The initial-value problem associated with the small-amplitude waves on the interface between two superposed viscous fluids is studied in the stable and in the unstable case (Rayleigh–Taylor instability). The results are illustrated with examples obtained by numerical and analytic inversion of the Laplace-transformed solution for the wave amplitude. The diffusion of vorticity from the free surface into the fluids is also shown.
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Andréa Prosperetti (1981) studied this question.
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