The αs and θs in Rayleigh–Taylor and Richtmyer–Meshkov instabilities

Cheng, Baolian; Glimm, James; Sharp, David H.

doi:10.1016/j.physd.2020.132356

Title: The αs and θs in Rayleigh–Taylor and Richtmyer–Meshkov instabilities

Journal Article · 21 January 2020 · Physica. D, Nonlinear Phenomena

DOI: https://doi.org/10.1016/j.physd.2020.132356 · OSTI ID:1770100

^[1]; Glimm, James ^[2];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Stony Brook Univ., NY (United States)

The alphas (α_b, α_s) and thetas (θ_b, θ_s) are the essential parameters describing the asymptotic growth behavior of the mixing layer driven by Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at the interface between the fluids. Extensive simulations and experiments have been conducted in the determination of these parameters. The results depend on numerical algorithms, resolutions, and the accuracy of experimental measurements. In this article, we present a unique relationship between the alphas and thetas by applying a simple buoyancy-drag mixing model. Our first main result is that, for the same fluids, these parameters are not independent because they are fundamentally connected by physics principles and they all are functions of the drag coefficients of the fluids. As a consequence, the alphas and thetas are intrinsically coupled. All are functions of any single one of these. Additionally, our second main result is that the RT bubble growth rate (α_b) is determined by the bubble competition process – a merger model – at the edge of the mixing layer. Together, these two main results determine all the alphas and thetas by strictly theoretical reasoning. Applications to both hydro and laser driven experiments at OMEGA are presented.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001; W-7405-ENG-36

OSTI ID:: 1770100

Report Number(s):: LA-UR--18-31801

Journal Information:: Physica. D, Nonlinear Phenomena, Journal Name: Physica. D, Nonlinear Phenomena Vol. 404; ISSN 0167-2789

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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