approximation and the anelastic liquid approximation. The tests of our numerical schemes against self-consistent criteria have shown that our numerical simulations are consistent from the point of view of energy dissipation, heat transfer and entropy budget. The equation of state of an ideal gas has been considered in this work. Specific effects arising because of the compressibility of the fluid are studied, like the scaling of viscous dissipation and the scaling of the heat flux contribution due to the mechanical power exerted by viscous forces. We analysed the solutions obtained with each model (fully compressible model, anelastic and anelastic liquid approximations) in a wide range of dimensionless parameters and determined the errors induced by each approximation with respect to the fully compressible solutions. Based on a rationale on the development of the thermal boundary layers, we can explain reasonably well the differences between the fully compressible and anelastic models, in terms of both the heat transfer and viscous dissipation dependence on compressibility. This could be mostly an effect of density variations on thermal diffusivity. Based on the different forms of entropy balance between exact and anelastic models, we find that a necessary condition for convergence of the anelastic results to the exact solutions is that the product 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 must be small compared to unity, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the ratio of the superadiabatic temperature difference to the adiabatic difference, and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the ratio of the superadiabatic heat flux to the heat flux conducted along the adiabat. The same condition seems also to be associated with a convergence of the computed heat fluxes. Concerning the anelastic liquid approximation, we confirm previous estimates by Anufriev 〈span〉et al.〈/span〉 (〈span〉Phys. Earth Planet. Inter.〈/span〉, vol. 152, 2005, pp. 163–190) and find that its results become generally close to those of the fully compressible model when 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is small compared to unity, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the isobaric thermal expansion coefficient, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the temperature (here 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for an ideal gas) and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190625082702251-0920:S0022112019004208:S0022112019004208_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the dissipation number.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor–Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (〈span〉Phys. Fluids〈/span〉, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉(corresponding to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉). We focus on the influence of the roughness height 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 up to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and by the friction factor 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is calculated to be 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (〈span〉VDI-Forsch.〈/span〉, vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621104521411-0582:S0022112019003768:S0022112019003768_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (〈span〉Proc. R. Soc. Lond.〈/span〉 A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621105221417-0357:S0022112019004282:S0022112019004282_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621105221417-0357:S0022112019004282:S0022112019004282_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621105221417-0357:S0022112019004282:S0022112019004282_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the linear prediction of the maximum slope at focusing and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621105221417-0357:S0022112019004282:S0022112019004282_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621105221417-0357:S0022112019004282:S0022112019004282_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We conduct direct numerical simulations (DNS) of the Cahn–Hilliard–Navier–Stokes (CHNS) equations to investigate the statistical properties of a turbulent phase-separating symmetric binary-fluid mixture. Turbulence causes an arrest of the phase separation which leads to the formation of a statistically steady emulsion. We characterise turbulent velocity fluctuations in an emulsion for different values of the Reynolds number and the Weber number. Our scale-by-scale kinetic energy budget analysis shows that the interfacial terms in the CHNS equations provide an alternative route for the kinetic energy transfer. By studying the probability distribution function (p.d.f.) of the energy dissipation rate, the vorticity magnitude and the joint-p.d.f. of the velocity-gradient invariants we show that the statistics of the turbulent fluctuations do not change with the Weber number.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉With the aim to characterize the near-wall flow structures and their interaction with large-scale motions in the log-law region, time-resolved planar and volumetric flow field measurements were performed in the near-wall and log-law region of an adverse pressure gradient turbulent boundary layer following a zero pressure gradient turbulent boundary layer at a friction Reynolds number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621113954055-0112:S0022112019004087:S0022112019004087_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Due to the high spatial and temporal resolution of the measurements, it was possible to resolve and identify uniform-momentum zones in the region 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621113954055-0112:S0022112019004087:S0022112019004087_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 or 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621113954055-0112:S0022112019004087:S0022112019004087_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and to relate them with well known coherent flow motions near the wall. The space–time results confirm that the turbulent superstructures have a strong impact even on the very near-wall flow motion and also their alternating appearance in time and intensity could be quantified over long time sequences. Using the time record of the velocity field, rare localized separation events appearing in the viscous sublayer were also analysed. By means of volumetric particle tracking velocimetry their three-dimensional topology and dynamics could be resolved. Based on the results, a conceptual model was deduced that explains their rare occurrence, topology and dynamics by means of a complex interaction process between low-momentum turbulent superstructures, near-wall low-speed streaks and tilted longitudinal and spanwise vortices located in the near-wall region.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We experimentally investigate the extensional flow of a sheet – or curtain – of viscoelastic liquid falling freely from a slot at constant flow rate under gravity. Extruded liquids are aqueous solutions of flexible polyethylene oxide (PEO) and of semi-rigid partially hydrolysed polyacrylamide (HPAM) with low shear viscosities. Velocimetry measurements reveal that the mean velocity field 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the distance from the slot exit) does not reduce to a free fall. More precisely, we show that the liquid falls initially with sub-gravitational accelerations up to a distance from the slot which scales as 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is gravity and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the extensional relaxation time of the liquid) due to the stretching of polymer molecules. Beyond this elastic length, inertia dominates and the local acceleration reaches the asymptotic free-fall value 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The length of the sub-gravitational part of the curtain is shown to be much larger than the equivalent viscous length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for Newtonian liquids of density 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and dynamic viscosity 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 which is usually small compared to the curtain length. By analogy with Newtonian curtains, we show that the velocity field 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621102720940-0917:S0022112019003896:S0022112019003896_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 rescales on a master curve. Besides, the flow is shown to be only weakly affected by the history of polymer deformations in the die upstream of the curtain. Furthermore, investigations on the curtain stability reveal that polymer addition reduces the minimum flow rate required to maintain a continuous sheet of liquid.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Previous experiments have revealed that shock waves driven through dissipative media may become unstable, for example, in granular gases, and in molecular gases undergoing strong relaxation effects. The current paper addresses this problem of shock stability at the Euler and Navier–Stokes continuum levels in a system of disks (two-dimensional) undergoing activated inelastic collisions. The dynamics of shock formation and stability is found to be in very good agreement with earlier molecular dynamic simulations (Sirmas & Radulescu, 〈span〉Phys. Rev.〈/span〉 E, vol. 91, 2015, 023003). It was found that the modelling of shock instability requires the introduction of molecular noise for its development and sustenance. This is confirmed in two stability problems. In the first, the evolution of shock formation dynamics is monitored without noise, with only initial noise and with continuous molecular noise. Only the latter reproduces the results of shock instability of molecular dynamics simulations. In the second problem, the steady travelling wave solution is obtained for the shock structure in the inviscid and viscous limits and its nonlinear stability is studied with and without molecular fluctuations, again showing that instability can be sustained only in the presence of fluctuations. The continuum results show that instability takes the form of a rippled front of a wavelength comparable with the relaxation thickness of the steady shock wave, at scales at which molecular fluctuations become important, in excellent agreement with the molecular dynamic simulations.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We performed two-way coupled direct numerical simulations of turbulent channel flow with Lagrangian tracking of small, heavy spheres at a dimensionless gravitational acceleration of 0.077 in wall units, which is based on the flow condition in the experiment by Gerashchenko 〈span〉et al.〈/span〉 (〈span〉J. Fluid Mech.〈/span〉, vol. 617, 2008, pp. 255–281). We removed deposited particles after several collisions with the lower wall and then released new particles near the upper wall to observe direct interactions between particles and coherent structures of near-wall turbulence during gravitational settling through the mean shear. The results indicate that when the Stokes number is approximately 1 on the basis of the Kolmogorov time scale of the flow (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190624134045701-0463:S0022112019004002:S0022112019004002_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), the so-called preferential sweeping occurs in association with coherent streamwise vortices, while the effect of crossing trajectories becomes significant for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190624134045701-0463:S0022112019004002:S0022112019004002_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Consequently, in either case, the settling particles deposit on the wall without strong accumulation in low-speed streaks in the viscous sublayer. When particles settle through near-wall turbulence from the upper wall, more small-scale vortical structures are generated in the outer layer as low-speed fluid is pulled farther in the direction of gravity, while the opposite is true near the lower wall.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Streaks have been found to be an important part of wall-turbulence dynamics. In this paper, we extend the analysis for unbounded shear flows, in particular a Mach 0.4 round jet, using measurements taken using dual-plane, time-resolved, stereoscopic particle image velocimetry (PIV) taken at pairs of jet cross-sections, allowing the evaluation of the cross-spectral density of streamwise velocity fluctuations resolved into azimuthal Fourier modes. From the streamwise velocity results, two analyses are performed: the evaluation of wavenumber spectra (assuming Taylor’s hypothesis for the streamwise coordinate) and a spectral proper orthogonal decomposition (SPOD) of the velocity field using PIV planes in several axial stations. The methods complement each other, leading to the conclusion that large-scale streaky structures are also present in turbulent jets where they experience large growth in the streamwise direction, energetic structures extending up to eight diameters from the nozzle exit. Leading SPOD modes highlight the large-scale, streaky shape of the structures, whose aspect ratio (streamwise over azimuthal length) is approximately 15. The data were further analysed using SPOD, resolvent and transient growth analyses, good agreement being observed between the models and the leading SPOD mode for the wavenumbers considered. The models also indicate that the lift-up mechanism is active in turbulent jets, with streamwise vortices leading to streaks. The results show that large-scale streaks are a relevant part of the jet dynamics.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We study single-phase and particle-laden turbulent channel flows bounded by two incompressible hyper-elastic walls with different deformability at bulk Reynolds number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621111752900-0025:S0022112019004130:S0022112019004130_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The solid volume fraction of finite-size neutrally buoyant rigid spherical particles considered is 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621111752900-0025:S0022112019004130:S0022112019004130_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The elastic walls are assumed to be of a neo-Hookean material. A fully Eulerian formulation is employed to model the elastic walls together with a direct-forcing immersed boundary method for the coupling between the fluid and the particles. The data show a significant drag increase and the enhancement of the turbulence activity with growing wall elasticity for both the single-phase and particle-laden flows when compared with the single-phase flow over rigid walls. Drag reduction and turbulence attenuation is obtained, on the other hand, with highly elastic walls when comparing the particle-laden flow with the single-phase flow for the same wall properties; the opposite effect, drag increase, is observed upon adding particles to the flow over less elastic walls. This is explained by investigating the near-wall turbulence, where the strong asymmetry in the magnitude of the wall-normal velocity fluctuations (favouring positive 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621111752900-0025:S0022112019004130:S0022112019004130_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), is found to push the particles towards the channel centre. The particle layer close to the wall contributes to turbulence production by increasing the wall-normal velocity fluctuations, so that in the absence of this layer, smaller wall deformations and in turn turbulence attenuation is observed. For a moderate wall elasticity, we increase the particle volume fraction up to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621111752900-0025:S0022112019004130:S0022112019004130_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and find that particle migration away from the wall is the cause of turbulence attenuation with respect to the flow over rigid walls. However, for this higher volume fractions, the particle induced stress compensates for the decreasing Reynolds shear stress, resulting in a higher overall drag for the case with elastic walls. The effect of the wall elasticity on the overall drag reduces significantly with increasing particle volume fraction.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present large-eddy simulation (LES) of flow past different airfoils with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, based on the free-stream velocity and airfoil chord length, ranging from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. To avoid the challenging resolution requirements of the near-wall region, we develop a virtual wall model in generalized curvilinear coordinates and incorporate the non-equilibrium effects via proper treatment of the momentum equations. It is demonstrated that the wall model dynamically captures the instantaneous skin-friction vector field on arbitrary curved surfaces at the resolved scale. By combining the present wall model with the stretched-vortex subgrid-scale model, we apply the wall-modelled LES approach to three different airfoil cases, spanning different geometrical parameters, different attack angles and low to high 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The numerical results are verified with direct numerical simulation (DNS) at low 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, and validated with experiment data at higher 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, including typical aerodynamic properties such as pressure coefficient distributions, velocity components and also more challenging measurements such as skin-friction coefficient and Reynolds stresses. All comparisons show reasonable agreement, providing a measure of validity that enables us to further probe simulation results into aspects of flow physics that are not available from experiments. Two techniques to quantify hitherto unexplored physics of flows past airfoils are employed: one is the construction of the anisotropy invariant map, and the second is skin-friction portraits with emphasis on flow transition and unsteady separation along the airfoil surface. The anisotropy maps for all three 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 cases, show clearly that a portion of the flow field is aligned along the axisymmetric expansion line, corresponding to the turbulent boundary layer log-law behaviour and the appearance of turbulent transition. The instantaneous skin-friction portraits reveal a monotonic shrinking of the near wall structure scale. At 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the interaction between the primary separation bubble and the secondary separation bubble contributes to turbulent transition, similar to the case of flow past a cylinder. At higher 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the primary separation breaks into several small separation bubbles. At even higher 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621103821391-0158:S0022112019003604:S0022112019003604_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, near the turbulent separation, the skin-friction lines show small-scale reversal flows that are similar to those observed in DNS of the flat plate turbulent separation. A notable feature of turbulent separation in flow past an airfoil is the appearance of turbulence structures and small-scale reversal flows in the spanwise direction due to the vortex shedding behaviour.