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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 ,
Pei Wang ,
Nansheng Liu Open the ORCID record for Nansheng Liu [Opens in a new window]  and
Xiyun Lu Open the ORCID record for Xiyun Lu [Opens in a new window]
Zhiye Zhao
Affiliation:
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
Affiliation:
Institute of Applied Physics and Computational Mathematics, Beijing10094, PR China
Nansheng Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui230026, PR China
Xiyun Lu*
Affiliation:
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
*
†Email address for correspondence: xlu@ustc.edu.cn
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Abstract

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 classification

Convection: Buoyancy-driven instability Instability: Nonlinear instability

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , A24
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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