Electrohydrodynamic solitons in Kelvin-Helmholtz flow: the case of a normal field in the absence of surface charges

Nonlinear electrohydrodynamic Kelvin—Helmholtz instability conditions are investigated. A charge-free surface separating two semi-infinite dielectric streaming fluids influenced by a normal electric field is subjected to nonlinear deformations. The method of multiple-scale perturbations is used in order to obtain two nonlinear Schrödinger (NLS) equations describing the behavior of the disturbed system. The stability and instability conditions of the perturbed system are discussed analytically. One of the two NLS equations is used to obtain the electrohydrodynamic (EHD) nonlinear cutoff wave number separating stable and unstable disturbances while the other equation is used to describe analytically the necessary condition for stability and instability for the system. For unstable cases, the solution starting with a solitary wave degenerates into a finite number of EHD solitons.