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉In the framework of the complete formulation of the conjugate problem, the liquid–gas flow structure arising upon local heating using thermal sources is investigated numerically. The two-layer system is confined by solid impermeable walls. The Navier–Stokes equations in the Boussinesq approximation in the ‘streamfunction–vorticity’ variables are used to describe the media motion. The dynamic conditions at the interface are formulated in terms of the tangential and normal velocities, while the temperature conditions at the external boundaries of the system take into account the presence of local heaters. The influence of the number of heaters and heating modes on the dynamics and character of the appearing convective regimes is analysed. The steady and commutated heating modes for one and two heaters arranged at the lower boundary are investigated. The heating initiates convective and thermocapillary mechanisms causing the fluid motion. Transient regimes with the successive formation of two-vortex, quadruple-vortex and two-vortex flows are observed before the stabilization of the system in the uniform heating mode. A stable thermocapillary deflection appears at the interface above the heater. The commutated mode of heating entails oscillations of the interface with a change in the deflection form and the formation of travelling vortices in the fluids. The impact of particular mechanisms on the flow patterns is analysed. The paper presents typical distributions of the velocity and temperature fields in the system and the position of the interface for the considered cases.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉In the context of dynamic wetting, wall slip is often treated as a microscopic effect for removing viscous stress singularity at a moving contact line. In most drop spreading experiments, however, a considerable amount of slip may occur due to the use of polymer liquids such as silicone oils, which may cause significant deviations from the classical Tanner–de Gennes theory. Here we show that many classical results for complete wetting fluids may no longer hold due to wall slip, depending crucially on the extent of de Gennes’s slipping ‘foot’ to the relevant length scales at both the macroscopic and microscopic levels. At the macroscopic level, we find that for given liquid height 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and slip length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the apparent dynamic contact angle 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 can change from Tanner’s law 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to the strong-slip law 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the capillary number and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the macroscopic length scale. Such a no-slip-to-slip transition occurs at the critical capillary number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, accompanied by the switch of the ‘foot’ of size 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 from the inner scale to the outer scale with respect to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. A more generalized dynamic contact angle relationship is also derived, capable of unifying Tanner’s law and the strong-slip law under 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. We not only confirm the two distinct wetting laws using many-body dissipative particle dynamics simulations, but also provide a rational account for anomalous departures from Tanner’s law seen in experiments (Chen, 〈span〉J. Colloid Interface Sci〈/span〉., vol. 122, 1988, pp. 60–72; Albrecht 〈span〉et al.〈/span〉, 〈span〉Phys. Rev. Lett.〈/span〉, vol. 68, 1992, pp. 3192–3195). We also show that even for a common spreading drop with small macroscopic slip, slip effects can still be microscopically strong enough to change the microstructure of the contact line. The structure is identified to consist of a strongly slipping precursor film of length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 followed by a mesoscopic ‘foot’ of width 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 ahead of the macroscopic wedge, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the molecular length. It thus turns out that it is the ‘foot’, rather than the film, contributing to the microscopic length in Tanner’s law, in accordance with the experimental data reported by Kavehpour 〈span〉et al.〈/span〉 (〈span〉Phys. Rev. Lett.〈/span〉, vol. 91, 2003, 196104) and Ueno 〈span〉et al.〈/span〉 (〈span〉Trans. ASME J. Heat Transfer〈/span〉, vol. 134, 2012, 051008). The advancement of the microscopic contact line is still led by the film whose length can grow as the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 power of time due to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619140754267-0248:S0022112019003525:S0022112019003525_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, as supported by the experiments of Ueno 〈span〉et al.〈/span〉 and Mate (〈span〉Langmuir〈/span〉, vol. 28, 2012, pp. 16821–16827). The present work demonstrates that the behaviour of a moving contact line can be strongly influenced by wall slip. Such slip-mediated dynamic wetting might also provide an alternative means for probing slippery surfaces.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We numerically investigated the unsteady dynamics of a two-dimensional airfoil undergoing a continuous, prescribed pitch-up motion and freely translating as a response to aerodynamic forces and the gravity field. The pitch-up motion was applied about an axis located 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190619142124772-0727:S002211201900421X:S002211201900421X_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 chord away from the leading edge and was parameterized using the shape change number, with a Reynolds number set to 2000. It was shown that the minimum kinetic energy reached by the airfoil depends stochastically and asymptotically on shape change numbers for values below and above 1, respectively. Very low kinetic energy levels (close to zero) can be reached in both stochastic and asymptotic regions but high shape change numbers are accompanied by significant gain in altitude which may be undesirable from a practical perspective. Rather, shape change numbers in the range [0.1–0.3] allow us to reach relatively low levels of kinetic energy for close perching locations. We showed that highly nonlinear fluid–structure interactions induced by massive flow separations and strong vortices are conducive to low kinetic energy, but responsible for the stochastic dependence of kinetic energy to shape change number, which can make perching manoeuvres hardly controllable for flying vehicles.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present a dynamic decomposition analysis of the wake flow in fluid–structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational FSI solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Reynolds number (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327055129472-0988:S002211201900140X:S002211201900140X_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉). The snapshot data from high-dimensional FSI simulations are projected to a low-dimensional subspace using the proper orthogonal decomposition (POD). We utilize each corresponding POD mode to detect features of the organized motions, namely, the vortex street, the shear layer and the near-wake bubble. We find that the vortex shedding modes contribute solely to the lift force, while the near-wake and shear layer modes play a dominant role in the drag force. We further examine the fundamental mechanism of this dynamical behaviour and propose a force decomposition technique via low-dimensional approximation. To elucidate the frequency lock-in, we systematically analyse the decomposed modes and their dynamical contributions to the force fluctuations for a range of reduced velocity at low Reynolds number laminar flow. These quantitative mode energy contributions demonstrate that the shear layer feeds the vorticity flux to the wake vortices and the near-wake bubble during the wake–body synchronization. Based on the decomposition of wake dynamics, we suggest an interaction cycle for the frequency lock-in during the wake–body interaction, which provides the interrelationship between the high-amplitude motion and the dominating wake features. Through our investigation of wake–body synchronization below critical 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327055129472-0988:S002211201900140X:S002211201900140X_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 range, we discover that the bluff body can undergo a synchronized high-amplitude vibration due to flexibility-induced unsteadiness. Owing to the wake turbulence at a moderate Reynolds number of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327055129472-0988:S002211201900140X:S002211201900140X_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, a distorted set of POD modes and the broadband energy distribution are observed, while the interaction cycle for the wake synchronization is found to be valid for the turbulent wake flow.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We use resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190325174522297-0677:S0022112019001630:S0022112019001630_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and a free-stream Mach number of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190325174522297-0677:S0022112019001630:S0022112019001630_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 are considered at two post-stall angles of attack of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190325174522297-0677:S0022112019001630:S0022112019001630_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190325174522297-0677:S0022112019001630:S0022112019001630_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327124217270-0217:S0022112019001198:S0022112019001198_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for the velocity field and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327124217270-0217:S0022112019001198:S0022112019001198_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for the temperature field, are identified. These variables separate the space of scales into a quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327124217270-0217:S0022112019001198:S0022112019001198_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327124217270-0217:S0022112019001198:S0022112019001198_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is smaller than the minimum values of the cross-over scales given by 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327124217270-0217:S0022112019001198:S0022112019001198_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near-wall region and the effects of the subgrid scales are more complex for filter lengths of the order of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327124217270-0217:S0022112019001198:S0022112019001198_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in large-eddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid-scale models.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Motivated by recent studies that have revealed the existence of trapped acoustic waves in subsonic jets (Towne 〈span〉et al.〈/span〉, 〈span〉J. Fluid Mech.〈/span〉, vol. 825, 2017, pp. 1113–1152), we undertake a more general exploration of the physics associated with acoustic modes in jets and wakes, using a double vortex-sheet model. These acoustic modes are associated with eigenvalues of the vortex-sheet dispersion relation; they are discrete modes, guided by the vortex sheet; they may be either propagative or evanescent; and under certain conditions they behave in the manner of acoustic-duct modes. By analysing these modes we show how jets and wakes may both behave as waveguides under certain conditions, emulating ducts with soft or hard walls, with the vortex-sheet impedance providing effective ‘wall’ conditions. We consider, in particular, the role that upstream-travelling acoustic modes play in the dispersion-relation saddle points that underpin the onset of absolute instability. The analysis illustrates how departure from duct-like behaviour is a necessary condition for absolute instability, and this provides a new perspective on the stabilising and destabilising effects of reverse flow, temperature ratio and compressibility; it also clarifies the differing symmetries of jet (symmetric) and wake (antisymmetric) instabilities. An energy balance, based on the vortex-sheet impedance, is used to determine stability conditions for the acoustic modes: these may become unstable in supersonic flow due to an energy influx through the shear layers. Finally, we construct the impulse response of flows with zero and finite shear-layer thickness. This allows us to show how the long-time wavepacket behaviour is indeed determined by interaction between Kelvin–Helmholtz and acoustic modes.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Following the recent observation that turbulent pipe flow can be relaminarised by a relatively simple modification of the mean velocity profile, we here carry out a quantitative experimental investigation of this phenomenon. Our study confirms that a flat velocity profile leads to a collapse of turbulence and in order to achieve the blunted profile shape, we employ a moving pipe segment that is briefly and rapidly shifted in the streamwise direction. The relaminarisation threshold and the minimum shift length and speeds are determined as a function of Reynolds number. Although turbulence is still active after the acceleration phase, the modulated profile possesses a severely decreased lift-up potential as measured by transient growth. As shown, this results in an exponential decay of fluctuations and the flow relaminarises. While this method can be easily applied at low to moderate flow speeds, the minimum streamwise length over which the acceleration needs to act increases linearly with the Reynolds number.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We investigate the gravity-driven flow of a thin film of liquid metal on a conducting conical substrate in the presence of a strong toroidal magnetic field (transverse to the flow and parallel to the substrate). We solve the leading-order governing equations in a physically relevant asymptotic limit to find the free-surface profile. We find that the leading-order fluid flow rate is a non-monotonic bounded function of the film height, and this can lead to singularities in the free-surface profile. We perform a detailed stability analysis and identify values of the relevant geometric, hydrodynamic and magnetic parameters such that the flow is stable.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present a local stability analysis to investigate the effects of differential diffusion between momentum and density (quantified by the Schmidt number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) on the three-dimensional, short-wavelength instabilities in planar vortices with a uniform stable stratification along the vorticity axis. Assuming small diffusion in both momentum and density, but arbitrary values for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, we present a detailed analytical/numerical analysis for three different classes of base flows: (i) an axisymmetric vortex, (ii) an elliptical vortex and (iii) the flow in the neighbourhood of a hyperbolic stagnation point. While a centrifugally stable axisymmetric vortex remains stable for any 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, it is shown that 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 can have significant effects in a centrifugally unstable axisymmetric vortex: the range of unstable perturbations increases when 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is taken away from unity, with the extent of increase being larger for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 than for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Additionally, for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, we report the possibility of oscillatory instability. In an elliptical vortex with a stable stratification, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is shown to non-trivially influence the three different inviscid instabilities (subharmonic, fundamental and superharmonic) that have been previously reported, and also introduce a new branch of oscillatory instability that is not present at 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The unstable parameter space for the subharmonic (instability IA) and fundamental (instability IB) inviscid instabilities are shown to be significantly increased for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, respectively. Importantly, for sufficiently small and large 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, respectively, the maximum growth rate for instabilities IA and IB occurs away from the inviscid limit. The new oscillatory instability (instability III) is shown to occur only for sufficiently small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the signature of which is nevertheless present with zero growth rate in the inviscid limit. The Schmidt number is then shown to play no role in the evolution of transverse perturbations on the flow around a hyperbolic stagnation point with a stable stratification. We conclude by discussing the physical length scales associated with the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190327085207695-0702:S0022112019001472:S0022112019001472_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 instabilities, and their potential relevance in various realistic settings.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Instabilities and flow characteristics in the far wake of a circular cylinder are examined through direct numerical simulations. The transitions to the two-layered and secondary vortex streets are quantified by a new method based on the time-averaged transverse velocity field. Two processes for the transition to the secondary vortex street are observed: (i) the merging of two same-sign vortices over a range of low Reynolds numbers (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) between 200 and 300, and (ii) the pairing of two opposite-sign vortices, followed by the merging of the paired vortices into subsequent vortices, over a range of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 between 400 and 1000. Single vortices may be generated between the merging cycles due to mismatch of the vortices. The irregular merging process results in flow irregularity and an additional frequency signal 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (in addition to the primary vortex shedding frequency 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) in the two-layered and secondary vortex streets. In particular, a gradual energy transfer from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 with distance downstream is observed in the two-layered vortex street prior to the merging. The frequency spectra of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 are broad-band for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉–300 but become increasingly sharp-peaked with increasing 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 because the vortex merging process becomes increasingly regular. The ratio of the sharp-peaked frequencies 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190326132244592-0183:S0022112019001678:S0022112019001678_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is equal to the ratio of the numbers of vortices observed after and before the merging. The general conclusions drawn from a circular cylinder are expected to be applicable to other bluff bodies.