The marker and cell method for high-speed computer was used to investigate the motion of a fluid whose free surface has been perturbed by an impulsive sinusoidal pressure. For gravity pointing out of the fluid, the resulting motion exhibits Rayleigh-Taylor instability, whose progress is followed from low amplitude to the asymptotic bubble and spike stage. The effects of small and large viscosity are contrasted. For gravity pointing into the fluid, the large-amplitude oscillatory motion exhibits a shift of resonance frequency and other effects of nonlinearity. Comparisons of results are presented wherever previous analytical or experimental work was available, and many new aspects of these types of flow are discussed. The calculations are based upon the full, time-dependent, nonlinear Navier-Stokes equations for an incompressible fluid.
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Harlow et al. (1966) studied this question.