A numerical study of Richtmyer–Meshkov instability in continuously stratified fluids

Abstract

Theory and calculations are presented for the evolution of Richtmyer–Meshkov instability in two-dimensional continuously stratified fluid layers. The initial acceleration and subsequent instability of the fluid layer are induced by means of an impulsive pressure distribution. The subsequent dynamics of the fluid layer are then calculated numerically using the incompressible equations of motion. Initial conditions representing 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. A frozen field approximation for the early-time dynamics of the instability is proposed, and shown to approximate the initial behavior of the layer 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 impulse is primarily used in the internal mixing of the layer rather than in the overall growth of the stratified layer. At intermediate times, some evidence for the existence of 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 derived using ideas of self-similarity due to Barenblatt [Non-Linear Dynamics and Turbulence, edited by G. I. Barenblatt, G. Ioos, and D. D. Joseph (Pitman, Boston, 1983), p. 48] even at low Atwood ratio, presumably because of the inhomogeneity and anisotropy due to the excitation of vortical plumes.