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Results are presented from a laboratory study on the free-surface signal generated over an array of submerged circular cylinders, representative of submerged aquatic vegetation. We aim to understand whether aquatic ecosystems generate a surface signature that is indicative of both what is beneath the water surface as well as how it is altering the flow. A shear layer forms over the canopy, generating coherent vortex structures which eventually manifest in the free-surface slope field. We connect the vortex properties measured at the surface with measurements of the bulk flow, and show that correlations between these quantities are adequate to create a parameterized model in which the interior velocity profile can be predicted solely from measurements taken at the free surface. Experimental surface observations yield a Strouhal number that is twice the most amplified mode predicted by linear stability theory, suggesting that vortices may evolve between generation at the canopy height and their manifestation at the water surface. Additionally, the surface signal continues evolving with distance downstream, with vortices becoming spread farther apart and the passage frequency gradually decreasing. By the trailing edge of the canopy, surface-impacting boils emerge for canopies with higher submergence ratios, suggesting a transition from coherent two-dimensional rollers to transversely varying structures.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Results of experimental and numerical investigations of a supersonic flow around a cylinder with a frontal gas-permeable insert made of a high-porosity cellular material are presented. The measurements are performed in a T-327 supersonic blowdown wind tunnel at the free-stream Mach numbers 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190325181423329-0720:S0022112019001654:S0022112019001654_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 7 and 21 in the range of the unit Reynolds numbers 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190325181423329-0720:S0022112019001654:S0022112019001654_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The drag coefficients for a cylinder with an aerospike and a cylinder with a frontal gas-permeable porous insert are obtained. For the cylinder with the frontal gas-permeable porous insert, variations of the insert length, cylinder diameter and pore size are considered, and the mechanism of drag reduction is found, which includes two supplementary processes: attenuation of the bow shock wave in a system of weaker shock waves, and formation of an effective pointed body. The experiments are accompanied by numerical simulations of the flow around the cylinder with the frontal high-porosity insert: the fields of parameters of the external flow and the flow inside the porous insert are obtained, the drag coefficients are calculated, and the shape of the effective body for the examined model is found. The structure of the high-porosity material is modelled by a system of staggered rings of different diameters aligned in the radial and longitudinal directions (skeleton model of a porous medium). Numerical simulations of the problem are performed by means of solving two-dimensional Reynolds-averaged Navier–Stokes equations written in an axisymmetric form. The experimental and numerical data reveal significant drag reduction in a wide range of supersonic flow conditions. The results obtained on the drag coefficient for the cylinder are generalized with the use of a parameter which includes the ratio of the cylinder diameter to the pore diameter in the insert and the Mach number. This parameter is proposed as a similarity criterion for the problem of a supersonic flow around a cylinder with a frontal high-porosity insert.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Decay of honeycomb-generated turbulence in a duct with a static transverse magnetic field is studied via direct numerical simulations. The simulations follow the revealing experimental study of Sukoriansky 〈span〉et al.〈/span〉 (〈span〉Exp. Fluids〈/span〉, vol. 4 (1), 1986, pp. 11–16), in particular the paradoxical observation of high-amplitude velocity fluctuations, which exist in the downstream portion of the flow when the strong transverse magnetic field is imposed in the entire duct including the honeycomb exit, but not in other configurations. It is shown that the fluctuations are caused by the large-scale quasi-two-dimensional structures forming in the flow at the initial stages of the decay and surviving the magnetic suppression. Statistical turbulence properties, such as the energy decay curves, two-point correlations and typical length scales are computed. The study demonstrates that turbulence decay in the presence of a magnetic field is a complex phenomenon critically depending on the state of the flow at the moment the field is introduced.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉〈img orientation="portrait" mimesubtype="gif" mimetype="image" position="float" type="simple" href="S0022112019008000_figAb" src="http://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0022112019008000/resource/name/S0022112019008000_figAb.gif?pub-status=live"〉〈/p〉〈/div〉 〈div data-abstract-type="normal"〉〈p〉We consider a Stokeslet applied to a viscous fluid next to an infinite, flat wall, or in between two parallel walls. We calculate the forces exerted by the resulting flow on the confining boundaries, and use the results obtained to estimate the hydrodynamic contribution to the pressure exerted on boundaries by force-free self-propelled particles.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉〈img orientation="portrait" mimesubtype="gif" mimetype="image" position="float" type="simple" href="S0022112019007973_figAb" src="http://static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0022112019007973/resource/name/S0022112019007973_figAb.gif?pub-status=live"〉〈/p〉〈/div〉 〈div data-abstract-type="normal"〉〈p〉By means of three-dimensional direct numerical simulations, we investigate the influence of the regular roughness of heated and cooled plates on the mean heat transport in a cylindrical Rayleigh–Bénard convection cell of aspect ratio one. The roughness is introduced by a set of isothermal obstacles, which are attached to the plates and have a form of concentric rings of the same width. The considered Prandtl number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 equals 1, the Rayleigh number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 varies from 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the number of rings on each plate is 1, 2, 4, 8 or 10, the height of the rings is varied from 1.5 % to 49 % of the cylinder height and the gap between the rings is varied from 1.5 % to 18.8 % of the cell diameter. Totally, 135 different cases are analysed. Direct numerical simulations show that with small 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and wide roughness rings, a small reduction of the mean heat transport (the Nusselt number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) is possible, but, in most cases, the presence of the heated and cooled obstacles generally leads to an increase of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, compared to the case of classical Rayleigh–Bénard convection with smooth plates. When the rings are very tall and the gaps between them are sufficiently wide, the effective mean heat flux can be several times larger than in the smooth case. For a fixed geometry of the obstacles, the scaling exponent in the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 versus 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 scaling first increases with growing 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20191105072504660-0909:S0022112019007973:S0022112019007973_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 up to approximately 0.5, but then smoothly decreases back towards the exponent in the no-obstacle case.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Direct numerical simulations (DNS) are reported for open-channel flow over streamwise-alternating patches of smooth and fully rough walls. The rough patch is a three-dimensional sinusoidal surface. Owing to the streamwise periodicity, the flow configuration consists of a step change from smooth to rough, and a step change from rough to smooth. The friction Reynolds number varies from 437 over the smooth patch to 704 over the rough patch. Through the fully resolved DNS dataset it is possible to explore many detailed aspects of this flow. Two aspects motivate this work. The first one is the equilibrium assumption that has been widely used in both experiments and computations. However, it is not clear where this assumption is valid. The detailed DNS data reveal a significant departure from equilibrium, in particular over the smooth patch. Over this patch, the mean velocity is recovered up to the beginning of the log layer after a fetch of five times the channel height. However, over the rough patch, the same recovery level is reached after a fetch of two times the channel height. This conclusion is arrived at by assuming that an error of up to 5 % is acceptable and the log layer, classically, starts from 30 wall units above the wall. The second aspect is the reported internal boundary-layer (IBL) growth rates in the literature, which are inconsistent with each other. This is conjectured to be partly caused by the diverse IBL definitions. Five common definitions are applied for the same DNS dataset. The resulting IBL thicknesses are different by 100 %, and their apparent power-law exponents are different by 50 %. The IBL concept, as a layer within which the flow feels the surface underneath, is taken as the basis to search for the proper definition. The definition based on the logarithmic slope of the velocity profile, as proposed by Elliot (〈span〉Trans. Am. Geophys. Union〈/span〉, vol. 39, 1958, pp. 1048–1054), yields better consistency with this concept based on turbulence characteristics.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Linear perturbation analyses of zero-pressure-gradient boundary layers at subcritical Reynolds numbers predict that transient disturbance amplification can take place due to the lift-up mechanism. Upstream, streamwise-elongated vortices yield the largest response per unit of inflow disturbance energy, which takes the form of streamwise-elongated streaks. In this work, we compute the linear and also nonlinear inflow disturbances that generate the largest response inside the boundary layer, for flow over a thin flat plate with a slender leading edge. In order to compare our results with earlier linear analyses, we constrain the inlet disturbance to be monochromatic in time, or a single frequency. The boundary layer effectively filters high frequencies, and only low-frequency perturbations induce a strong response downstream. The low-frequency optimal inflow disturbance has a spanwise wavenumber that scales with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190305083235689-0438:S0022112019000910:S0022112019000910_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, and it consists of streamwise and normal vorticity components: the latter is tilted around the leading edge into the streamwise direction and, further downstream, generates streaks. While none of the computed monochromatic disturbances alone can lead to breakdown to turbulence, secondary instability analyses demonstrate that the streaky base state is unstable. Nonlinear simulations where the inflow disturbance is supplemented with additional white noise undergo secondary instability and breakdown to turbulence.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉A variational principle is given for the motion of a rigid body dynamically coupled to its interior fluid sloshing in three-dimensional rotating and translating coordinates. The fluid is assumed to be inviscid and incompressible. The Euler–Poincaré reduction framework of rigid body dynamics is adapted to derive the coupled partial differential equations for the angular momentum and linear momentum of the rigid body and for the motion of the interior fluid relative to the body coordinate system attached to the moving rigid body. The variational principle is extended to the problem of interactions between gravity-driven potential flow water waves and a freely floating rigid body dynamically coupled to its interior fluid motion in three dimensions.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Direct numerical simulations are performed to study zero-pressure-gradient turbulent boundary layers beneath quiescent and vortical free streams. The inflow boundary layer is computed in a precursor simulation of laminar-to-turbulence transition, and the free-stream vortical forcing is obtained from direct numerical simulations of homogeneous isotropic turbulence. A level-set approach is employed in order to objectively distinguish the boundary-layer and free-stream fluids, and to accurately evaluate their respective contributions to flow statistics. When free-stream turbulence is present, the skin friction coefficient is elevated relative to its value in the canonical boundary-layer configuration. An explanation is provided in terms of an increase in the power input into production of boundary-layer turbulence kinetic energy. This increase takes place deeper than the extent of penetration of the external perturbations towards the wall, and also despite the free-stream perturbations being void of any Reynolds shear stress. Conditional statistics demonstrate that the free-stream turbulence has two effects on the boundary layer: one direct and the other indirect. The low-frequency components of the free-stream turbulence penetrate the logarithmic layer. The associated wall-normal Reynolds stress acts against the mean shear to enhance the shear stress, which in turn enhances turbulence production. This effect directly enlarges the scale and enhances the energy of outer large-scale motions in the boundary layer. The second, indirect effect is the influence of these newly formed large-scale structures. They modulate the near-wall shear stress and, as a result, increase the turbulence kinetic energy production in the buffer layer, which is deeper than the extent of penetration of free-stream turbulence towards the wall.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Turbulent flow over a series of increasingly high, two-dimensional bumps is studied by well-resolved large-eddy simulation. The mean flow and Reynolds stresses for the lowest bump are in good agreement with experimental data. The flow encounters a favourable pressure gradient over the windward side of the bump, but does not relaminarize, as is evident from near-wall fluctuations. A patch of high turbulent kinetic energy forms in the lee of the bump and extends into the wake. It originates near the surface, before flow separation, and has a significant influence on flow development. The highest bumps create a small separation bubble, whereas flow over the lowest bump does not separate. The log law is absent over the entire bump, evidencing strong disequilibrium. This dataset was created for data-driven modelling. An optimization method is used to extract fields of variables that are used in turbulence closure models. From this, it is shown how these models fail to correctly predict the behaviour of these variables near to the surface. The discrepancies extend further away from the wall in the adverse pressure gradient and recovery regions than in the favourable pressure gradient region.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Tunnel noise in supersonic testing facilities is known to be a decisive factor in boundary layer transition experiments. It defines initial conditions for the growth of modal instabilities by the receptivity mechanism. That is, to interpret experimental results, the determination of tunnel noise is of crucial importance. It is common to use stagnation point probes equipped with pressure transducers in supersonic flows, but since tunnel noise undergoes modulation during the measurement, the probes must be calibrated. The predominant component of tunnel noise is caused by the nozzle boundary layer which radiates highly inclined slow acoustic waves. Therefore, the calibration of stagnation point probes for these disturbances is essential. For quasi-steady deviations from the free stream, an analytic reduced-order method holds. A corresponding conflicting model derived by Stainback & Wagner (1972, 〈span〉AIAA Paper〈/span〉 72-1003) is revised and corrected. Inclined slow acoustic waves generate higher pressure perturbations at the probe than non-inclined waves. In general, costly three-dimensional direct numerical simulations can be used for calibration. In this study, however, new axisymmetric boundary conditions are proposed to reduce the problem to two dimensions to efficiently investigate the detection of incident inclined slow acoustic waves by stagnation point probes. A cylindrical probe with a rounded edge is investigated in supersonic flow at a Mach number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312092103836-0442:S0022112019001216:S0022112019001216_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. For the inclination angle of radiated slow acoustic waves, stagnation point pressure fluctuations abruptly decay with increasing Strouhal number and a similar behaviour can be seen at constant Strouhal number with increasing inclination angle. Two simple criteria for the onset of decay based on the radial wavenumber are deduced. Furthermore, stagnation point pressure fluctuations were decomposed into an initial pulse impact and resonant amplification to separately investigate the effects. The initial pulse determines the overall pressure signal. At high inclination angles, a new mechanism for resonance caused by a surface pressure wave travelling at the phase speed of the incident wave was found to supersede resonance caused by oscillating acoustic waves prevailing at low inclination angles.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Studies of the effects of constructive or destructive interference on the transmission of internal waves through non-uniform stratifications have typically been performed for internal wave fields that are spatiotemporally harmonic. To understand the impacts of spatiotemporal localization, we present a theoretical and experimental study of the transmission of two-dimensional internal waves that are generated by a boundary forcing that is localized in both space and time. The model analysis reveals that sufficient localization leads to the disappearance of transmission peaks and troughs that would otherwise be present for a harmonic forcing. The corresponding laboratory experiments that we perform provide clear demonstration of this effect. Based on the group velocity and angle of propagation of the internal waves, a practical criterion that assesses when the transmission peaks or troughs are evident is obtained.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Vortex is a central concept in the understanding of turbulent dynamics. Objective algorithms for the detection and extraction of vortex structures can facilitate the physical understanding of turbulence regeneration dynamics by enabling automated and quantitative analyses of these structures. Despite the wide availability of vortex identification criteria, they only label spatial regions belonging to vortices, without any information on the identity, topology and shape of individual vortices. This latter information is stored in the axis lines lining the contours of vortex tubes. In this study, a new tracking algorithm is proposed which propagates along the vortex axis lines and iteratively searches for new directions for growth. The method is validated in flow fields from transient simulations where vortices of different shapes are controllably generated. It is then applied to statistical turbulence for the analysis of vortex configurations and distributions. It is shown to reliably extract axis lines for complex three-dimensional vortices generated from the walls. A new procedure is also proposed that classifies vortices into commonly observed shapes, including quasi-streamwise vortices, hairpins, hooks and branches, based on their axis-line topology. Clustering analysis is performed on the extracted axis lines to reveal vortex organization patterns and their potential connection to large-scale motions in turbulence.