NONLINEAR ELECTROHYDRODYNAMIC KELVIN-HELMHOLTZ INSTABILITY UNDER THE INFLUENCE OF AN OBLIQUE ELECTRIC-FIELD

The electrohydrodynamic stability of a horizontal interface separating two dielectric streaming fluids stressed by an oblique electric field is studied. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable and unstable deformations. Two nonlinear Schrodinger equations are obtained, one of which leads to the determination of the cutoff wavenumber. The other Schrodinger equation is used to analyze the stability of the system. These equations are derived when the difference between the velocities of the two fluids is less than or equal to the critical velocity. It is shown that, for subcritical values of the velocity difference, the wave train of constant amplitude is unstable against modulations whereas for the supercritical values the instability is governed by a nonlinear Klein-Gordon equation. From the latter equation, the various stability criteria are obtained.