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Initial perturbation dependence on Richtmyer–Meshkov instability with reshock

Published online by Cambridge University Press:  21 July 2025

Yumeng Zhang ,
Yong Zhao ,
Zhangbo Zhou Open the ORCID record for Zhangbo Zhou [Opens in a new window] ,
Juchun Ding Open the ORCID record for Juchun Ding [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yumeng Zhang
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Yong Zhao
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Zhangbo Zhou
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
Juchun Ding*
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China Laoshan Laboratory, Qingdao 266237, PR China
Xisheng Luo*
Affiliation:
State Key Laboratory of High Temperature Gas Dynamics, School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
*
Corresponding authors: Xisheng Luo, xluo@ustc.edu.cn; Juchun Ding, djc@ustc.edu.cn
Corresponding authors: Xisheng Luo, xluo@ustc.edu.cn; Juchun Ding, djc@ustc.edu.cn
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Abstract

The Richtmyer–Meshkov instability at gas interfaces with controllable initial perturbation spectra under reshock conditions is investigated both experimentally and theoretically. A soap-film method is adopted to generate well-defined single-, dual- and triple-mode air/SF$_6$ interfaces. By inserting an acrylic block into the test section, a reflected shock with controllable reshock timing is created. The results reveal a complex relationship between the post-reshock perturbation growth rate and the pre-reshock interface morphology. For single-mode interfaces, the post-reshock growth rate exhibits a strong dependence on pre-reshock conditions. In contrast, for multi-mode interfaces, this dependence weakens significantly due to mode-coupling effects. It is found that, following reshock, each fundamental mode develops independently and later is significantly influenced by mode-coupling effects. Based on this finding, we propose an empirical model that matches the initial linear growth rate and the asymptotic growth rate, accurately predicting the evolution of fundamental modes from early to late stages across all three configurations. Furthermore, a theoretical formula is derived, linking the empirical coefficient in the model of Charakhch’An (2020 J. Appl. Mech. Tech. Phys. vol. 41, no. 1, pp. 23–31) to the initial perturbation. This provides a unified framework to explain the varying dependence of post-reshock growth rates on pre-reshock morphology observed in previous experiments.

JFM classification

Compressible Flows: Shock waves Instability: Shear-flow instability

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Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A44
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© The Author(s), 2025. Published by Cambridge University Press

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