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Two-phase bubbly flows are found in many industrial applications. These flows involve complex local phenomena that are still poorly understood. For instance, two-phase turbulence modelling is still commonly based on single-phase flow analyses. A direct numerical simulation (DNS) database is described here to improve the understanding of two-phase turbulent channel flow at a parietal Reynolds number of 127. Based on DNS results, a physical interpretation of the Reynolds stress and momentum budgets is proposed. First, surface tension is found to be the strongest force in the direction of migration so that budgets of the momentum equations suggest a significant impact of surface tension in the migration process, whereas most modelling used in industrial application does not include it. Besides, the suitability of the design of our cases to study the interaction between bubble-induced fluctuations (BIF) and single-phase turbulence (SPT) is shown. Budgets of the Reynolds stress transport equation computed from DNS reveal an interaction between SPT and BIF, revealing weaknesses in the classical way in which pseudoturbulence and perturbations to standard single-phase turbulence are modelled. An SPT reduction is shown due to changes in the diffusion because of the presence of bubbles. An increase of the redistribution leading to a more isotropic SPT has been observed as well. BIF is comprised of a turbulent (wake-induced turbulence, WIT) and a non-turbulent (wake-induced fluctuations, WIF) part which are statistically independent. WIF is related to averaged wake and potential flow, whereas WIT appears when wakes become unstable or interact with each other for high-velocity bubbles. In the present low gravity conditions, BIF is reduced to WIF only. A thorough analysis of the transport equations of the Reynolds stresses is performed in order to propose an algebraic closure for the WIF towards an innovative two-phase turbulence model.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉An acoustically forced fluid system is known to generate a time-averaged mean, or streaming, flow that evolves on a slow time scale compared to the acoustic-wave period. Classical acoustic streaming in a homogeneous fluid is typically associated with a one-way coupled system wherein the oscillatory acoustic fields inform the streaming mean flow, without any appreciable feedback. In contrast, Michel & Chini (〈span〉J. Fluid Mech.〈/span〉, vol. 858, 2019, pp. 536–564) investigate acoustic streaming in a stratified fluid and demonstrate that the streaming is sufficiently strong to induce significant rearrangements of the background temperature and density fields, resulting in a strong coupling between the acoustic waves and mean flow. This new class of streaming, referred to as baroclinic acoustic streaming, is shown to result in altered streaming patterns with enhanced heat transport that makes possible a range of new applications.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We propose a statistical model for homogeneous turbulence undergoing distortions, which improves and extends the MCS model by Mons, Cambon & Sagaut (〈span〉J. Fluid Mech.〈/span〉, vol. 788, 2016, 147–182). The spectral tensor of two-point second-order velocity correlations is predicted in the presence of arbitrary mean-velocity gradients and in a rotating frame. For this, we numerically solve coupled equations for the angle-dependent energy spectrum 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190228123831336-0609:S0022112019001010:S0022112019001010_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 that includes directional anisotropy, and for the deviatoric pseudo-scalar 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190228123831336-0609:S0022112019001010:S0022112019001010_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, that underlies polarization anisotropy (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190228123831336-0609:S0022112019001010:S0022112019001010_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the wavevector, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190228123831336-0609:S0022112019001010:S0022112019001010_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the time). These equations include two parts: (i) exact linear terms representing the viscous spectral linear theory (SLT) when considered alone; (ii) generalized transfer terms mediated by two-point third-order correlations. In contrast with MCS, our model retains the complete angular dependence of the linear terms, whereas the nonlinear transfer terms are closed by a reduced anisotropic eddy damped quasi-normal Markovian (EDQNM) technique similar to MCS, based on truncated angular harmonics expansions. And in contrast with most spectral approaches based on characteristic methods to represent mean-velocity gradient terms, we use high-order finite-difference schemes (FDSs). The resulting model is applied to homogeneous rotating turbulent shear flow with several Coriolis parameters and constant mean shear rate. First, we assess the validity of the model in the linear limit. We observe satisfactory agreement with existing numerical SLT results and with theoretical results for flows without rotation. Second, fully nonlinear results are obtained, which compare well to existing direct numerical simulation (DNS) results. In both regimes, the new model improves significantly the MCS model predictions. However, in the non-rotating shear case, the expected exponential growth of turbulent kinetic energy is found only with a hybrid model for nonlinear terms combining the anisotropic EDQNM closure and Weinstock’s return-to-isotropy model.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present results on the drag on, and the flow field around, a submerged rectangular normal flat plate, which is uniformly accelerated to a constant target velocity along a straight path. The plate aspect ratio is chosen to be 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190311095401186-0030:S0022112019001022:S0022112019001022_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 to resemble an oar blade in (competitive) rowing, the sport which inspired this study. The plate depth, i.e. the distance from the top of the plate to the air–water interface, the plate acceleration and the plate target velocity are varied, resulting in a plate width based Reynolds number of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190311095401186-0030:S0022112019001022:S0022112019001022_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. In our analysis we distinguish three phases; (i) the acceleration phase during which the plate drag is enhanced, (ii) the transition phase during which the plate drag decreases to a constant steady value upon which (iii) the steady phase is reached. The plate drag force is measured as function of time which showed that the steady-phase plate drag at a depth of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190311095401186-0030:S0022112019001022:S0022112019001022_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 plate height (20 mm depth for a plate height of 100 mm) increased by 45 % compared to the plate top at the surface (0 mm). Also, it is shown that the drag force during acceleration of the plate increases over time and is not captured by a single added mass coefficient for prolonged accelerations. Instead, an entrainment rate is defined that captures this behaviour. The formation of starting vortices and the wake development during the time of acceleration and transition towards a steady wake are studied using hydrogen bubble flow visualisations and particle image velocimetry. The formation time, as proposed by Gharib 〈span〉et al.〈/span〉 (〈span〉J. Fluid Mech.〈/span〉, vol. 360, 1998, pp. 121–140), appears to be a universal time scale for the vortex formation during the transition phase.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Parametrically forced gravity waves can give rise to high-velocity surface jets via the wave-depression cavity implosion. The present results have been obtained in circular cylindrical containers of 10 and 15 cm in diameter (Bond number of order 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) in the large fluid depth limit. First, the phase diagrams of instability threshold and wave breaking conditions are determined for the working fluid used, here water with 1 % detergent added. The collapse of the wave-depression cavity is found to be self-similar. The exponent 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the variation of the cavity radius 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 with time 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, in the form 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, is close to 0.5, indicative of inertial collapse, followed by a viscous cut-off of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304144947658-0960:S0022112019000867:S0022112019000867_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. This supports a Froude number scaling of the surface jet velocity caused by cavity collapse. The dimensionless jet velocity scales with the cavity depth that is shown to be proportional to the last stable wave amplitude. It can be expressed by a power law or in terms of finite time singularity related to a singular wave amplitude that sets the transition from a non-pinching to pinch-off cavity collapse scenario. In terms of forcing amplitude, cavity collapse and jetting are found to occur in bands of events of non-pinching and pinching of a bubble at the cavity base. At large forcing amplitudes, incomplete cavity collapse and splashing can occur and, at even larger forcing amplitudes, wave growth is again stable up to the singular wave amplitude. When the cavity is formed, an impulse model shows the importance of the singular cavity diameter that determines the strength of the impulse.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The partial coalescence dynamics of a compound drop in a liquid pool is numerically investigated. We study the effect of the ratio of the inner to outer radii 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304182056746-0191:S002211201900137X:S002211201900137X_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the compound drop while maintaining a constant liquid volume in the outer shell of the compound droplet. It is observed that for small values of the radius ratio, the coalescence dynamics is similar to that of a ‘simple’ drop, but the partial coalescence is suppressed for large values of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304182056746-0191:S002211201900137X:S002211201900137X_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Increasing the value of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304182056746-0191:S002211201900137X:S002211201900137X_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 decreases the distance migrated by the inner bubble in the downward direction inside the pool. The location of the bubble after coalescence is found to play an important role in the pinch-off process of the satellite drop. The influence of the governing dimensionless parameters on the coalescence dynamics has also been investigated.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We investigate the flow around an oscillating nearly spherical particle at low, yet non-vanishing, Reynolds numbers (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190228133414432-0794:S0022112019001307:S0022112019001307_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), and the potential resulting locomotion. We analytically demonstrate that no net motion can arise up to order one in 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190228133414432-0794:S0022112019001307:S0022112019001307_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and order one in the asphericity parameter, regardless of the particle’s shape. Therefore, geometry-induced acoustic streaming propulsion, if any, must arise at higher order.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We experimentally investigate the two-phase interplay in an open-channel turbulent boundary layer laden with finite-size particles at global volume fractions between 4 and 25 %. The working fluid (water) and the dispersed phase (hydrogel spheres) have closely matched refractive indices, allowing us to measure the properties of both phases using particle image velocimetry and particle tracking velocimetry, respectively. The particles have a diameter of approximately 9 % of the channel depth and are slightly denser than the fluid. The negative buoyancy causes a strong vertical concentration gradient, characterized by discrete and closely spaced particle layers parallel to the wall. Even at the lowest considered volume fractions, the near-wall fluid velocity and velocity gradients are strongly reduced, with large mean shear throughout most of the channel height. This indicates that the local effective viscosity of the suspension is greatly increased due to the friction between particle layers sliding over one another. The particles consistently lag the fluid and leave their footprint on its mean and fluctuating velocity profiles. The turbulent activity is damped near the wall, where the nearly packed particles disrupt and suppress large-scale turbulent fluctuations and redistribute some of the kinetic energy to smaller scales. On the other hand, in the outer region of the flow where the local particle concentration is low, the mean shear produces strong Reynolds stresses, with enhanced sweeps and ejections and frequent swirling events.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We investigate optimal perturbation in the flow past a finite aspect ratio (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312082601927-0323:S0022112019001101:S0022112019001101_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) wing. The optimization is carried out in the regime where the fully developed flow is steady. Parametric study over time horizon (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312082601927-0323:S0022112019001101:S0022112019001101_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), Reynolds number (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312082601927-0323:S0022112019001101:S0022112019001101_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312082601927-0323:S0022112019001101:S0022112019001101_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, angle of attack and geometry of the wing cross-section (flat plate and NACA0012 airfoil) shows that the general shape of linear optimal perturbation remains the same over the explored parameter space. Optimal perturbation is located near the surface of the wing in the form of chord-wise periodic structures whose strength decreases from the root towards the tip. Direct time integration of the disturbance equations, with and without nonlinear terms, is carried out with linear optimal perturbation as initial condition. In both cases, the optimal perturbation evolves as a downstream travelling wavepacket whose speed is nearly the same as that of the free stream. The energy of the wavepacket increases in the near wake region, and is found to remain nearly constant beyond the vortex roll-up distance in nonlinear simulations. The nonlinear wavepacket results in displacement of the tip vortex. In this situation, the motion of the tip vortex resembles that observed during vortex meandering/wandering in wind tunnel experiments. Results from computation carried out at higher 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312082601927-0323:S0022112019001101:S0022112019001101_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 suggest that, even beyond the steady flow regime, a perturbation wavepacket originating near the wing might cause meandering of tip vortices.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Isolated patches of turbulence in transitional straight pipes are sustained by a strong instability at their upstream front, where the production of turbulent kinetic energy (TKE) is up to five times higher than in the core. Direct numerical simulations presented in this paper show no evidence of such strong fronts if the pipe is bent. We examine the temporal and spatial evolution of puffs and slugs in a toroidal pipe with pipe-to-torus diameter ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312084232394-0643:S0022112019001204:S0022112019001204_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 at several subcritical Reynolds numbers. Results show that the upstream overshoot of TKE production is at most one-and-a-half times the value in the core and that the average cross-flow fluctuations at the front are up to three times lower if compared to a straight pipe, while attaining similar values in the core. Localised turbulence can be sustained at smaller energies through a redistribution of turbulent fluctuations and vortical structures by the in-plane Dean motion of the mean flow. This asymmetry determines a strong localisation of TKE production near the outer bend, where linear and nonlinear mechanisms optimally amplify perturbations. We further observe a substantial reduction of the range of Reynolds numbers for long-lived intermittent turbulence, in agreement with experimental data from the literature. Moreover, no occurrence of nucleation of spots through splitting could be detected in the range of parameters considered. Based on the present results, we argue that this mechanism gradually becomes marginal as the curvature of the pipe increases and the transition scenario approaches a dynamical switch from subcritical to supercritical.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Non-isothermal liquid evaporation in micro-pore structures is studied experimentally and numerically using the lattice Boltzmann method. A hybrid thermal entropic multiple-relaxation-time multiphase lattice Boltzmann model (T-EMRT-MP LBM) is implemented and validated with experiments of droplet evaporation on a heated hydrophobic substrate. Then liquid evaporation is investigated in two specific pore structures, i.e. spiral-shaped and gradient-shaped micro-pillar cavities, referred to as SMS and GMS, respectively. In SMS, the liquid receding front follows the spiral pattern; while in GMS, the receding front moves layer by layer from the pillar rows with large pitch to the rows with small one. Both simulations agree well with experiments. Moreover, evaporative cooling effects in liquid and vapour are observed and explained with simulation results. Quantitatively, in both SMS and GMS, the change of liquid mass with time coincides with experimental measurements. The evaporation rate generally decreases slightly with time mainly because of the reduction of liquid–vapour interface. Isolated liquid films in SMS increase the evaporation rate temporarily resulting in local peaks in evaporation rate. Reynolds and capillary numbers show that the liquid internal flow is laminar and that the capillary forces are dominant resulting in menisci pinned to the pillars. Similar Péclet number is found in simulations and experiments, indicating a diffusive type of heat, liquid and vapour transport. Our numerical and experimental studies indicate a method for controlling liquid evaporation paths in micro-pore structures and maintaining high evaporation rate by specific geometry designs.