ALBERT

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: Turbulence is ubiquitous in nature and engineering applications. Although Kolmogorov’s (C. R. Acad. Sci. URSS, vol. 30, 1941a, pp. 301–305;Dokl. Akad. Nauk URSS, vol. 30, 1941b, pp. 538–540) theory suggested a unique turbulent state for high Reynolds numbers, multiple states were reported for several flow problems, such as Rayleigh–Bénard convection and Taylor–Couette flows. In this paper, we report that multiple states also exist for turbulent plane Couette flow with spanwise rotation through direct numerical simulations at rotation number$Ro=0.2$and Reynolds number$Re_{w}=1300$based on the angular velocity in the spanwise direction and half of the wall velocity difference. With two different initial flow fields, our results show that the flow statistics, including the mean streamwise velocity and Reynolds stresses, show different profiles. These different flow statistics are closely related to the flow structures in the domain, where one state corresponds to two pairs of roll cells, and the other shows three pairs. The present result enriches the studies on multiple states in turbulence.

Description: In this study, the behaviours of subgrid-scale (SGS) turbulence are investigated with direct numerical simulations when an isotropic turbulence is brought to interact with imposed rapid waves. A partition of the velocity field is used to decompose the SGS stress into three parts, namely, the turbulent part $unicode[STIX]{x1D749}^{T}$, the wave-induced part $unicode[STIX]{x1D749}^{W}$ and the cross-interaction part $unicode[STIX]{x1D749}^{C}$. Under strong wave straining, $unicode[STIX]{x1D749}^{T}$ is found to follow the Kolmogorov scaling $unicode[STIX]{x1D6E5}_{c}^{2/3}$, where $unicode[STIX]{x1D6E5}_{c}$ is the filter width. Based on the linear Airy wave theory, $unicode[STIX]{x1D749}^{W}$ and the filtered strain-rate tensor due to the wave motion, $ilde{unicode[STIX]{x1D64E}}^{W}$, are found to have different phases, posing a difficulty in applying the usual eddy-viscosity model. On the other hand, $unicode[STIX]{x1D749}^{T}$ and the filtered strain-rate tensor due to the turbulent motion, $ilde{unicode[STIX]{x1D64E}}^{T}$, are only weakly wave-phase-dependent and could be well related by an eddy-viscosity model. The linear wave theory is also used to describe the vertical distributions of SGS statistics driven by the wave-induced motion. The predictions are in good agreement with the direct numerical simulation results. The budget equation for the turbulent SGS kinetic energy shows that the transport terms related to turbulence are important near the free surface and they compensate the imbalance between the energy flux and the SGS energy dissipation.

Description: We argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.

Description: In self-excited combustion systems, the application of open-loop forcing is known to be an effective strategy for controlling periodic thermoacoustic oscillations, but it is not known whether and under what conditions such a strategy would work on thermoacoustic oscillations that are not simply periodic. In this study, we experimentally examine the effect of periodic acoustic forcing on a prototypical thermoacoustic system consisting of a ducted laminar premixed flame oscillating quasiperiodically on an ergodic torus at two incommensurate natural frequencies, and. Compared with that of a classical period-1 system, complete synchronization of this system is found to occur via a more intricate route involving three sequential steps: As the forcing amplitude, , increases at a fixed forcing frequency, , the system transitions first (i)to ergodic quasiperiodicity; then (ii)to resonant quasiperiodicity as the weaker of the two natural modes, , synchronizes first, leading to partial synchronization; and finally (iii)to a limit cycle as the remaining natural mode, , also synchronizes, leading to complete synchronization. The minimum required for partial and complete synchronization decreases as approaches either or , resulting in two primary Arnold tongues. However, when forced at an amplitude above that required for complete synchronization, the system can transition out of and into or . The optimal control strategy is to apply off-resonance forcing at a frequency around the weaker natural mode and at an amplitude just sufficient to cause , because this produces the largest reduction in thermoacoustic amplitude via asynchronous quenching. Analysis of the Rayleigh index shows that this reduction is physically caused by a disruption of the positive coupling between the unsteady heat release rate of the flame and the and acoustic modes. If the forcing is applied near the stronger natural mode , however, resonant amplification can occur. We then phenomenologically model this thermoacoustic system as two reactively coupled van der Pol oscillators subjected to external sinusoidal forcing, and find that many of its synchronization features-such as the three-step route to , the double Arnold tongues, asynchronous quenching and resonant amplification-can be qualitatively reproduced. This shows that these features are not limited to our particular system, but are universal features of forced self-excited oscillators. This study extends the applicability of open-loop control from classical period-1 systems with just a single time scale to ergodic quasiperiodic systems with two incommensurate time scales. © 2019 The Author(s).

