PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES |
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Weakly nonlinear multi-mode Bell–Plesset growth in cylindrical geometry |
Hong-Yu Guo(郭宏宇)1,2, †, Tao Cheng(程涛)1,2, and Ying-Jun Li(李英骏)1,2,, ‡ |
1 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, China 2 School of Science, China University of Mining and Technology, Beijing 100083, China |
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Abstract Bell–Plesset (BP) effect caused perturbation growth plays an important role in better understanding of characteristics of the convergence effect. Governing equations for multi-mode perturbation growth on a cylindrically convergent interface are derived. The second-order weakly nonlinear (WN) solutions for two-mode perturbations at the interface which is subject to uniformly radical motion are obtained. Our WN theory is consistent with the numerical result in terms of mode-coupling effect in converging Richtmyer–Meshkov instability. Nonlinear mode-coupling effects will cause irregular deformation of the convergent interface. The mode-coupling behavior in convergent geometry depends on the mode number, Atwood number A and convergence ratio Cr. The A = –1.0 at the interface results in larger perturbation growth than A = 1.0. The growth of generated perturbation modes from two similar modes at the initial stage are smaller than that from two dissimilar modes.
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Received: 26 April 2020
Revised: 07 June 2020
Accepted manuscript online: 12 June 2020
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Fund: the Fundamental Research Funds for the Central Universities, China (Grant No. 2019QS04), the National Natural Science Foundation of China (Grant No. 11574390), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDA 25051000). |
Corresponding Authors:
†Corresponding author. E-mail: ghy@cumtb.edu.cn ‡Corresponding author. E-mail: lyj@aphy.iphy.ac.cn
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Cite this article:
Hong-Yu Guo(郭宏宇), Tao Cheng(程涛), and Ying-Jun Li(李英骏) Weakly nonlinear multi-mode Bell–Plesset growth in cylindrical geometry 2020 Chin. Phys. B 29 115202
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