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Title: Weakly nonlinear Rayleigh-Taylor instability of a finite-thickness fluid layer

A weakly nonlinear (WN) model has been developed for the Rayleigh-Taylor instability of a finite-thickness incompressible fluid layer (slab). We derive the coupling evolution equations for perturbations on the (upper) “linearly stable” and (lower) “linearly unstable” interfaces of the slab. Expressions of temporal evolutions of the amplitudes of the perturbation first three harmonics on the upper and lower interfaces are obtained. The classical feedthrough (interface coupling) solution obtained by Taylor [Proc. R. Soc. London A 201, 192 (1950)] is readily recovered by the first-order results. Our third-order model can depict the WN perturbation growth and the saturation of linear (exponential) growth of the perturbation fundamental mode on both interfaces. The dependence of the WN perturbation growth and the slab distortion on the normalized layer thickness (kd) is analytically investigated via the third-order solutions. Comparison is made with Jacobs-Catton's formula [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988)] of the position of the “linearly unstable” interface. Using a reduced formula, the saturation amplitude of linear growth of the perturbation fundamental mode is studied. It is found that the finite-thickness effects play a dominant role in the WN evolution of the slab, especially when kd < 1. Thus, it shouldmore » be included in applications where the interface coupling effects are important, such as inertial confinement fusion implosions and supernova explosions.« less
Authors:
; ; ;  [1] ;  [2] ;  [3] ; ;  [1]
  1. Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)
  2. (China)
  3. Graduate School, China Academy of Engineering Physics, Beijing 100088 (China)
Publication Date:
OSTI Identifier:
22407918
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DISTURBANCES; EXPLOSIONS; FLUIDS; HARMONICS; IMPLOSIONS; INERTIAL CONFINEMENT; LAYERS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; RAYLEIGH-TAYLOR INSTABILITY; SUPERNOVAE; THERMONUCLEAR REACTIONS; THICKNESS; TIME DEPENDENCE