The Stability of Flows of Two Different Fluids which are Separated by a Thin Elastic Plate
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The stability of flows of two different fluids which are separated by a thin elastic plate is studied on the basis of hydrodynamical stability with respect to small disturbances. The governing equations are derived assuming that both fluids are inviscid and incompressible, and compressive or tensile in-plane forces act on the elastic plate. The growth rate as a function of the wave number, the critical wave number and the critical in-plane force are found with the aid of an eigen relation. For long waves the stability of the system depends only on the density defference of both fluids and does not depend on the properties of the elastic plate at all. In the case in which the lower fluid is heavier than the upper one, instability does not arise, unless magnitude of compressive in-plane force exceeds the critical value.
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