Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

http://amirs1987.persiangig.com/DNS%20and%20LES%20of%20decaying%20isotropic%20turbulence%20with%20and%20without%20frame%20rotation%20using%20lattice%20Boltzmann%20method.pdf

DNS and LES of decaying isotropic turbulence with and without frame rotation using lattice Boltzmann method

In diverse areas of science and technology, including inertial confinement fusion (ICF), astrophysics, geophysics, and engineering processes, turbulent mixing induced by hydrodynamic instabilities is of scientific interest as well as practical significance. Because of the fundamental roles they often play in ICF and other applications, three classes of hydrodynamic instability-induced turbulent flows—those arising from the Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities—have attracted much attention. ICF implosions, supernova explosions, and other applications illustrate that these phases of instability growth do not occur in isolation, but instead are connected so that growth in one phase feeds through to initiate growth in a later phase. Essentially, a description of these flows must encompass both the temporal and spatial evolution of the flows from their inception. Hydrodynamic instability will usually start from potentially infinitesimal spatial perturbations, will eventually transition to a turbulent flow, and then will reach a final state of a true multiscale problem. Indeed, this change in the spatial scales can be vast, with hydrodynamic instability evolving from just a few microns to thousands of kilometers in geophysical or astrophysical problems. These instabilities will evolve through different stages before transitioning to turbulence, experiencing linear, weakly, and highly nonlinear states. The challenges confronted by researchers are enormous. The inherent difficulties include characterizing the initial conditions of such flows and accurately predicting the transitional flows. Of course, fully developed turbulence, a focus of many studies because of its major impact on the mixing process, is a notoriously difficult problem in its own right. In this pedagogical review, we will survey challenges and progress, and also discuss outstanding issues and future directions.

Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities

Turbulence theories and statistical closure approaches

A second order turbulence model for compressible one-dimensional mixing flows is used to calculate the experiment performed by Poggi et al. [18] where mixtures were induced by Richtmyer–Meshkov instability. This R ij −ϵ model is supplemented by equations for the turbulent mass flux and the density variance . In Poggi's experiments, beside usual mixing length measurement, the laser Doppler anemometry technique gave temporal evolution of the turbulent kinetic energy. The present study shows that a statistical turbulence model can reproduce these strongly differential experimental data. Indeed, evolution of the radial component of the Reynolds stress tensor as well as that of the anisotropy are satisfactorily calculated. Nevertheless, discrepancies are observed at the very beginning of the process where the turbulence is probably not fully developed. The three-layer Meshkov experiment [16] is also successfully interpreted with the same procedure. In addition, the dependence of the evolution of turbulent quan...

A second-order turbulence model for gaseous mixtures induced by Richtmyer—Meshkov instability

The relaxation in time of an arbitrary isotropic turbulent state to a state of statistical equilibrium is identified as a transition to a state which is invariant under a symmetry group. We deduce the allowed self-similar forms and time-decay laws for equilibrium states by applying Lie-group methods (a) to a family of scaling symmetries, for the limit of high Reynolds number, as well as (b) to a unique scaling symmetry, for nonzero viscosity or nonzero hyperviscosity. This explains why a diverse collection of turbulence models, going back half a century, arrived at the same time-decay laws, either through derivations embedded in the mechanics of a particular model, or through numerical computation. Because the models treat the same dynamical variables having the same physical dimensions, they are subject to the same scaling invariances and hence to the same time-decay laws, independent of the eccentricities of their different formulations. We show in turn, by physical argument, by an explicitly solvable a...

Symmetries and the approach to statistical equilibrium in isotropic turbulence

Because a spectral model describes distributions of turbulent energy and stress in wave‐number space or, equivalently, in terms of a distribution of length scales, it can account for the variation of evolution rates with length scale. A spectral turbulence model adapted from a model introduced by Besnard, Rauenzahn, Harlow, and Zemach is applied here to homogeneous turbulent flows driven by constant mean‐flow gradients and to free decay of such flows. To the extent permitted by the experimental data, initial turbulent spectra are inferred, and their evolutions in time are computed to obtain detailed quantitative predictions of the spectra, relaxation times to self‐similarity, self‐similar spectrum shapes, growth rates, and power‐law time dependence of turbulent energies and dominant‐eddy sizes, and integral data, such as the components of the Reynolds stress tensor and the Reynolds stress anisotropy tensor. The match to experimental data, within the limits of experimental uncertainties, is good. Some qual...

A spectral model applied to homogeneous turbulence

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Symmetries and the approach to statistical equilibrium in isotropic turbulence

A spectral model applied to homogeneous turbulence