A Stability Analysis of Superposed Fluids

Abstract

An analysis is made of the stability of two fluid layers in the gravity field. The upper layer is incompressible, inviscid and of infinite extent. The lower layer is incompressible, viscous and bounded below by a rigid plane. Both fluids are moving in the same direction parallel to the interface. It is found that the controlling mechanism for instability is of the Rayleigh-Taylor type which is inherent in inviscid flows. The main effect of viscosity is to diminish the rate of growth of the disturbances while the presence of linear shear flow in the lower layer has a tendency to stabilize the system.

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