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Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability

Published online by Cambridge University Press:  31 August 2021

Naifu Peng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China Center for Applied Physics and Technology and HEDPS, Peking University, Beijing100871, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China Center for Applied Physics and Technology and HEDPS, Peking University, Beijing100871, PR China Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing100871, PR China
Zuoli Xiao
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing100871, PR China Center for Applied Physics and Technology and HEDPS, Peking University, Beijing100871, PR China Beijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing100871, PR China
*
Email address for correspondence: yyg@pku.edu.cn

Abstract

We investigate the effect of the secondary baroclinic vorticity (SBV) on the energy cascade in the mixing induced by the multi-mode Richtmyer–Meshkov instability (RMI). With the aid of vorticity-based simplified models and the vortex-surface field, we find that the effect of the SBV peaks at a critical time when the vortex reconnection widely occurs in the mixing zone. Before the critical time, spikes and bubbles evolve almost independently, and we demonstrate that the variation of the kinetic energy spectrum induced by the SBV has the $-1$ scaling law at intermediate wavenumbers using the model of vortex rings. This SBV effect causes the slope of the total energy spectrum at intermediate wavenumbers to evolve towards $-3/2$ at the critical time. Subsequently, the SBV effect diminishes and the energy spectrum decays to the $-5/3$ law. Inspired by the vortex dynamics, we develop a model for estimating the mixing width and validate the model using numerical simulations of the multi-mode RMI with various modes of initial perturbations. This model captures the nonlinear growth of the mixing width before the self-similar growth stage.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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