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Modelling the evolution of Richtmyer–Meshkov mixing width during shock compression phases

Published online by Cambridge University Press:  15 May 2025

Yu Song ,
You-sheng Zhang Open the ORCID record for You-sheng Zhang [Opens in a new window]  and
Yu-hui Wang
Yu Song
Affiliation:
College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, PR China
You-sheng Zhang*
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China Center for Applied Physics and Technology, HEDPS, and College of Engineering, Peking University, Beijing 100871, PR China National Key Laboratory of Computational Physics, Beijing 100088, PR China
Yu-hui Wang
Affiliation:
College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, Beijing 100029, PR China
*
Corresponding authors: You-sheng Zhang, qwwzys@163.com; Yu-hui Wang, aowuki@163.com
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Abstract

Turbulent mixing driven by the reshocked Richtmyer–Meshkov (RM) instability plays a critical role in numerous natural phenomena and engineering applications. As the most fundamental physical quantity characterizing the mixing process, the mixing width transitions from linear to power-law growth following the initial shock. However, there is a notable absence of quantitative models for predicting the pronounced compression of initial interface perturbations or mixing regions at the moment of shock impact. This gap has restricted the development of integrated algebraic models to only the pre- and post-shock evolution stages. To address this limitation, the present study develops a predictive model for the compression of the mixing width induced by shocks. Based on the general principle of growth rate decomposition proposed by Li et al. (Phy. Rev. E, vol. 103, issue 5, 2021, 053109), two distinct types of shock-induced compression processes are identified, differentiated by the dominant mechanism governing their evolution: light–heavy and heavy–light shock-induced compression. For light–heavy interactions, both stretching (compression) and penetration mechanisms are influential, whereas heavy–light interactions are governed predominantly by the stretching (compression) mechanism. To characterize these mechanisms, the average velocity difference between the extremities of the mixing zone is quantified, and a physical model of RM mixing is utilized. A quantitative theoretical model is subsequently formulated through the independent algebraic modelling of these two mechanisms. The proposed model demonstrates excellent agreement with numerical simulations of reshocked RM mixing, offering valuable insights for the development of integrated algebraic models for mixing width evolution.

JFM classification

Compressible Flows: Shock waves Interfacial Flows (free surface): Fingering instability Mixing: Turbulent mixing

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , A39
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© The Author(s), 2025. Published by Cambridge University Press

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