ALBERT

Description: We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but statistically stationary flow. We also develop a new method to solve the governing equations, based on the HelmholtzHodge decomposition, that guarantees discrete mass conservation regardless of iteration errors. Whilst some statistics were found to be sensitive to the computational box size, we show, from inner-scaled planar spectra, that the small scales exhibit similarity independent of Reynolds number, density ratio and aspect ratio. We also perform LES of the present flow using the stretched-vortex subgrid-scale (SGS) model. The utility of an SGS scalar flux closure for passive scalars is demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale character of the stretched-vortex SGS model is shown to enable extension of some second-order statistics to subgrid scales. Comparisons with DNS velocity spectra and velocity-density cospectra show that both the resolved-scale and SGS-extended components of the LES spectra accurately capture important features of the DNS spectra, including small-scale anisotropy and the shape of the viscous roll-off. © 2009 Cambridge University Press.

Description: A study of the flow past an oscillatory rotating cylinder has been conducted, where the frequency of oscillation has been matched to the natural frequency of the vortex street generated in the wake of a stationary cylinder, at Reynolds number 300. The focus is on the wake transition to three-dimensional flow and, in particular, the changes induced in this transition by the addition of the oscillatory rotation. Using Floquet stability analysis, it is found that the fine-scale three-dimensional mode that typically dominates the wake at a Reynolds number beyond that at the second transition to three-dimensional flow (referred to as mode B) is suppressed for amplitudes of rotation beyond a critical amplitude, in agreement with past studies. However, the rotation does not suppress the development of three-dimensionality completely, as other modes are discovered that would lead to three-dimensional flow. In particular, the longer-wavelength mode that leads the three-dimensional transition in the wake of a stationary cylinder (referred to as mode A) is left essentially unaffected at low amplitudes of rotation. At higher amplitudes of oscillation, mode A is also suppressed as the two-dimensional near wake changes in character from a single-to a double-row wake; however, another mode is predicted to render the flow three-dimensional, dubbed mode D (for double row). This mode has the same spatio-temporal symmetries as mode A. © 2009 Cambridge University Press.

Description: We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (full cylinder or wedge). The current of density c is released from rest from a lock of radius r0 and height h0 into an ambient fluid of density a in a container of height H. When the Reynolds number is large, the resulting flow is governed by the parameters pc/pa and H* = H/h 0. We show that the one-layer shallow-water model, carefully combined with a Benjamin-type front condition, provides a versatile formulation for the thickness and speed of the current, without any adjustable constants. The results cover in a continuous manner the range of light pc/pa〈1, Boussinesq pc/pa≈1, and heavy pc/pa*GT;1 currents in a fairly wide range of depth ratio, H*. We obtain finite-difference solutions for the propagation and show that a self-similar behaviour develops for large times. This reveals the main features, in particular: (a) The heavy current propagates faster and its front is thinner than that for the light counterpart; (b) For large time, t, both the heavy and light currents spread like t1/2, but the thickness profiles display significant differences; (c) The energy-constrained propagation with the thickness of half-ambient-depth (when H* is close to 1) is a very limited occurrence, in contrast to the rectangular geometry counterpart in which this effect plays a major role. The predictions of the simple model are supported by some axisymmetric NavierStokes finite-difference simulations. © 2009 Cambridge University Press.

Description: An experimental investigation of the flow generated by a homogeneous population of bubbles rising in water is reported for three different bubble diameters (d = 1.6, 2.1 and 2.5 mm) and moderate gas volume fractions (0.005 ≤ α ≥0.1). The Reynolds numbers, Re = V0d/, based on the rise velocity V0 of a single bubble range between 500 and 800. Velocity statistics of both the bubbles and the liquid phase are determined within the homogeneous bubble swarm by means of optical probes and laser Doppler anemometry. Also, the decaying agitation that takes place in the liquid just after the passage of the bubble swarm is investigated from high-speed particle image velocimetry measurements. Concerning the bubbles, the average velocity is found to evolve as V0α0.1 whereas the velocity fluctuations are observed to be almost independent of. Concerning the liquid fluctuations, the probability density functions adopt a self-similar behaviour when the gas volume fraction is varied, the characteristic velocity scaling as V0α0.4. The spectra of horizontal and vertical liquid velocity fluctuations are obtained with a resolution of 0.6 mm. The integral length scale is found to be proportional to V02/g or equivalently to d/Cd0, where g is the gravity acceleration and Cd0 the drag coefficient of a single rising bubble. Normalized by using, the spectra are independent on both the bubble diameter and the volume fraction. At large scales, the spectral energy density evolves as the power 3 of the wavenumber. This range starts approximately from δ and is followed for scales smaller than δ/4 by a classic 5/3 power law. Although the Kolmogorov microscale is smaller than the measurement resolution, the dissipation rate is however obtained from the decay of the kinetic energy after the passage of the bubbles. It is found to scale as α0.9 V 03/δ. The major characteristics of the agitation are thus expressed as functions of the characteristics of a single rising bubble. Altogether, these results provide a rather complete description of the bubble-induced turbulence. © 2009 Cambridge University Press.