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The average patterns of the velocity and scalar fields near turbulent/non-turbulent interfaces (TNTI), obtained from direct numerical simulations (DNS) of planar turbulent jets and shear free turbulence, are assessed in the strain eigenframe. These flow patterns help to clarify many aspects of the flow dynamics, including a passive scalar, near a TNTI layer, that are otherwise not easily and clearly assessed. The averaged flow field near the TNTI layer exhibits a saddle-node flow topology associated with a vortex in one half of the interface, while the other half of the interface consists of a shear layer. This observed flow pattern is thus very different from the shear-layer structure consisting of two aligned vortical motions bounded by two large-scale regions of uniform flow, that typically characterizes the average strain field in the fully developed turbulent regions. Moreover, strain dominates over vorticity near the TNTI layer, in contrast to internal turbulence. Consequently, the most compressive principal straining direction is perpendicular to the TNTI layer, and the characteristic 45-degree angle displayed in internal shear layers is not observed at the TNTI layer. The particular flow pattern observed near the TNTI layer has important consequences for the dynamics of a passive scalar field, and explains why regions of particularly high scalar gradient (magnitude) are typically found at TNTIs separating fluid with different levels of scalar concentration. Finally, it is demonstrated that, within the fully developed internal turbulent region, the scalar gradient exhibits an angle with the most compressive straining direction with a peak probability at around 20〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304190458745-0066:S0022112019000855:S0022112019000855_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The scalar gradient and the most compressive strain are not preferentially aligned, as has been considered for many years. The misconception originated from an ambiguous definition of the positive directions of the strain eigenvectors.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉When there exists slip on the surface of a solid body moving in an unsteady manner, the extent of slip is not fixed but constantly changes with the time-varying Stokes boundary layer thickness 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in competition with the slip length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Here we revisit the unsteady motion of a slippery spherical particle to elucidate this dynamic slip situation. We find that even if the amount of slip is minuscule, it can dramatically change the characteristics of the history force, markedly different from those due to non-spherical and fluid particles (Lawrence & Weinbaum, 〈span〉J. Fluid Mech.〈/span〉, vol. 171, 1986, pp. 209–218; Yang & Leal, 〈span〉Phys. Fluids〈/span〉 A, vol. 3, 1991, pp. 1822–1824). For an oscillatory translation of such a particle of radius 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, two distinctive features are identified in the frequency response of the viscous drag: (i) the high-frequency constant force plateau of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 much greater than the steady drag due to a constant shear stress caused by 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 much thinner than 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and (ii) the persistence of the plateau while lowering the frequency until the slip–stick transition point 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, beyond which 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 becomes thicker and the usual Basset decay reappears. Similar features can also be observed in the short-term force response for the particle subject to a sudden movement, as well as in the behaviour of the torque when it undergoes rotary oscillations. In addition, for both translational and rotary oscillations, slip can further introduce a phase jump from the no-slip value to zero in the high-frequency limit. As these features and the associated slip–stick transitions become more evident as 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190312090638125-0973:S0022112019000570:S0022112019000570_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 becomes smaller and are exclusive to the situation where surface slip is present, they might have potential uses for extracting the slip length of a colloidal particle from experiments.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We investigated experimentally the motion of elongated finite-length cylinders (length 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, diameter 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) freely falling under the effect of buoyancy in a low-viscosity fluid otherwise at rest. For cylinders with densities 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 close to the density 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the fluid (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), we explored the effect of the body volume by varying the Archimedes number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (based on the body equivalent diameter) between 200 and 1100, as well as the effect of their length-to-diameter ratios 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 ranging from 2 to 20. A shadowgraphy technique involving two cameras mounted on a travelling cart was used to track the cylinders along their fall over a distance longer than 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. A dedicated image processing algorithm was further implemented to properly reconstruct the position and orientation of the cylinders in the three-dimensional space. In the range of parameters explored, we identified three main types of paths, matching regimes known to exist for three-dimensional bodies (short-length cylinders, disks and spheres). Two of these are stationary, namely, the rectilinear motion and the large-amplitude oscillatory motion (also referred to as fluttering or zigzag motion), and their characterization is the focus of the present paper. Furthermore, in the transitional region between these two regimes, we observed irregular low-amplitude oscillatory motions, that may be assimilated to the A-regimes or quasi-vertical regimes of the literature. Flow visualization using dye released from the bodies uncovered the existence of different types of vortex shedding in the wake of the cylinders, according to the style of path. The detailed analysis of the body kinematics in the fluttering regime brought to light a series of remarkable properties. In particular, when normalized with the characteristic velocity scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the characteristic length scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the mean vertical velocity 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the frequency 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the oscillations become almost independent of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The use of the length scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and of the gravitational velocity scale to build the Strouhal number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 allowed us to generalize to short (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) and elongated cylinders (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), the result 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline19.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. An interpretation of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline20.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 as a characteristic length scale associated with the oscillatory recirculation thickness generated near the body ends is proposed. In addition, the rotation rate of the cylinders scales with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline21.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, for all 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline22.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline23.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 investigated. Furthermore, the phase difference between the oscillations of the velocity component 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline24.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 along the cylinder axis and of the inclination angle 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline25.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the cylinder is approximately constant, whatever the elongation ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline26.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the Archimedes number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304105206942-0883:S0022112019000776:S0022112019000776_inline27.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉In this paper a model for viscous boundary and shear layers in three dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the layer are represented by a two-dimensional surface having its own internal tangential flow. Namely, the sheet has a mass density per-unit-area making it dynamically distinct from the surrounding outer fluid and allowing the sheet to support a pressure jump. The mechanism of entrainment is represented by a discontinuity in the normal component of the velocity across the sheet. The velocity field induced by the vortex-entrainment sheet is given by a generalized Birkhoff–Rott equation with a complex sheet strength. The model was applied to the case of separation at a sharp edge. No supplementary Kutta condition in the form of a singularity removal is required as the flow remains bounded through an appropriate balance of normal momentum with the pressure jump across the sheet. A pressure jump at the edge results in the generation of new vorticity. The shedding angle is dictated by the normal impulse of the intrinsic flow inside the bound sheets as they merge to form the free sheet. When there is zero entrainment everywhere the model reduces to the conventional vortex sheet with no mass. Consequently, the pressure jump must be zero and the shedding angle must be tangential so that the sheet simply convects off the wedge face. Lastly, the vortex-entrainment sheet model is demonstrated on several example problems.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size segregation in the downstream direction, resulting in a flow front composed of large particles. Since the large particles are often more frictional than the small, the mobility of the flow front is reduced, resulting in a so-called bulbous head. This study focuses on the formation and evolution of this bulbous head, which we show to emerge in both a depth-averaged continuum framework and discrete particle simulations. Furthermore, our numerical solutions of the continuum model converge to a travelling wave solution, which allows for a very efficient computation of the long-time behaviour of the flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum framework, and validate the simple one-dimensional (1-D) model with full-scale 3-D discrete particle simulations. The comparison shows that there are conditions under which the model works surprisingly well given the strong approximations made; for example, instantaneous vertical segregation.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Manipulation of an array of surface droplets organised in an ordered structure turns out to be of immense consequence in a wide variety of applications ranging from photonics, near field imaging and inkjet printing on the one hand to bio-molecular analysis and DNA sequencing on the other. While evaporation of a single isolated sessile droplet has been well studied, the collective evaporative dynamics of an ordered array of droplets on a solid substrate remains elusive. Physically, the closed region between the centre and side droplets in the ordered array reduces the mobility of the diffusing vapour, resulting in its accumulation along with enhanced local concentration and a consequent increment in the lifetime of the centre droplet. Here, we present a theoretical model to account for evaporation lifetime scaling in closely placed ordered linear droplet arrays. In addition, the present theory predicts the limiting cases of droplet interaction; namely, critical droplet separation for which interfacial interaction ceases to exist and minimum possible droplet separation (droplets on the verge of coalescence) for which the droplet system achieves maximum lifetime scaling. Further experimental evidence demonstrates the applicability of the present scaling theory to extended dimensions of the droplet array, generalising our physical conjecture. It is also worth noting that the theoretical time scale is applicable across a wide variety of drop–substrate combinations and initial droplet volumes. We also highlight that the scaling law proposed here can be extended seamlessly to other forms of confinement such as an evaporating droplet inside a mini-channel, as encountered in countless applications ranging from biomedical engineering to surface patterning.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Here we provide a self-consistent analytical solution describing the unsteady flow in the slender thin film which is expelled radially outwards when a drop hits a dry solid wall. Thanks to the fact that the fluxes of mass and momentum entering into the toroidal rim bordering the expanding liquid sheet are calculated analytically, we show here that our theoretical results closely follow the measured time-varying position of the rim with independence of the wetting properties of the substrate. The particularization of the equations describing the rim dynamics at the instant the drop reaches its maximal extension which, in analogy with the case of Savart sheets, is characterized by a value of the local Weber number equal to one, provides an algebraic equation for the maximum spreading radius also in excellent agreement with experiments. The self-consistent theory presented here, which does not make use of energetic arguments to predict the maximum spreading diameter of impacting drops, provides us with the time evolution of the thickness and of the velocity of the rim bordering the expanding sheet. This information is crucial in the calculation of the diameters and of the velocities of the droplets ejected radially outwards for drop impact velocities above the splashing threshold.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Thermoacoustic instability – self-sustained pressure oscillations triggered by temperature gradients – has become an increasingly studied topic in the context of energy conversion. Generally, the process relies on conductive heat transfer between a solid and the fluid in which the generated pressure oscillations are sustained. In the present study, the thermoacoustic theory is extended to include mass transfer; specifically, the working fluid is modified so as to incorporate a ‘reactive’ gas, able to exchange phase with a solid/liquid boundary through a sorption process (or through evaporation/condensation), such that most heat is transferred in the form of latent heat rather than through conduction. A set of differential equations is derived, accounting for phase-exchange heat and mass transfer, and de-coupled via a small-amplitude asymptotic expansion. These equations are solved and subsequently manipulated into the form of a wave equation, representing the small perturbation on the pressure field, and used to derive expressions for the time-averaged, second-order heat and mass fluxes. A stability analysis is performed on the wave equation, from which the marginal stability curve is calculated in terms of the temperature difference, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304132813781-0140:S0022112019000879:S0022112019000879_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, required for initiation of self-sustained oscillations. Calculated stability curves are compared with published experimental results, showing good agreement. Effects of gas mixture composition are studied, indicating that a lower heat capacity of the inert component, combined with a low boiling temperature and high latent heat of the reactive component substantially lower 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304132813781-0140:S0022112019000879:S0022112019000879_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Furthermore, an increase in the average mole fraction of the reactive gas, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304132813781-0140:S0022112019000879:S0022112019000879_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 strongly affects onset conditions, leading to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304132813781-0140:S0022112019000879:S0022112019000879_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 at the highest value of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190304132813781-0140:S0022112019000879:S0022112019000879_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 achievable under atmospheric pressure. An analysis of the system limit cycle is performed for a wide range of parameters, indicating a systematic decrease in the temperature difference capable of sustaining the limit cycle, as well as a significant distortion of the acoustic wave form as the phase-exchange mechanism becomes dominant. These findings, combined, reveal the underlying mechanisms by which a phase-exchange engine may produce more acoustic power than its counterpart ‘classical’ thermoacoustic system, while its temperature difference is substantially lower.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The shear-induced collective diffusivity down a concentration gradient in a viscous emulsion is computed using direct numerical simulation. A layer of randomly packed drops subjected to a shear flow, shows the layer width to increase with the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190402101259227-0380:S0022112019001228:S0022112019001228_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 power of time, consistent with a semi-dilute theory that assumes a diffusivity linear with concentration. This characteristic scaling and the underlying theory are used to compute the collective diffusivity coefficient. This is the first ever computation of this quantity for a system of deformable particles using fully resolved numerical simulation. The results match very well with previous experimental observations. The coefficient of collective diffusivity varies non-monotonically with the capillary number, due to the competing effects of increasing deformation and drop orientation. A phenomenological correlation for the collective diffusivity coefficient as a function of capillary number is presented. We also apply an alternative approach to compute collective diffusivity, developed originally for a statistically homogeneous rigid sphere suspension – computing the dynamic structure factor from the simulated droplet positions and examining its time variation at small wavenumber. We show that the results from this alternative approach qualitatively agree with our computation of collective diffusivity including the prediction of the non-monotonic variation of diffusivity with the capillary number.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Large internal solitary waves with subsurface cores have recently been observed in the South China Sea. Here fully nonlinear solutions of the Dubreil–Jacotin–Long equation are used to study the conditions under which such cores exist. We find that the location of the cores, either at the surface or below the surface, is largely determined by the sign of the vorticity of the near-surface background current. The results of a numerical simulation of a two-dimensional shoaling internal solitary wave are presented which illustrate the formation of a subsurface core.