Instability of Three-Layer Viscous Stratified Flow

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Abstract
Instability of plane Couette flow of three superposed layers of fluids of different viscosity between two horizontal planes is investigated. It is found that there are two modes of disturbance dominated, respectively, by the two interfaces. The flow is found to be unstable in the zero-order approximation of wavenumber α for certain values of the depth and viscosity ratios. This is owing to a sort of resonance which prevails when a free wave at the lower interface forces a free wave at the upper interface. As is known from results previously obtained, the existence of a single surface of viscosity discontinuity will cause instability. The presence of an additional surface of discontinuity may or may not be stabilizing, depending upon the values of the depth and viscosity ratios at the additional interface.

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