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Prediction of long-time single-mode Rayleigh–Taylor bubble evolution: a rotational flow model

Published online by Cambridge University Press:  19 November 2025

Changwen Liu ,
Hongzhi Wu-Wang ,
Yousheng Zhang Open the ORCID record for Yousheng Zhang [Opens in a new window]  and
Zuoli Xiao Open the ORCID record for Zuoli Xiao [Opens in a new window]
Changwen Liu
Affiliation:
HEDPS, Center for Applied Physics and Technology, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University , Beijing 100871, PR China
Hongzhi Wu-Wang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University , Beijing 100871, PR China
Yousheng Zhang*
Affiliation:
HEDPS, Center for Applied Physics and Technology, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China Institute of Applied Physics and Computational Mathematics, Beijing 100094, PR China National Key Laboratory of Computational Physics, Beijing 100088, PR China
Zuoli Xiao*
Affiliation:
HEDPS, Center for Applied Physics and Technology, School of Mechanics and Engineering Science, Peking University, Beijing 100871, PR China State Key Laboratory for Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University , Beijing 100871, PR China Nanchang Innovation Institute, Peking University, Nanchang 330008, PR China
*
Corresponding authors: Yousheng Zhang, qwwzys@163.com; Zuoli Xiao, z.xiao@pku.edu.cn
Corresponding authors: Yousheng Zhang, qwwzys@163.com; Zuoli Xiao, z.xiao@pku.edu.cn
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Abstract

The nonlinear growth of perturbations in hydrodynamic interfacial instabilities can be of particular importance in both scientific research (e.g. supernova explosion) and engineering applications (e.g. inertial confinement fusion). One of the most significant issues in these instabilities is the long-time nonlinear bubble evolution of a single-mode Rayleigh–Taylor instability (RTI), which remains as an unsolved and challenging problem since Taylor’s seminal work more than seven decades ago. Introduced in this paper is an analytical model for the long-time evolution of bubble velocity, curvature and vorticity, which is established by considering the vorticity accumulation around the bubble in a bilaterally rotational flow system under the classical planar potential-flow theory framework. The proposed theoretical model incorporates not only the classical linear, nonlinear and quasi-steady stages, but the late re-acceleration stage. Meanwhile, the new model can capture the phenomenon of secondary velocity saturation following the stage of bubble re-acceleration. The good agreement between the present model and numerical simulations for all density ratios and dimensions confirms that the accumulation in vorticity tends to break the early stage buoyancy-drag equilibrium mechanism and leads to the establishment of a new equilibrium in the late-stage RTI.

JFM classification

Instability: Nonlinear instability Interfacial Flows (free surface): Fingering instability

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JFM Papers
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Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A23
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© The Author(s), 2025. Published by Cambridge University Press

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