New perspectives on turbulent mixing induced by Rayleigh-Taylor and Richtmyer-Meshkov instabilities*

Astronomy and Astrophysics – Astrophysics

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Turbulent hydrodynamic mixing induced by the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities occurs in settings as varied as exploding stars (supernovae), inertial confinement fusion (ICF) capsule implosions, and macroscopic flows on fluid dynamics facilities such as shock tubes. We have for the first time developed a quantitative description of turbulence from the onset to the asymptotic end-state. Our treatment, based on a combined approach of theory, direct numerical simulation (DNS), and subgrid-scale modeling, has broad generality. We will report three key areas in our progress. First, we have developed a robust, easy to apply criteria for the mixing transition in a time-dependent flow. This allows an assessment of whether flows, be they from supernova explosions or ICF experiments, should be turbulent or not. Note, the spatial and time scales in these diverse settings can differ by as much as 14-16 orders of magnitude, yet our theoretical framework still applies. The turbulent energy spectra appropriate for RT and RM flows are obtained, and are shown to be different. Second, we inspect the structure and energy transfer processes within the mixing layer using DNS, and illustrate for the first time the influences of unresolved scales on resolved quantities, such as the final mixing profiles. Finally, using these new physical insights, we have developed and validated a two-scale, dynamic mix model that can be applied to simulations of ICF experiments and astrophysics calculations alike. Our theoretical treatment of turbulence will be presented, and applications to several published experimental results will be described. *Work performed for the US DOE by UC LLNL under contract W-7405-Eng-48.

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