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

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.