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The linear stability of Couette–Poiseuille flow of two superposed fluid layers in a horizontal channel is considered. The lower fluid layer is populated with surfactants that appear either in the form of monomers or micelles and can also get adsorbed at the interface between the fluids. A mathematical model is formulated which combines the Navier–Stokes equations in each fluid layer, convection–diffusion equations for the concentration of monomers (at the interface and in the bulk fluid) and micelles (in the bulk), together with appropriate coupling conditions at the interface. The primary aim of this study is to investigate when the system is unstable to arbitrary wavelength perturbations, and in particular, to determine the influence of surfactant solubility and/or sorption kinetics on the instability. A linear stability analysis is performed and the growth rates are obtained by solving an eigenvalue problem for Stokes flow, both numerically for disturbances of arbitrary wavelength and analytically using long-wave approximations. It is found that the system is stable when the surfactant is sufficiently soluble in the bulk and if the fluid viscosity ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190614123955401-0233:S0022112019003926:S0022112019003926_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and thickness ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190614123955401-0233:S0022112019003926:S0022112019003926_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 satisfy the condition 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190614123955401-0233:S0022112019003926:S0022112019003926_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. On the other hand, the effect of surfactant solubility is found to be destabilising if 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190614123955401-0233:S0022112019003926:S0022112019003926_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Both of the aforementioned results are manifested for low bulk concentrations below the critical micelle concentration; however, when the equilibrium bulk concentration is sufficiently high (and above the critical micelle concentration) so that micelles are formed in the bulk fluid, the system is stable if 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190614123955401-0233:S0022112019003926:S0022112019003926_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in all cases examined.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The fundamental challenge to characterize and quantify thermal transport in the strongly nonlinear regime of Rayleigh–Bénard convection – the buoyancy-driven flow of a horizontal layer of fluid heated from below – has perplexed the fluid dynamics community for decades. Rayleigh proposed controlling the temperature of thermally conducting boundaries in order to study the onset of convection, in which case vertical heat transport gauges the system response. Conflicting experimental results for ostensibly similar set-ups have confounded efforts to discriminate between two competing theories for how boundary layers and interior flows interact to determine transport through the convecting layer asymptotically far beyond onset. In a conceptually new approach, Bouillaut, Lepot, Aumaître and Gallet (〈span〉J. Fluid Mech.〈/span〉, vol. 861, 2019, R5) devised a procedure to radiatively heat a portion of the fluid domain bypassing rigid conductive boundaries and allowing for dissociation of thermal and viscous boundary layers. Their experiments reveal a new level of complexity in the problem suggesting that heat transport scaling predictions of both theories may be realized depending on details of the thermal forcing.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present an extension of Thomson’s (〈span〉J. Fluid Mech.〈/span〉, vol. 210, 1990, pp. 113–153) two-particle Lagrangian stochastic model that is constructed to be consistent with the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190328093140631-0005:S0022112019001149:S0022112019001149_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 law of turbulence. The rate of separation in the new model is reduced relative to the original model with zero skewness in the Eulerian longitudinal relative velocity distribution and is close to recent measurements from direct numerical simulations of homogeneous isotropic turbulence. The rate of separation in the equivalent backwards dispersion model is approximately a factor of 2.9 larger than the forwards dispersion model, a result that is consistent with previous work.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The large-scale structure of many turbulent flows encountered in practical situations such as aeronautics, industry, meteorology is nowadays successfully computed using the Kolmogorov–Kármán–Howarth energy cascade picture. This theory appears increasingly inaccurate when going down the energy cascade that terminates through intermittent spots of energy dissipation, at variance with the assumed homogeneity. This is problematic for the modelling of all processes that depend on small scales of turbulence, such as combustion instabilities or droplet atomization in industrial burners or cloud formation. This paper explores a paradigm shift where the homogeneity hypothesis is replaced by the assumption that turbulence contains singularities, as suggested by Onsager. This paradigm leads to a weak formulation of the Kolmogorov–Kármán–Howarth–Monin equation (WKHE) that allows taking into account explicitly the presence of singularities and their impact on the energy transfer and dissipation. It provides a local in scale, space and time description of energy transfers and dissipation, valid for any inhomogeneous, anisotropic flow, under any type of boundary conditions. The goal of this article is to discuss WKHE as a tool to get a new description of energy cascades and dissipation that goes beyond Kolmogorov and allows the description of small-scale intermittency. It puts the problem of intermittency and dissipation in turbulence into a modern framework, compatible with recent mathematical advances on the proof of Onsager’s conjecture.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Flow-induced rotation of an S-shaped rotor is investigated using an adaptive numerical scheme based on a vortex particle method. The boundary integral equation with respect to Bernoulli’s function is solved using a panel method for obtaining the pressure distribution on the rotor surface which applies the torque to the rotor. The present work first addresses the validation of the scheme against the previous studies of a rotating circular cylinder. Then, we compute the automatic rotation start of an S-shaped rotor from a quiescent state for various values of the moment of inertia. The computed flow patterns where the rotor supplies (or is supplied with) the torque to (or from) the fluid are shown during one cycle of rotation. The vortex shedding from the tip of the advancing bucket is found to play a key role in generating positive torque on the rotor. A remarkable finding is the fact that, after the rotor reaches a stable rotation, the trajectory of the limit cycle in the present autonomous system accounts for the stable rotating movement of the rotor. Furthermore, the hydrodynamic scenario of the rotor automatically starting up from a quiescent state and entering the limit cycle is elucidated for various values of the moment of inertia and the initial angle of the rotor.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The transient force exerted by a low-speed liquid droplet impinging onto a flat rigid surface is investigated experimentally. The measurements employ a high-sensitivity piezo-electric sensor, along with a high-speed camera, and cover four decades in droplet Reynolds number and greater than two decades in Weber number. Across these ranges, the peak of individual force profiles span from 3 mN to over 1300 mN. Once normalised, the force–time profiles support the existence of an inertially dominated self-similar regime. Within this regime, previous numerical and theoretical studies predict a 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320110638211-0139:S0022112019001411:S0022112019001411_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 dependence of impact normal force during the initial pre-peak rise. While our measurements confirm this finding, they also indicate that, after the peak force the profiles exhibit an exponential decay. This long-time decay law suggests treatment of the momentum transport from the droplet using a lumped model. An observed linear dependence between the force and force decay rate supports this approach. The reason for the efficacy of treating this system via a lumped model apparently connects to the physics right at the surface that limit the rate of momentum transport from the droplet to the surface. This is explored by estimating the momentum transfer by solely using the deforming droplet shape, but under the condition of negligible momentum gradients within the droplet. The short- and long-time solutions are combined and the resulting model equation is shown to accurately cover the entire force–time profile.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉A pressure impulse model is presented for wave impact on vertical circular cylinders. Pressure impulse is the time integral of the pressure during an impact of short time scale. The model is derived for a simplistic geometry and has relative impact height, crest length and cylinder radius as effective variables. The last parameter, the maximum angle of impact, is free and can be calibrated to yield the right force impulse. A progression of simpler pressure impulse models are derived in terms of a three-dimensional box generalization of the two-dimensional wall model and an axisymmetric model for vertical cylinders. The dependence on the model parameters is investigated in the simpler models and linked to the behaviour of the three-dimensional cylinder model. The model is next validated against numerical results for a wave impact for a phase- and direction-focused wave group. The maximum impact angle is determined by calibration against the force impulse. A good match of the pressure impulse fields is found. Further comparison to the force impulse of two common models in marine engineering reveals improved consistency for the present model. The model is found to provide a promising representation of the pressure impulse field, based on a limited number of input parameters. Its further validation and potential as a robust tool in force and response prediction is discussed.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The second-order structure functions (SFs) of the velocity field, which characterize the velocity difference at two points, are widely used in research into non-reacting turbulent flows. In the present paper, the approach is extended in order to study the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush. For this purpose, SFs conditioned to various combinations of mixture states at two different points (reactant–reactant, reactant–product, product–product, etc.) are introduced in the paper and a relevant exact transport equation is derived in the appendix. Subsequently, in order to demonstrate the capabilities of the newly developed approach for advancing the understanding of turbulent reacting flows, the conditioned SFs are extracted from three-dimensional (3-D) direct numerical simulation data obtained from two statistically 1-D planar, fully developed, weakly turbulent, premixed, single-step-chemistry flames characterized by significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results show that the conditioned SFs differ significantly from standard mean SFs and convey a large amount of important information on various local phenomena that stem from the influence of combustion-induced thermal expansion on turbulent flow. In particular, the conditioned SFs not only (i) indicate a number of already known local phenomena discussed in the paper, but also (ii) reveal a less recognized phenomenon such as substantial influence of combustion-induced thermal expansion on turbulence in constant-density unburned reactants and even (iii) allow us to detect a new phenomenon such as the appearance of strong local velocity perturbations (shear layers) within flamelets. Moreover, SFs conditioned to heat-release zones indicate a highly anisotropic influence of combustion-induced thermal expansion on the evolution of small-scale two-point velocity differences within flamelets, with the effects being opposite (an increase or a decrease) for different components of the local velocity vector.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319105803211-0804:S0022112019001162:S0022112019001162_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319105803211-0804:S0022112019001162:S0022112019001162_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The flow around a sphere descending at constant speed in a very strongly stratified fluid (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 that satisfies 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The Froude number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 here is in the range of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 or lower, while the Reynolds number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is in the range of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e. 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 or 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, this predicts that the jet becomes unstable when it becomes thinner than approximately 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the Brunt–Väisälä frequency, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the radius of the sphere and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319093956805-0211:S002211201900123X:S002211201900123X_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing homoclinic snaking (Schneider 〈span〉et al.〈/span〉, 〈span〉Phys. Rev. Lett.〈/span〉, vol. 104, 2010, 104501). These branches can be used to generate a number of spatially localized initial conditions whose transition can be investigated. From the low Reynolds numbers where homoclinic snaking is first observed (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322083610382-0756:S002211201900154X:S002211201900154X_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) to transitional ones (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322083610382-0756:S002211201900154X:S002211201900154X_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), these spatially localized states traverse various regimes where their relaminarization time and dynamics are affected by the dynamical structure of phase space. These regimes are reported and characterized in this paper for a 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322083610382-0756:S002211201900154X:S002211201900154X_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉-periodic domain in the streamwise direction as a function of the two remaining variables: the Reynolds number and the width of the localized pattern. Close to the snaking, localized states are attracted by spatially localized periodic orbits before relaminarizing. At larger values of the Reynolds number, the flow enters a chaotic transient of variable duration before relaminarizing. Very long chaotic transients (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322083610382-0756:S002211201900154X:S002211201900154X_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) can be observed without difficulty for relatively low values of the Reynolds number (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322083610382-0756:S002211201900154X:S002211201900154X_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉).〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Here we provide a theoretical framework describing the generation of the fast jet ejected vertically out of a liquid when a bubble, resting on a liquid–gas interface, bursts. The self-consistent physical mechanism presented here explains the emergence of the liquid jet as a consequence of the collapse of the gas cavity driven by the low capillary pressures that appear suddenly around its base when the cap, the thin film separating the bubble from the ambient gas, pinches. The resulting pressure gradient deforms the bubble which, at the moment of jet ejection, adopts the shape of a truncated cone. The dynamics near the lower base of the cone, and thus the jet ejection process, is determined by the wavelength 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the smallest capillary wave created during the coalescence of the bubble with the atmosphere which is not attenuated by viscosity. The minimum radius at the lower base of the cone decreases, and hence the capillary suction and the associated radial velocities increase, with the wavelength 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. We show that 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 increases with viscosity as 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the Ohnesorge number, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 the bubble radius and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 indicating respectively the liquid density, viscosity and interfacial tension coefficient. The velocity of the extremely fast and thin jet can be calculated as the flow generated by a continuous line of sinks extending along the axis of symmetry a distance proportional to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. We find that the jet velocity increases with the Ohnesorge number and reaches a maximum for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the value for which the crest of the capillary wave reaches the vertex of the cone, and which depends on the Bond number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. For 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190322102515033-0808:S0022112019001617:S0022112019001617_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the jet is ejected after a bubble is pinched off; in this regime, viscosity delays the formation of the jet, which is thereafter emitted at a velocity which is inversely proportional to the liquid viscosity.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present a study of Lagrangian intermittency and its characteristic time scales. Using the concepts of flying and diving residence times above and below a given threshold in the magnitude of turbulence quantities, we infer the time spectra of the Lagrangian temporal fluctuations of dissipation, acceleration and enstrophy by means of a direct numerical simulation in homogeneous and isotropic turbulence. We then relate these time scales, first, to the presence of extreme events in turbulence and, second, to the local flow characteristics. Analyses confirm the existence in turbulent quantities of holes mirroring bursts, both of which are at the core of what constitutes Lagrangian intermittency. It is shown that holes are associated with quiescent laminar regions of the flow. Moreover, Lagrangian holes occur over few Kolmogorov time scales while Lagrangian bursts happen over longer periods scaling with the global decorrelation time scale, hence showing that loss of the history of the turbulence quantities along particle trajectories in turbulence is not continuous. Such a characteristic partially explains why current Lagrangian stochastic models fail at reproducing our results. More generally, the Lagrangian dataset of residence times shown here represents another manner for qualifying the accuracy of models. We also deliver a theoretical approximation of mean residence times, which highlights the importance of the correlation between turbulence quantities and their time derivatives in setting temporal statistics. Finally, whether in a hole or a burst, the straining structure along particle trajectories always evolves self-similarly (in a statistical sense) from shearless two-dimensional to shear bi-axial configurations. We speculate that this latter configuration represents the optimum manner to dissipate locally the available energy.