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Numerical studies of incompressible Richtmyer-Meshkov instability in a stratified fluid


Pham, Thu (1991) Numerical studies of incompressible Richtmyer-Meshkov instability in a stratified fluid. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ryrb-cg53.


Theory and calculations are presented for the evolution of Richtmyer-Meshkov instability in continuously stratified fluid layers. The initial acceleration and subsequent instability of the fluid layer are induced by means of an impulsive pressure distribution. It is shown that such an initial condition is an adequate approximation of the effect of a weak shock impinging on a stratified layer of fluid. We then calculate the subsequent dynamics of the fluid layer numerically using the incompressible equations of motion.

Both initial conditions having single scale perturbations and multiple scale random perturbations are considered. It is found that the growth rates for Richtmyer-Meshkov instability of stratified fluid layers are substantially lower than those predicted by Richtmyer for a sharp fluid interface with an equivalent jump in density. The initial behavior is linear over a time equivalent to the traversal of several layer thicknesses. It is observed that the nonlinear development of the instability results in the formation of plumes of penetrating fluid. Late in the process, the initial momentum deposited by the shock is primarily used in the internal mixing of the layer rather than in the overall growth of the stratified layer.

At intermediate time, the existence of a weak scaling behavior in the width of the mixing layer of the instability is observed for the multiple scale random perturbations, but not for the single scale perturbations. The time variation of the layer thickness differs from the scaling hypothesized by Barenblatt even at low Atwood ratio, presumably because of the inhomogeneity and anisotropy due to the excitation of vortical plumes. The emergence of these plumes at the boundaries of the density layer is characterized by the elongation of the internal spikes which have weak interactions and grow proportionally to their intial perturbed amplitudes. It is conjectured that the formations of the plumes may correspond to weakly interacting single scale modes.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Meiron, Daniel I. (advisor)
  • Saffman, Philip G. (co-advisor)
Thesis Committee:
  • Meiron, Daniel I. (chair)
  • Cohen, Donald S.
  • Leal, L. Gary
  • Saffman, Philip G.
Defense Date:17 October 1990
Record Number:CaltechETD:etd-07122007-143228
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2864
Deposited By: Imported from ETD-db
Deposited On:02 Aug 2007
Last Modified:19 Apr 2021 22:40

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