Description: The present paper is devoted to the formation of sand patterns by laminar flows. It focuses on the rhomboid beach pattern, formed during the backswash. A recent bedload transport model, based on a moving-grains balance, is generalized in three dimensions for viscous flows. The water flow is modelled by the full incompressible NavierStokes equations with a free surface. A linear stability analysis then shows the simultaneous existence of two distinct instabilities, namely ripples and bars. The comparison of the bar instability characteristics with laboratory rhomboid patterns indicates that the latter could result from the nonlinear evolution of unstable bars. This result, together with the sensibility of the stability analysis with respect to the parameters of the transport law, suggests that the rhomboid pattern could help improving sediment transport models, so critical to geomorphologists. © 2010 Cambridge University Press.

Description: The boundary value problem for the nonlinear shallow-water equations with a beach source term is solved by direct use of physical variables, so that solutions are more easily inspected than those obtained by means of hodograph transformations. Beyond an overall description of the near-shoreline flows in terms of the nonlinear shallow-water equations, significant results are provided by means of a perturbation approach which enables much of the information on the flow to be retained. For sample waves of interest (periodic and solitary), first-order solutions of the shoreline motion and of the near-shoreline flows are computed, illustrated and successfully compared with the equivalent ones obtained through a hodograph transformation method previously developed by the authors. Wavewave interaction, both at the seaward boundary and within the domain, is also accurately described. Analytical conditions for wave breaking within the domain are provided. These, compared with the authors' hodograph model, show that the first-order condition of the present model is comparable to the second-order condition of that model. © 2009 Cambridge University Press.

Description: The effects of an axial rotation on the turbulent convective flow because of an adverse temperature gradient in a water-filled upright cylindrical vessel are investigated. Both direct numerical simulations and experiments applying stereoscopic particle image velocimetry are performed. The focus is on the gathering of turbulence statistics that describe the effects of rotation on turbulent RayleighBnard convection. Rotation is an important addition, which is relevant in many geophysical and astrophysical flow phenomena. A constant Rayleigh number (dimensionless strength of the destabilizing temperature gradient) Ra = 109 and Prandtl number (describing the diffusive fluid properties)σ = 6.4 are applied. The rotation rate, given by the convective Rossby number Ro (ratio of buoyancy and Coriolis force), takes values in the range 0.045 ≤ Ro ≥ ∞, i.e. between rotation-dominated flow and zero rotation. Generally, rotation attenuates the intensity of the turbulence and promotes the formation of slender vertical tube-like vortices rather than the global circulation cell observed without rotation. Above Ro ≈ 3 there is hardly any effect of the rotation on the flow. The root-mean-square (r.m.s.) values of vertical velocity and vertical vorticity show an increase when Ro is lowered below Ro ≈ 3, which may be an indication of the activation of the Ekman pumping mechanism in the boundary layers at the bottom and top plates. The r.m.s. fluctuations of horizontal and vertical velocity, in both experiment and simulation, decrease with decreasing Ro and show an approximate power-law behaviour of the shape Ro0.2 in the range 0.1 ≤ Ro ≥ 2. In the same Ro range the temperature r.m.s. fluctuations show an opposite trend, with an approximate negative power-law exponent Ro0.32. In this Rossby number range the r.m.s. vorticity has hardly any dependence on Ro, apart from an increase close to the plates for Ro approaching 0.1. Below Ro ≈ 0.1 there is strong damping of turbulence by rotation, as the r.m.s. velocities and vorticities as well as the turbulent heat transfer are strongly diminished. The active Ekman boundary layers near the bottom and top plates cause a bias towards cyclonic vorticity in the flow, as is shown with probability density functions of vorticity. Rotation induces a correlation between vertical vorticity and vertical velocity close to the top and bottom plates: near the top plate downward velocity is correlated with positive/cyclonic vorticity and vice versa (close to the bottom plate upward velocity is correlated with positive vorticity), pointing to the vortical plumes. In contrast with the well-mixed mean isothermal bulk of non-rotating convection, rotation causes a mean bulk temperature gradient. The viscous boundary layers scale as the theoretical Ekman and Stewartson layers with rotation, while the thermal boundary layer is unaffected by rotation. Rotation enhances differences in local anisotropy, quantified using the invariants of the anisotropy tensor: under rotation there is strong turbulence anisotropy in the centre, while near the plates a near-isotropic state is found. © 2010 Cambridge University Press.