On Rayleigh-Taylor and Richtmyer-Meshkov Dynamics With Inverse-Quadratic Power-Law Acceleration

D. L. Hill,S. I. Abarzhi

doi:10.3389/fams.2021.735526

Abstract

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities occur in many situations in Nature and technology from astrophysical to atomic scales, including stellar evolution, oceanic flows, plasma fusion, and scramjets. While RT and RM instabilities are sister phenomena, a link of RT-to-RM dynamics requires better understanding. This work focuses on the long-standing problem of RTI/RMI induced by accelerations, which vary as inverse-quadratic power-laws in time, and on RT/RM flows, which are three-dimensional, spatially extended and periodic in the plane normal to the acceleration direction. We apply group theory to obtain solutions for the early-time linear and late-time nonlinear dynamics of RT/RM coherent structure of bubbles and spikes, and investigate the dependence of the solutions on the acceleration’s parameters and initial conditions. We find that the dynamics is of RT type for strong accelerations and is of RM type for weak accelerations, and identify the effects of the acceleration’s strength and the fluid density ratio on RT-to-RM transition. While for given problem parameters the early-time dynamics is uniquely defined, the solutions for the late-time dynamics form a continuous family parameterised by the interfacial shear and include special solutions for RT/RM bubbles/spikes. Our theory achieves good agreement with available observations. We elaborate benchmarks that can be used in future research and in design of experiments and simulations, and that can serve for better understanding of RT/RM relevant processes in Nature and technology.

Highlights

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities and RT/RM interfacial mixing are fluid dynamics phenomena controlling a broad range of processes in nature and technology, at celestial and at molecular scales, in high and in low energy density regimes [1,2,3,4,5,6]
We have studied RT/RM instabilities induced by an acceleration having an inverse-quadratic power-law time dependence, and considered a broad range of acceleration strengths and density ratios, for a three-dimensional spatially extended period flow with square symmetry in the plane normal to the acceleration
By applying the group theory approach, we have found solutions for the early-time linear and late-time nonlinear dynamics of RT/RM coherent structures of bubbles and spikes, and have thoroughly investigated the dependence of the solutions on the acceleration parameters and initial conditions

Summary

Introduction

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities and RT/RM interfacial mixing are fluid dynamics phenomena controlling a broad range of processes in nature and technology, at celestial and at molecular scales, in high and in low energy density regimes [1,2,3,4,5,6]. The case of constant acceleration is referred as classical RT instability (RTI), whereas the case of shock induced. RT-to-RM Bubbles and Spikes impulsive acceleration is referred as classical Richtmyer-Meshkov instability (RMI) [1,2,3,4, 6]. In the work we present the first detailed investigation of RTI/RMI induced by an acceleration being an inverse-quadratic power-law function of time in a three-dimensional flow. We apply group theory to find solutions for the early-time linear and the late-time nonlinear scale-dependent RT/RM dynamics, explore properties of RT-to-RM transition, compare with existing observations achieving good agreement, and elaborate theory benchmarks for future experiments and simulations

Methods

Results

Conclusion