Nonlinear electrohydrodynamic Kelvin-Helmholtz instability: effect of a normal field producing surface charges

The electrohydrodynamic stability of a horizontal interface separating two dielectric streaming fluids stressed by a normal electric field is studied. The interface is assumed to support surface charges. The method of multiple scale perturbations is used in order to obtain uniformly valid expansions. Two nonlinear Schrodinger equations describing the perturbed system are obtained. The electrohydrodynamic cutoff wavenumber separating stable and unstable disturbances is calculated. It is found that both streaming and electric field play a dual role on the stability criterion. It is possible that the destabilising effect of streaming can be supressed by the stabilizing effect of the electric field and vice versa. Electrohydrodynamic solitary waves are also discussed.