Rayleigh-Taylor and Richtmyer-Meshkov instabilities in multilayer fluids with surface tension.

Abstract

Surface tension modifies the evolution of the Rayleigh-Taylor and the Richtmyer-Meshkov instabilities in fluids undergoing a constant acceleration or a shock, respectively. We analyze the general case of N fluids with arbitrary densities and surface tensions and derive the eigenvalue equation determining the growth rate of the perturbations. For N=2 we recover the classical case of two semi-infinite fluids and extend it to the case of two finite-thickness fluids between fixed boundaries. The N=3 case is studied in detail; we find universal modes that are independent of the thickness of the intermediate fluid, and we find how surface tension modifies Taylor's modes for a single fluid with free boundaries. We also analyze in detail recent and future two- or three-fluid experiments. Representing a shock as an impulsive acceleration we find that post-shock oscillations have frequencies and amplitudes that depend on the wave number k, leading to a nontrivial evolution for the spectrum of perturbations. Finally, we study turbulence at the interface between two fluids with surface tension and present specific predictions for the turbulent energy ${\mathit{E}}_{\mathrm{turbulent}}$ as function of the surface tension ${\mathit{T}}^{(\mathit{s})}$. We propose new experiments, physical and/or numerical, to test our predictions.