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Chin. Phys. B, 2021, Vol. 30(4): 044702    DOI: 10.1088/1674-1056/abcf44

A simplified approximate analytical model for Rayleigh-Taylor instability in elastic-plastic solid and viscous fluid with thicknesses

Xi Wang(王曦)1, Xiao-Mian Hu(胡晓棉)1, Sheng-Tao Wang(王升涛)1, and Hao Pan(潘昊)1,2,†
1 Institute of Applied Physics and Computational Mathematics, Beijing 100094, China; 2 Center for Applied Physics and Technology, Peking University, Beijing 100871, China
Abstract  A simplified theoretical model for the linear Rayleigh-Taylor instability of finite thickness elastic-plastic solid constantly accelerated by finite thickness viscous fluid is performed. With the irrotational assumption, it is possible to consider viscosity, surface tension, elasticity or plasticity effects simultaneously. The model considers thicknesses at rigid wall boundary conditions with the velocity potentials, and deals with solid elastic-plastic transition and fluid viscosity based on the velocity continuity and force equilibrium at contact interface. The complete analytical expressions of the amplitude motion equation, the growth rate, and the instability boundary are obtained for arbitrary Atwood number, viscosity, thicknesses of solid and fluid. The thicknesses effects of two materials on the growth rate and the instability boundary are discussed.
Keywords:  Rayleigh-Taylor instability      viscosity      plasticity      thicknesses effects  
Received:  31 August 2020      Revised:  29 October 2020      Accepted manuscript online:  01 December 2020
PACS:  47.20.Ma (Interfacial instabilities (e.g., Rayleigh-Taylor))  
  66.20.-d (Viscosity of liquids; diffusive momentum transport)  
  46.35.+z (Viscoelasticity, plasticity, viscoplasticity)  
  68.55.jd (Thickness)  
Fund: Project supported by of the Science Challenge Project of China (Grant No. TZ2018001).
Corresponding Authors:  Corresponding author. E-mail:   

Cite this article: 

Xi Wang(王曦), Xiao-Mian Hu(胡晓棉), Sheng-Tao Wang(王升涛), and Hao Pan(潘昊) A simplified approximate analytical model for Rayleigh-Taylor instability in elastic-plastic solid and viscous fluid with thicknesses 2021 Chin. Phys. B 30 044702

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