NONLINEAR INSTABILITY OF CAPILLARY-GRAVITY WAVES IN THE PRESENCE OF AN AIR STREAM

Using multiple time scale method, the weakly non-linear waves on the interface between a liquid layer and a subsonic gas flowing parallel to the undisturbed interface are investigated. The evolution of the complex amplitude of a quasi-monochromatic progressive wave is shown to be governed by a nonlinear Schrodinger equation(NLSE). The wave train of constant amplitude is unstable against modulation. On the otherhand, the amplitude of the standing wave near the cut-off is governed by a NLSE in which the roles of time and space variables are interchanged. This equation makes it possible to determine the non-linear cut-off wave number.