Nonlinear electrohydrodynamic Kelvin-Helmholtz instability conditions of a cylindrical interface under the influence of an axial electric field

The electrohydrodynamic Kelvin-Helmholtz instability of a cylindrical interface separating two dielectric streaming fluids, stressed by an axial electric field in the absence of surface charges on the interface, is studied. We have used the method of multiple scales. Two nonlinear Schrodinger equations are obtained, one of them leads to the determination of the cut-off wavenumber and the cut-off electric field. The other Schrodinger equation is used to analyze the stability of the system. The stability conditions of the perturbed system is discussed analytically and numerically At the critical point, a generalized formulation of the evolution equation is developed, which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation.