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

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 Eturbulent as function of the surface tension T⁽ˢ⁾. We propose new experiments, physical and/or numerical, to test our predictions.