Evolution of Perturbations of a Charged Interface between Immiscible Inviscid Fluids in the Interelectrode Gap

Perturbations of the interface between two immiscible ideal fluids of finite thickness (the lower and upper fluids are the conductor and the dielectric, respectively) located in the gap between two electrodes are considered. In the cases of the "shallow" and "deep" upper fluid the dispersion relations of linear waves and their longwave expansions are found. The methods of determining the space-time evolution of an initial surface perturbation are developed on the basis of the linear approximation. In the cases of the "shallow" and "deep" upper fluid examples of the development of an initial perturbation of the "step" type are given. The development of an initial perturbation of the "step" type are also considered in the near-critical electric fields and in the case of degeneration of cubic dispersion.