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

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

We perform direct numerical simulations (DNS) of the hyperviscous Navier–Stokes equations in a periodic box. We consider values of the hyperviscosity index h=1, 2, 8, and vary the hyperviscosity to obtain the largest range of lengthscale ratios possible for well-resolved pseudo-spectral DNS. It is found that the spectral bump, or bottleneck, in the energy spectrum observed at the start of the dissipation range becomes more pronounced as the hyperviscosity index is increased. The calculated energy spectra are used to develop an empirical model for the dissipation range which accurately represents the bottleneck. This model is used to predict the approach of the turbulent kinetic energy k to its asymptotic value, k∞, as the hyperviscosity tends to zero.

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Direct numerical simulation of homogeneous turbulence with hyperviscosity

The Euler similarity criteria for laboratory experiments and time-dependent mixing transition are important concepts introduced recently for application to prediction and analysis of astrophysical phenomena. However, Euler scaling by itself provides no information on the distinctive spectral range of high Reynolds number turbulent flows found in astrophysics situations. On the other hand, time-dependent mixing transition gives no indication on whether a flow that just passed the mixing transition is sufficient to capture all of the significant dynamics of the complete astrophysical spectral range. In this paper, a new approach, based on additional insight gained from review of Navier-Stokes turbulence theory, is developed. It allows for revelations about the distinctive spectral scale dynamics associated with high Reynolds number astrophysical flows. From this perspective, the energy-containing range of the turbulent flow measured in a laboratory setting must not be unintentionally contaminated in such a ...

Unification and extension of the similarity scaling criteria and mixing transition for studying astrophysics using high energy density laboratory experiments or numerical simulations

Renormalization group theory for fluid and plasma turbulence

The fundamental aspects of isotropic turbulence are reviewed in reviewed in order to gain a betterinsight into the physical processes of turbulence. After first reviewing the Kolmogorov energyspectrum and the energy cascade, the Kolmogorov hypothesis of local isotropy is discussed in depth.Then, the detailed physical processes involving energy transfer and interacting scales in isotropicturbulence, including triad interactions, are reviewed. The inertial range and self-similarity are alsodiscussed along with tile response of the small scales to large-scale anisotropy and the final stagesof the decay process. Results from direct and large-eddy simulations of isotropic turbulenceincluding a discussion of subgrig scale modeling--are then discussed in detail to illustrate these points. The article closes with a review of self-preservation in isotropic turbulence and a discussion of the prospects for future research. It contains 155 references.

Ye Zhou

Papers

Advances in the Fundamental Aspects of Turbulence: Energy Transfer, Interacting Scales, and Self-Preservation in Isotropic Decay