Abstract
The nonlinear stability of a liquid film adjacent to a supersonic gas stream is investigated. The gas is assumed to exert a mean shear stress at the liquid/gas interface which in turn establishes a linear mean velocity profile in the liquid. The analysis takes into account the pressure perturbation exerted by the gas on the liquid assuming the disturbed gas motion to be inviscid and the mean gas velocity profile to be uniform. The problem is formulated within the long wave approximation, and solutions are obtained for finite amplitude waves by using the method of multiple scales. The results predict the existence of finite amplitude periodic waves, in qualitative agreement with recent experimental observations.
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