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In this paper the small-amplitude motion of multiple superposed viscousfluids is studied as a linearized initial-value problem. The analysis resultsin a closed set of equations for the Laplace transformed amplitudes of theinterfaces that can be inverted numerically. The derived equations also containthe general normal mode equations, which can be used to determine theasymptotic growth-rates of the systems directly. After derivation, theequations are used to study two different problems involving three fluid layer.The first problem is the effect of initial phase difference on the developmentof a Rayleigh-Taylor instability and the second is the damping effect of athin, highly viscous, surface layer.

Linear motion of multiple superposed viscous fluids