Rayleigh–Taylor and Richtmyer–Meshkov instabilities in finite-thickness fluid layers

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Abstract
Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities are considered in a fluid layer of thickness t having perturbations of arbitrary wave number k at either one or both interfaces. The evolution of the perturbation amplitudes η1,2(τ), τ =time, is given analytically in terms of a coupling angle θ which measures the strength of the coupling between interfaces 1 and 2. A new type of freeze‐out in shocked layers is reported according to which, the proximity of the two interfaces can, under proper conditions, lead to the complete freeze‐out of one, but not both, perturbations. For example, to freeze the first interface one needs η1(0)/η2(0)= sin θ. Freeze‐out cannot be achieved in the RT case; instead, one can kill one of the modes. For example, setting η1(0)/η2(0)= tan(θ/2) will kill the exponentially growing mode, leaving only the oscillatory mode at both interfaces.