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Single-mode Rayleigh–Taylor instability in time-dependent rarefaction-driven flows

Published online by Cambridge University Press:  30 July 2025

Yue Li ,
Xing Gao ,
Xu Guo Open the ORCID record for Xu Guo [Opens in a new window] ,
Zhigang Zhai Open the ORCID record for Zhigang Zhai [Opens in a new window]  and
Xisheng Luo Open the ORCID record for Xisheng Luo [Opens in a new window]
Yue Li
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xing Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xu Guo*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Zhigang Zhai*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xisheng Luo
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China State Key Laboratory of High-Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
*
Corresponding authors: Zhigang Zhai, sanjing@ustc.edu.cn; Xu Guo, clguoxu@ustc.edu.cn
Corresponding authors: Zhigang Zhai, sanjing@ustc.edu.cn; Xu Guo, clguoxu@ustc.edu.cn
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Abstract

Rayleigh–Taylor instability (RTI) caused by rarefaction waves not only features variable acceleration but also incorporates time-dependent density, which introduces great challenges in predicting the finger growth behaviours. In this work, we propose a model for predicting the single-mode finger behaviours by extending the Layzer potential-flow framework to account for time-dependent acceleration and density. Relative to the previous models, the present model can evaluate the effect of time-dependent density on finger growth, and can describe the growth behaviours of both bubbles and spikes in rarefaction-driven RTI flows. In addition, the time-dependent curvature of the finger tip as it evolves from its initial value to the quasi-steady value is quantified. To validate the model, rarefaction-tube experiments and numerical simulations are conducted across a wide range of initial conditions. The results show that the present model can accurately capture the amplitude growth and curvature evolution of bubbles and spikes across various density ratios. Moreover, both the present model and experiments demonstrate that the continuous density reduction in rarefaction-driven flows causes larger asymptotic velocities of bubbles and spikes, leading to higher Froude numbers relative to those under constant or time-dependent acceleration.

JFM classification

Compressible Flows: Gas dynamics

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Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A27
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© The Author(s), 2025. Published by Cambridge University Press

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