Development of the Rayleigh–Taylor instability due to interaction of a diffusion mixing layer of two gases with compression waves

Abstract

A mathematical model of mechanics of a two-velocity and two-temperature mixture of gases is developed. Based on this model, the evolution of the mixing layer of two gases of different densities, which are accelerated by a compression wave, is considered by methods of numerical simulation. A solution of an initial-boundary problem is obtained in a one-dimensional approximation. This solution describes the formation of a diffusion layer between the two gases. The problem of interaction of this layer with the compression wave, the heavy medium being accelerated by the light medium, is solved numerically. Problems of instability development in a sine-perturbed mixing layer accelerated by a compression wave are solved numerically in a two-dimensional unsteady formulation. The calculated width of the mixing region is in reasonable agreement with experimental data.