NONLINEAR EHD STABILITY OF THE INTERFACIAL WAVES OF 2 SUPERPOSED DIELECTRIC FLUIDS

The slow modulation of the interfacial capillary-gravity waves of two superposed dielectric fluids with uniform depths and solid horizontal boundaries, under the influence of a normal electric field and in the absence of surface charges at their interface, is investigated by usin g the multiple-time scales method. It is found that the complex amplit ude of quasi-monochromatic traveling waves can be described by a nonli near Schrodinger equation in a frame of reference moving with the grou p velocity. The stability characteristics of a uniform wave train are examined analytically and numerically on the basis of the nonlinear Sc hrodinger equation, and some limiting cases are recovered. Three cases appear, depending on whether the depth of the lower fluid is equal to , greater than, or less than the depth of the upper fluid. The effect of the normal electric field is determined for the three stability reg ions of the pure hydrodynamic case. It is found that the normal electr ic field has a destabilizing influence in the first stability region a nd a stabilizing effect in the second and third stability regions. Mor eover, one new unstable region or two new stable and unstable regions appear, all of which increase when the electric field increases. On th e other hand, the complex amplitude of quasi-monochromatic standing wa ves near the cutoff wavenumber is governed by a similar type of nonlin ear Schrodinger equation in which the roles of time and space are inte rchanged. This equation makes it possible to estimate the nonlinear ef fect on the cutoff wavenumber. (C) 1998 Academic Press.