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Analytical model of nonlinear evolution of single-mode Rayleigh–Taylor instability in cylindrical geometry

Published online by Cambridge University Press:  06 August 2020

Zhiye Zhao
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China Institute of Applied Physics and Computational Mathematics, Beijing10094, PR China
Pei Wang
Institute of Applied Physics and Computational Mathematics, Beijing10094, PR China
Nansheng Liu
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China
Xiyun Lu*
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui230026, PR China
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We present an analytical model of nonlinear evolution of two-dimensional single-mode Rayleigh–Taylor instability (RTI) in cylindrical geometry at arbitrary Atwood number for the first time. Our model covers a full scenario of bubble evolution from the earlier exponential growth to the nonlinear regime with the bubbles growing in time as $\frac {1}{2}a_{b}t^2$ for cylindrical RTI, other than as $V_{b}t$ for planar RTI, where $a_{b}$ and $V_{b}$ are the bubble acceleration and velocity, respectively. It is found that from this model the saturating acceleration $a_{b}$ is formulated as a simplified function of the external acceleration, Atwood number and number of perturbation waves. This model's predictions are in good agreement with data from direct numerical simulations.

JFM Papers
© The Author(s), 2020. Published by Cambridge University Press

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