On stability of parametric resonances of nonlinear surface waves propagating between two superposed electrified fluids

摘要

Resonances of interfacial waves in a nonlinear interfacial instability of two superposed electrified fluids stressed by a time-dependent electric field are studied. Two subharmonic resonances have been distinguished and investigated. Based on the method of multiple-scale expansion, for a small amplitude of periodic field, two parametric nonlinear Schrödinger equations are derived to describe the propagation of capillary waves on the fluid interface in the resonance cases. A classical nonlinear Schrödinger equation is derived in the nonresonant case. A temporal solution for a travelling wave is obtained analytically. The necessary and sufficient conditions for stability are obtained. It is found that the stability criteria are significantly affected by the amplitude of the temporal solution. Further the formula for the surface elevation is obtained in each case. Numerical calculations show that the constant electric field plays a dual role in the stability analysis. It is observed that the field frequency changes the mechanism due to the dual role of the electric fiel