Description: 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 -5/3 scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The -5/3 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. © 2019 Cambridge University Press.

Description: Kinetic energy transfer in compressible isotropic turbulence is studied using numerical simulations with solenoidal forcing at turbulent Mach numbers ranging from 0.4 to 1.0 and at a Taylor Reynolds number of approximately 250. The pressure dilatation plays an important role in the local conversion between kinetic energy and internal energy, but its net contribution to the average kinetic energy transfer is negligibly small, due to the cancellation between compression and expansion work. The right tail of probability density function (PDF) of the subgrid-scale (SGS) flux of kinetic energy is found to be longer at higher turbulent Mach numbers. With an increase of the turbulent Mach number, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux. Average of SGS flux conditioned on the filtered velocity divergence is studied by numerical analysis and a heuristic model. The conditional average of SGS flux is shown to be proportional to the square of filtered velocity divergence in strong compression regions for turbulent Mach numbers from 0.6 to 1.0. Moreover, the antiparallel alignment between the large-scale strain and the SGS stress is observed in strong compression regions. The inter-scale transfer of solenoidal and compressible components of kinetic energy is investigated by Helmholtz decomposition. The SGS flux of solenoidal kinetic energy is insensitive to the change of turbulent Mach number, while the SGS flux of compressible kinetic energy increases drastically as the turbulent Mach number becomes larger. The compressible mode persistently absorbs energy from the solenoidal mode through nonlinear advection. The kinetic energy of the compressible mode is transferred from large scales to small scales through the compressible SGS flux, and is dissipated by viscosity at small scales. © 2018 Cambridge University Press.

Description: Based on recent numerical simulations and field experiments, the mechanism behind wake meandering is increasingly accepted to be through the amplification of upstream disturbances owing to the convectively unstable nature of the flow. In this paper, we deduce a low-order phenomenological model for the far-wake region, which is based on a modified form of the complex Ginzburg-Landau (CGL) equation for flows that are in the amplifier regime, i.e. are only convectively unstable. The model reproduces the main qualitative features of wake meandering: (i) its origin via amplification of upstream structures, (ii) dependence of oscillation frequency on the upstream disturbance amplitude (higher amplitudes lead to lower frequencies), (iii) shift towards lower frequencies as the wake flow evolves in the streamwise direction and, to an extent, (iv) the transfer of energy from very low frequencies towards relatively higher frequencies. Additionally, the model also predicts the increase in the meandering amplitude and an advancement in its onset with increasing thrust coefficient. To our knowledge, this is the first low-order dynamical system in the literature that models wake meandering. The model coefficients are obtained from the mean flow local stability results that we show correctly account for the changing operating conditions and thus pave way for the prediction of wake meandering features. Its low order makes it suitable to use inside an energy farm design model, where it can help to mitigate the adverse effects of wake meandering. © The Author(s) 2019Â This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (.

Description: In an earlier paper (Wan et al., J. Fluid Mech., vol. 697, 2012, pp. 296–315), the authors showed that a similarity solution for anisotropic incompressible three-dimensional magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field B^0, exists if the ratio of parallel to perpendicular (with respect to B^0 similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor–Kármán-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, mean field strength, and cross-helicity, on the nature of similarity decay is discussed.