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Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability

Published online by Cambridge University Press:  02 February 2021

Naifu Peng Open the ORCID record for Naifu Peng [Opens in a new window] ,
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window] ,
Jinxin Wu Open the ORCID record for Jinxin Wu [Opens in a new window]  and
Zuoli Xiao Open the ORCID record for Zuoli Xiao [Opens in a new window]
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
Jinxin Wu
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, 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
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Abstract

We elucidate the effect of the secondary baroclinic vorticity (SBV) on the Richtmyer–Meshkov instability (RMI) accelerated by a weak incident shock and develop a vortex-based model for spike and bubble growth rates. Two major mechanisms of the single-mode RMI, the primary baroclinic vorticity (PBV) and the pressure perturbation, are distinguished by simplified models with the vortex-surface field. We find that the effect of the pressure perturbation can be neglected in the present RMI, and the growth of the interface or vortex surface is first driven by the PBV. Subsequently, the SBV, generated by the misalignment between the density gradient across the interface and the pressure gradient produced by the PBV-induced velocity, leads to the nonlinear growth of the interface with the generation of spikes and bubbles. Inspired by this mechanism, we develop a predictive model of spike and bubble growth rates using the motion of viscous vortex rings. The circulation of the vortex ring is modelled with the SBV effect. This model is validated by five data sets of direct numerical simulations and experiments of the single-mode RMI with various initial conditions.

JFM classification

Vortex Flows: Vortex dynamics Compressible Flows: Shock waves
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A56
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© The Author(s), 2021. Published by Cambridge University Press

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References

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