Parametric Third-Subharmonic Resonance in Nonlinear Electrohydrodynamic Rayleigh-Taylor Instability with Mass and Heat Transfer

Abstract

The nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer is investigated. The fluids are stressed by a periodic acceleration and a normal electric field. Based on the method of multiple scales, a parametric nonlinear Schrodinger equation with complex coefficients is derived in the third-subharmonic resonance case. A standard nonlinear Schrodinger equation with complex coefficients is obtained in the non-resonance case. A temporal solution is carried out for the parametric nonlinear Schrodinger equation. Necessary and sufficient conditions for stability are obtained. Numerical calculations show that the thickness of the fluid, the normal electric field, and the coefficient of mass and heat transfer have destabilizing effect. It is found that the external frequency plays a dual role in the stability criteria.