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The standard resonance conditions for Bragg scattering as well as weakly nonlinear wave triads have been traditionally derived in the absence of any background velocity. In this paper, we have studied how these resonance conditions get modified when uniform, as well as various piecewise linear velocity profiles, are considered for two-layered shear flows. Background velocity can influence the resonance conditions in two ways: (i) by causing Doppler shifts, and (ii) by changing the intrinsic frequencies of the waves. For Bragg resonance, even a uniform velocity field changes the resonance condition. Velocity shear strongly influences the resonance conditions since, in addition to changing the intrinsic frequencies, it can cause unequal Doppler shifts between the surface, pycnocline and the bottom. Using multiple scale analysis and Fredholm alternative, we analytically obtain the equations governing both the Bragg resonance and the wave triads. We have also extended the higher-order spectral method, a highly efficient computational tool usually used to study triad and Bragg resonance problems, to incorporate the effect of piecewise linear velocity profile. A significant aspect, both on the theoretical and numerical fronts, has been extending the potential flow approximation, which is the basis of the study of these kinds of problems, to incorporate piecewise constant background shear.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Self-preservation analyses of the equations for the mean temperature and the second-order temperature structure function on the axis of a slightly heated turbulent round jet are exploited in an attempt to develop an analytical expression for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the mean dissipation rate of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the temperature variance. The analytical approach follows that of Thiesset 〈span〉et al.〈/span〉 (〈span〉J. Fluid Mech.〈/span〉, vol. 748, 2014, R2) who developed an expression for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the mean turbulent kinetic energy dissipation rate, using the transport equation for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as: 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (all representing characteristic length scales), the mean temperature excess 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the mixed velocity–temperature moments 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Simple models are proposed for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline19.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in order to derive an analytical expression for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline20.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, the prefactor of the power law describing the streamwise evolution of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190321115044598-0207:S0022112019001642:S0022112019001642_inline21.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Further, expressions are also derived for the turbulent Péclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in stratified flows as a function of the turbulent Froude number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Here, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the buoyancy frequency, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the turbulent kinetic energy, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the rate of dissipation of turbulent kinetic energy and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the rate of dissipation of turbulent potential energy. We show that for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. These scaling results are tested using high-resolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 that encompasses weakly stratified to strongly stratified flow conditions. Given that the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 from readily measurable quantities in the field. Scaling analyses show that 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline19.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline20.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline21.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline22.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the Thorpe length scale and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320133914837-0850:S0022112019001423:S0022112019001423_inline23.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The turbulence state in a supersonic boundary layer subjected to a transverse sonic jet is studied by conducting direct numerical simulations. Turbulence statistics for two jet-to-cross-flow momentum flux ratios 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320093504744-0896:S0022112019001587:S0022112019001587_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of 2.3 and 5.5 based on the previous simulation (Sun & Hu, 〈span〉J. Fluid Mech.〈/span〉, vol. 850, 2018, pp. 551–583) are given and compared with a flat-plate boundary layer without a jet 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320093504744-0896:S0022112019001587:S0022112019001587_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. The instantaneous and time-averaged flow features around the transverse jet in the supersonic boundary layer are analysed. It is found that, in the near-wall region, turbulence is suppressed significantly with increasing 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320093504744-0896:S0022112019001587:S0022112019001587_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in the lateral boundary layer around the jet and the turbulence decay is retained in the downstream recovery region. The local boundary-layer thickness decreases noticeably in the lateral downstream of the jet. Analysis of the cross-flow streamlines reveals a double-expansion character in the vicinity of the jet, which involves the reattachment expansion related to the flow over the jet windward separation bubble and the jet lateral expansion related to the flow around the jet barrel shock. The double expansion leads to the turbulence decay in the jet lateral boundary layer and causes a slow recovery of the outer layer in the far-field boundary layer. A preliminary experiment based on the nanoparticle laser scattering technique is conducted and confirms the existence of the turbulence decay phenomenon.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Finite-amplitude wave groups with multiple near-resonances are investigated to extend the existing results due to Liu 〈span〉et al.〈/span〉 (〈span〉J. Fluid Mech.〈/span〉, vol. 835, 2018, pp. 624–653) from steady-state wave groups in deep water to steady-state wave groups in finite water depth. The slow convergence rate of the series solution in the homotopy analysis method and extra unpredictable high-frequency components in finite water depth make it hard to obtain finite-amplitude wave groups accurately. To overcome these difficulties, a solution procedure that combines the homotopy analysis method-based analytical approach and Galerkin method-based numerical approaches has been used. For weakly nonlinear wave groups, the continuum of steady-state resonance from deep water to finite water depth is established. As nonlinearity increases, the frequency bands broaden and more steady-state wave groups are obtained. Finite-amplitude wave groups with steepness no less than 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320134645422-0805:S0022112019001502:S0022112019001502_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 are obtained and the resonant sets configuration of steady-state wave groups are analysed in different water depths. For waves in deep water, the majority of non-trivial components appear around the primary ones due to four-wave, six-wave, eight-wave or even ten-wave resonant interactions. The dominant role of four-wave resonant interactions for steady-state wave groups in deep water is demonstrated. For waves in finite water depth, additional non-trivial high-frequency components appear in the spectra due to three-wave, four-wave, five-wave or even six-wave resonant interactions with the components around the primary ones. The amplitude of these high-frequency components increases further as the water depth decreases. Resonances composed by components only around the primary ones are suppressed while resonances composed by components around the primary ones and from the high-frequency domain are enhanced. The spectrum of steady-state resonant wave groups changes with the water depth and the significant role of three-wave resonant interactions in finite water depth is demonstrated.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Turbulent miscible fountains discharged vertically from a round source into quiescent uniform unbounded environments of density 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 are investigated numerically using large-eddy simulations. Both upward and downward fountains are considered. The numerical simulations cover a wide range of the density ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the source density of the released fluid. These simulations are used to evaluate how the initial maximum height 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the steady state height 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 of the fountains are affected by large density contrasts, i.e. in the general non-Boussinesq case. For both upward and downward non-Boussinesq fountains, the ratio 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 remains close to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, as usually observed for Boussinesq fountains. However the Froude (linear) scaling originally introduced by Turner (〈span〉J. Fluid Mech.〈/span〉, vol. 26 (4), 1966, pp. 779–792) for Boussinesq fountains is no longer valid to determine the steady fountain height. The ratio between 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 and the height predicted by the Turner’s relation turns out to be proportional to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. Remarkably, it is found that the power exponent 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 differs following the direction in which the buoyant fluid is released (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for downward fountains and 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190320114940105-0890:S0022112019001496:S0022112019001496_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for upward fountains). This new result demonstrates that for non-Boussinesq turbulent fountains the configurations heavy/light and light/heavy are not equivalent. Finally, scalings are proposed for fountains, regardless of the direction (upwards and downwards) and of the density difference (Boussinesq and non-Boussinesq).〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The flow of a gravity current of finite volume and density 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 released from rest from a rectangular lock (of height 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) into an ambient fluid of density 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) in a system rotating with 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 about the vertical 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is investigated by means of fully resolved direct numerical simulations (DNS) and a theoretical model (based on shallow-water and Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉-direction accompanied by Coriolis acceleration/deflection in the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉-direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline9.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, followed by a spin-up reduction of 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline10.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 accompanied by a slow 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline11.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 drift, and oscillation. The theoretical model aims to provide useful insights and approximations concerning the formation time and shape of wedge, and the subsequent spin-up effect. The main parameter is the Coriolis number, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline12.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline13.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 is the reduced gravity. The DNS results are focused on a range of relatively small Coriolis numbers, 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline14.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (i.e. Rossby number 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline15.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 in the range 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline16.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), and a large range of Schmidt numbers 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline17.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉; the Reynolds number is large in all cases. The current spreads out in the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline18.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 direction until it is arrested by the Coriolis effect (in 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline19.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 revolution of the system). A complex motion develops about this state. First, we record oscillations on the inertial time scale 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline20.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (which are a part of the geostrophic adjustment), accompanied by vortices at the interface. Second, we note the spread of the wedge on a significantly longer time scale; this is an indirect spin-up effect – mixing and entrainment reduce the lateral (angular) velocity, which in turn decreases the Coriolis support to the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline21.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 slope of the wedge shape. Contrary to non-rotating gravity currents, the front does not remain sharp as it is subject to (i) local stretching along the streamwise direction and (ii) convective mixing due to Kelvin–Helmholtz vortices generated by shear along the spanwise direction and stemming from Coriolis effects. The theoretical model predicts that the length of the wedge scales as 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline22.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (in contrast to the Rossby radius 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline23.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 which is relevant for large 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline24.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉; and in contrast to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190319101231250-0462:S0022112019001526:S0022112019001526_inline25.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 for the axisymmetric lens).〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We examine the high-speed flow of pressurized gases between non-concentric cylinders where the inner cylinder rotates at constant speed while the outer cylinder is stationary. The flow is taken to be steady, two-dimensional, compressible, laminar, single phase and governed by a Reynolds lubrication equation. Approximations for the lubricating force and friction loss are derived using a perturbation expansion for large speed numbers. The present theory is valid for general Navier–Stokes fluids at nearly all states corresponding to ideal, dense and supercritical gases. Results of interest include the observation that pressurization gives rise to large increases in the lubricating force and decreases in the fluid friction. The lubrication force is found to scale with the bulk modulus. Within the context of the Reynolds equation an exact relation between total heat transfer and power loss is developed.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We develop a new boundary integral method for solving the coupled electro- and hydrodynamics of vesicle suspensions in Stokes flow. This relies on a well-conditioned boundary integral equation formulation for the leaky-dielectric model describing the electric response of the vesicles and an efficient numerical solver capable of handling highly deflated vesicles. Our method is applied to explore vesicle electrohydrodynamics in three cases. First, we study the classical prolate–oblate–prolate transition dynamics observed upon application of a uniform DC electric field. We discover that, in contrast to the squaring previously found with nearly spherical vesicles, highly deflated vesicles tend to form buds. Second, we illustrate the capabilities of the method by quantifying the electrorheology of a dilute vesicle suspension. Finally, we investigate the pairwise interactions of vesicles and find three different responses when the key parameters are varied: (i) chain formation, where they self-assemble to form a chain that is aligned along the field direction; (ii) circulatory motion, where they rotate about each other; (iii) oscillatory motion, where they form a chain but oscillate about each other. The last two are unique to vesicles and are not observed in the case of other soft particle suspensions such as drops.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The perturbations triggered by free-stream vortical disturbances in compressible boundary layers developing over concave walls are studied numerically and through asymptotic methods. We employ an asymptotic framework based on the limit of high Görtler number, the scaled parameter defining the centrifugal effects; we use an eigenvalue formulation where the free-stream forcing is neglected; and we solve the receptivity problem by integrating the compressible boundary-region equations complemented by appropriate initial and boundary conditions that synthesize the influence of the free-stream vortical flow. Near the leading edge, the boundary-layer perturbations develop as thermal Klebanoff modes and, when centrifugal effects become influential, these modes turn into thermal Görtler vortices, i.e. streamwise rolls characterized by intense velocity and temperature perturbations. The high-Görtler-number asymptotic analysis reveals the condition for which the Görtler vortices start to grow. The Mach number is destabilizing when the spanwise diffusion is negligible and stabilizing when the boundary-layer thickness is comparable with the spanwise wavelength of the vortices. When the Görtler number is large, the theoretical analysis also shows that the vortices move towards the wall as the Mach number increases. These results are confirmed by the receptivity analysis, which additionally clarifies that the temperature perturbations respond to this reversed behaviour further downstream than the velocity perturbations. A matched-asymptotic composite profile, found by combining the inviscid core solution and the near-wall viscous solution, agrees well with the receptivity profile sufficiently downstream and at high Görtler number. The Görtler vortices tend to move towards the boundary-layer core when the flow is more stable, i.e. as the frequency or the Mach number increase, or when the curvature decreases. As a consequence, a region of unperturbed flow is generated near the wall. We also find that the streamwise length scale of the boundary-layer perturbations is always smaller than the free-stream streamwise wavelength. During the initial development of the vortices, only the receptivity calculations are accurate. At streamwise locations where the free-stream disturbances have fully decayed, the growth rate and wavelength are computed with sufficient accuracy by the eigenvalue analysis, although the correct amplitude and evolution of the Görtler vortices can only be determined by the receptivity calculations. It is further proved that the eigenvalue predictions of the growth rate and wavenumber worsen as the Mach number increases as these quantities show a dependence on the wall-normal direction. We conclude by qualitatively comparing our results with the direct numerical simulations available in the literature.