Solitary Electrohydrodynamic Waves with Submerged Point Vortices

Abstract

We consider the existence of two-dimensional solitary gravity-capillary wave solutions propagating under a normal electric field with submerged point vortices. While some literature has discussed the incompressible Euler equations with spatially localized vorticity, little is known about the extent to which the combined effects of electrohydrodynamics influence the flow. This study aims to fill this gap by investigating the impact of a normal electric field on the behavior of point vortex system. By applying the implicit function theorem, we construct a continuous curve of small-amplitude solitary gravity-capillary wave solutions to the point vortex system. Notably, the solutions exhibit a surface depression at the origin, induced by the submerged point vortex. This depression becomes more pronounced as the vortex approaches the free surface.