Rayleigh–Taylor and Richtmyer–Meshkov instabilities for fluids with a finite density ratio

Abstract

We report non-linear solutions describing the large-scale coherent motion of bubbles and spikes in the Rayleigh–Taylor and Richtmyer–Meshkov instabilities for fluids with a finite density ratio in general three-dimensional case. The non-local character of the interface dynamics is taken into account with a multiple harmonic analysis. The theory yields a non-trivial dependence of the bubble velocity and curvature on the density ratio and reveals an important qualitative distinction between the dynamics of Rayleigh–Taylor and Richtmyer–Meshkov bubbles.