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We present a model for capillary-scale objects that bounce on a fluid bath as they also translate horizontally. The rebounding objects are hydrophobic spheres that impact the interface of a bath of incompressible fluid whose motion is described by linearised quasi-potential flow. Under a quasi-normal impact assumption, we demonstrate that the problem can be decomposed into an axisymmetric impact onto a quiescent bath surface, and the unforced evolution of the surface waves. We obtain a walking model that is free of impact parametrisation and we apply this formulation to model droplets walking on a vibrating bath. We show that this model accurately reproduces experimental reports of bouncing modes, impact phases and time-dependent wave field topography for bouncing and walking droplets. Moreover, we revisit the modelling of horizontal drag during droplet impacts to incorporate the effects of the changes in the pressed area during droplet–surface contacts. Finally, we show that this model captures the recently discovered phenomenon of superwalkers.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The dynamics of large gravity waves are known to be modified from the linear model by nonlinear physics. In this paper we analyse Eulerian surface elevation time histories measured from two sites, Lake George (Australia) and the North Sea, to examine how weak nonlinearity has modified the shape of extreme wave groups relative to linear theory. We analyse the asymmetry of the extreme wave groups and find that, on average, the wave in front of an extreme wave is smaller than the wave following it. We also observe a contraction in the envelope width of the wave group relative to linear theory. The departures from linear theory are strongly correlated with the steepness of the underlying sea state and are generally consistent with theoretical expectations, providing strong evidence that such nonlinear phenomena arise in naturally occurring water waves.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉A novel wavelet-based adaptive delayed detached eddy simulation (W-DDES) approach for simulations of wall-bounded compressible turbulent flows is proposed. The new approach utilizes anisotropic wavelet-based mesh refinement and its effectiveness is demonstrated for flow simulations using the Spalart–Allmaras DDES model. A variable wavelet thresholding strategy blending two distinct thresholds for the Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) regimes is used. A novel mesh adaptation on mean and fluctuating quantities with different wavelet threshold levels is proposed. The new strategy is more accurate and efficient compared to the adaptation on instantaneous quantities using 〈span〉a priori〈/span〉 defined uniform thresholds. The effectiveness of the W-DDES method is demonstrated by comparing the results of the W-DDES simulations with results already available in the literature. Supersonic plane channel flow for two different configurations is tested as benchmark wall-bounded flows. Both the accuracy indicated by the threshold and efficiency in terms of degrees of freedom for the novel adaptation strategy are successfully gained compared with the wavelet-based adaptive LES method. Moreover, the newly proposed W-DDES resolves the typical log-layer match issue encountered in the conventional non-adaptive DDES method mainly due to the use of wavelet-based adaptive mesh refinement. The W-DDES capability for simulations of complex turbulent flows is validated by two other flow configurations – a subsonic channel flow with periodic hill constrictions and a supersonic flow over a compression ramp inducing the shock wave–turbulent boundary layer interaction. The current study serves as a crucial step towards construction of a unified wavelet-based adaptive hierarchical RANS/LES modelling framework, capable of performing simulations of varying fidelities from no-modelling direct numerical simulations to full-modelling RANS simulations.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The dynamics of a conducting liquid film flowing down a cylindrical fibre, subjected to a radial electric field, is investigated using a long-wave model (Ding 〈span〉et al.〈/span〉, 〈span〉J. Fluid Mech.〈/span〉, vol. 752, 2014, p. 66). In this study, to account for the complicated interactions between droplets, we consider two large droplets in a periodic computational domain and find two distinct types of travelling wave solutions, which consist of either two identical droplets (type I) or two slightly different droplets (type II). Both are ‘relative’ equilibria, i.e. steady in a frame moving at their phase speed, and are stable in smaller domains when the electric field is weak. We also study relative periodic orbits, i.e. temporally recurrent dynamic solutions of the system. In the presence of the electric field, we show how these invariant solutions are linked to the dynamics, where the system can evolve into one of the steady travelling wave states, into an oscillatory state, or into a ‘singular structure’ (Wray 〈span〉et al.〈/span〉, 〈span〉J. Fluid Mech.〈/span〉, vol. 735, 2013, pp. 427–456; Ding 〈span〉et al.〈/span〉, 〈span〉J. Fluid Mech.〈/span〉, vol. 752, 2014, p. 66). We find that the oscillation between two similarly sized large droplets in the oscillatory state is well represented by relative periodic orbits. Varying the electric field strength, we demonstrate that relative periodic solutions arise as the dynamically important solution once the type-I or type-II travelling wave solutions lose stability. Oscillation can be either enhanced or impeded as the electric field’s strength increases. When the electric field is strong, no relative periodic solutions are found and a spike-like singular structure is observed. For the case where the electric field is not present, the oscillation is instead caused by the interaction between a large droplet and a nearby much smaller droplet. We show that this oscillation phenomenon originates from the instability of the type-I travelling wave solution in larger domains, and that the oscillatory state can again be represented by an exact relative periodic orbit. The relative periodic orbit solution is also compared with experimental study for this case. The present study demonstrates that the relative periodic solutions are better at capturing the wave speed and oscillatory dynamics than the travelling wave solutions in the unsteady flow regime.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We investigate the interaction of a downslope gravity current with an internal wave propagating along a two-layer density jump. Direct numerical simulations confirm earlier experimental findings of a reduced gravity current mass flux, as well as the partial removal of the gravity current head from its body by large-amplitude waves (Hogg 〈span〉et al.〈/span〉, 〈span〉Environ. Fluid Mech.〈/span〉, vol. 18 (2), 2018, pp. 383–394). The current is observed to split into an intrusion of diluted fluid that propagates along the interface and a hyperpycnal current that continues to move downslope. The simulations provide detailed quantitative information on the energy budget components and the mixing dynamics of the current–wave interaction, which demonstrates the existence of two distinct parameter regimes. Small-amplitude waves affect the current in a largely transient fashion, so that the post-interaction properties of the current approach those in the absence of a wave. Large-amplitude waves, on the other hand, perform a sufficiently large amount of work on the gravity current fluid so as to modify its properties over the long term. The ‘decapitation’ of the current by large waves, along with the associated formation of an upslope current, enhance both viscous dissipation and irreversible mixing, thereby strongly reducing the available potential energy of the flow.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow are studied using Floquet theory. High-frequency secondary instability modes of ‘y’ mode on top of stationary cross-flow vortices, and ‘z’ mode concentrating on the shoulder of the stationary cross-flow vortex are found. The most unstable secondary instability mode is always the ‘z’ mode as in incompressible swept wing flows. A new secondary instability mode concentrating on the trough of the stationary cross-flow vortex is found. The balance analysis of disturbance kinetic energy shows that the new mode belongs to the class of ‘y’ mode. The growth rate of the new ‘y’ mode located on the trough of the stationary cross-flow vortex is significantly larger than that of the ‘y’ mode on top of the stationary cross-flow vortex, and is comparable with the growth rate of the ‘z’ mode. It is also found that the new ‘y’ mode with higher frequency can evolve into the ‘z’ mode further downstream. The role of the pressure fluctuation term, including the pressure diffusion and pressure dilatation, in the energy production of secondary instability modes, is also investigated. It is shown that the pressure diffusion will only enhance the growth rate of the ‘z’ mode with higher frequency, but has little influence on other types of secondary instability mode. However, the pressure dilatation term arising from non-vanishing velocity divergence will reduce the growth rates of all secondary instability modes.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We propose a new framework to evaluate input–output amplification properties of nonlinear models of wall-bounded shear flows, subject to both square integrable and persistent disturbances. We focus on flows that are spatially invariant in one direction and whose base flow can be described by a polynomial, e.g. streamwise-constant channel, Couette and pipe flows. Our methodology is based on the notion of dissipation inequalities in control theory and provides a single unified approach for examining flow properties such as energy growth, worst-case disturbance amplification and stability to persistent excitations (i.e. input-to-state stability). It also enables direct analysis of the nonlinear partial differential equation rather than of a discretized form of the equations, thereby removing the possibility of truncation errors. We demonstrate how to numerically compute the input–output properties of the flow as the solution of a (convex) optimization problem. We apply our theoretical and computational tools to plane Couette, channel and pipe flows. Our results demonstrate that the proposed framework leads to results that are consistent with theoretical and experimental amplification scalings obtained in the literature.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉This paper considers a free vorticity wave packet propagating within a rapidly rotating vortex in the quasi-steady regime, a long time after the wave packet strongly and unsteadily interacted with the vortex. We study a singular, nonlinear, helical and asymmetric shear mode inside a linearly stable, columnar and axisymmetric vortex on the 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627064544313-0235:S0022112019003744:S0022112019003744_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉-plane. The amplitude-modulated mode enters resonance with the vortex at a certain radius 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627064544313-0235:S0022112019003744:S0022112019003744_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, where the phase angular speed is equal to the rotation frequency. The singularity in the modal equation at 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627064544313-0235:S0022112019003744:S0022112019003744_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 strongly modifies the flow in the three-dimensional helical critical layer, the region around 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190627064544313-0235:S0022112019003744:S0022112019003744_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 where the wave/vortex interaction occurs. This interaction generates a vertically sheared three-dimensional mean flow of higher amplitude than the wave packet. The chosen envelope regime assumes the formation of a mean radial velocity of the same order as the wave packet amplitude, leading to the streamlines exhibiting a spiral motion in the neighbourhood of the critical layer. Radar images frequently show such spiral bands in tropical cyclones or tornadoes. Through matched asymptotic expansions, we find an analytical solution of the leading-order equations inside the critical layer. The generalized Batchelor integral condition applied to the quasi-steady, three-dimensional motion inside the separatrices yields a leading-order, non-uniform three-dimensional vorticity. The critical-layer pattern, strongly deformed by the mean radial velocity, loses its symmetries with respect to the azimuthal and radial directions, which makes the leading-order mean radial wave fluxes non-zero. Finally, a stronger wave/vortex interaction occurs with respect to previous studies where a steady neutral vortical mode or an envelope of larger extent was involved.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉We investigate the effect of a light turbulent wind on a liquid surface, below the onset of wave generation. In that regime, the liquid surface is populated by small disorganised deformations elongated in the streamwise direction. Formally identified recently by Paquier 〈span〉et al.〈/span〉 (〈span〉Phys. Fluids〈/span〉, vol. 27, 2015, art. 122103), the deformations that occur below the wave onset were named wrinkles. We provide here a theoretical framework for this regime, using the viscous response of a free liquid surface submitted to arbitrary normal and tangential interfacial stresses at its upper boundary. We relate the spatio-temporal spectrum of the surface deformations to that of the applied interfacial pressure and shear stress fluctuations. For that, we evaluate the spatio-temporal statistics of the turbulent forcing using direct numerical simulation of a turbulent channel flow, assuming no coupling between the air and the liquid flows. Combining theory and numerical simulation, we obtain synthetic wrinkles fields that reproduce the experimental observations. We show that the wrinkles are a multi-scale superposition of random wakes generated by the turbulent fluctuations. They result mainly from the nearly isotropic pressure fluctuations generated in the boundary layer, rather than from the elongated shear stress fluctuations. The wrinkle regime described in this paper naturally arises as the viscous-saturated asymptotic of the inviscid growth theory of Phillips (〈span〉J. Fluid Mech.〈/span〉, vol. 2 (05), 1957, pp. 417–445). We finally discuss the possible relation between wrinkles and the onset of regular quasi-monochromatic waves at larger wind velocity. Experiments indicate that the onset of regular waves increases with liquid viscosity. Our theory suggests that regular waves are triggered when the wrinkle amplitude reaches a fraction of the viscous sublayer thickness. This implies that the turbulent fluctuations near the onset may play a key role in the triggering of exponential wave growth.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉Experimental investigations of laminar swirling jets had revealed a new form of vortex breakdown, named conical vortex breakdown, in addition to the commonly observed bubble form. The present study explores these breakdown states that develop for the Maxworthy profile (a model of swirling jets) at inflow, from streamwise-invariant initial conditions, with direct numerical simulations. For a constant Reynolds number based on jet radius and a centreline velocity of 200, various flow states were observed as the inflow profile’s swirl parameter 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline1.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (scaled centreline radial derivative of azimuthal velocity) was varied up to 2. At low swirl (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline2.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉) a helical mode of azimuthal wavenumber 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline3.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉 (co-winding, counter-rotating mode) was observed. A ‘swelling’ appeared at 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline4.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, and a steady bubble breakdown at 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline5.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉. On further increase to 〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline6.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, a helical, self-excited global mode (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline7.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉, counter-winding and co-rotating) was observed, originating in the bubble’s wake but with little effect on the bubble itself – a bubble vortex breakdown with a spiral tail. Local and global stability analyses revealed this to arise from a linear instability mechanism, distinct from that for the spiral breakdown which has been studied using Grabowski profile (a model of wing-tip vortices). At still higher swirl (〈span〉〈span〉〈img data-mimesubtype="gif" data-type="simple" src="http://static.cambridge.org/resource/id/urn:cambridge.org:id:binary:20190621114754070-0585:S0022112019004014:S0022112019004014_inline8.gif"〉 〈span data-mathjax-type="texmath"〉 〈/span〉 〈/span〉〈/span〉), a pulsating type of bubble breakdown occurred, followed by conical breakdown at 1.6. The latter consists of a large toroidal vortex confined by a radially expanding conical sheet, and a weaker vortex core downstream. For the highest swirls, the sheet was no longer conical, but curved away from the axis as a wide-open breakdown. The applicability of two classical inviscid theories for vortex breakdown – transition to a conjugate state, and the dominance of negative azimuthal vorticity – was assessed for the conical form. As required by the former, the flow transitioned from a supercritical to subcritical state in the vicinity of the stagnation point. The deviations from the predictions of the latter model were considerable.〈/p〉〈/div〉

Description: 〈div data-abstract-type="normal"〉〈p〉A number of applications utilise the energy focussing potential of imploding shells to dynamically compress matter or magnetic fields, including magnetised target fusion schemes in which a plasma is compressed by the collapse of a liquid metal surface. This paper examines the effect of fluid rotation on the Rayleigh–Taylor (RT) driven growth of perturbations at the inner surface of an imploding cylindrical liquid shell which compresses a gas-filled cavity. The shell was formed by rotating water such that it was in solid body rotation prior to the piston-driven implosion, which was propelled by a modest external gas pressure. The fast rise in pressure in the gas-filled cavity at the point of maximum convergence results in an RT unstable configuration where the cavity surface accelerates in the direction of the density gradient at the gas–liquid interface. The experimental arrangement allowed for visualisation of the cavity surface during the implosion using high-speed videography, while offering the possibility to provide geometrically similar implosions over a wide range of initial angular velocities such that the effect of rotation on the interface stability could be quantified. A model developed for the growth of perturbations on the inner surface of a rotating shell indicated that the RT instability may be suppressed by rotating the liquid shell at a sufficient angular velocity so that the net surface acceleration remains opposite to the interface density gradient throughout the implosion. Rotational stabilisation of high-mode-number perturbation growth was examined by collapsing nominally smooth cavities and demonstrating the suppression of small spray-like perturbations that otherwise appear on RT unstable cavity surfaces. Experiments observing the evolution of low-mode-number perturbations, prescribed using a mode-6 obstacle plate, showed that the RT-driven growth was suppressed by rotation, while geometric growth remained present along with significant nonlinear distortion of the perturbations near final convergence.〈/p〉〈/div〉