Abstract
A theoretical analysis of the subharmonic response of two resonant modes of interfacial gravity-capillary waves between two electrified fluids of infinite depth under the influence of a constant horizontal electric field is investigated. The method of multiple scales is used to derive two parametrically nonlinear Schrödinger equations that describe the behavior of the disturbed system in the resonance case. One of them contains the first derivatives in space for a complex-conjugate type while the second contains a linear complex-conjugate term. A time-dependent solution of a traveling wave is obtained. Stability conditions are obtained analytically and are discussed numerically. It is found that the stability criteria are significantly affected by the amplitude of the temporal solution. The numerical calculations show that instability is produced in the system except for small stable areas due to the periodic forcing. It is observed that the acceleration frequency plays a dual role in the stability criterion. The results show that the horizontal electric field plays a dual role in the resonance case.
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