An investigation of the flow structure beneath solitary waves with constant vorticity on a conducting fluid under normal electric fields

TL;DR

This study numerically investigates the flow structure beneath solitary waves with constant vorticity on a conducting fluid under electric fields, revealing how electric fields influence stagnation point formation in depression waves.

Contribution

It introduces a numerical approach to analyze the velocity field beneath solitary waves with electric field effects, highlighting the electric field's role in stagnation point emergence.

Findings

Electric fields do not significantly alter stagnation points in elevation waves.

Electric fields enable stagnation points in depression waves where none exist without the field.

The study provides insights into wave-fluid interactions under electromagnetic influences.

Abstract

The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave properties, very few works have examined the associated velocity field within the bulk of the fluid. Therefore, in this paper, we investigate numerically the flow structure beneath solitary waves with constant vorticity on an inviscid conducting fluid bounded above by a dielectric gas under normal electric fields in the framework of a weakly nonlinear theory. Elevation and depression solitary waves with constant vorticity are computed by a pseudo-spectral method and a parameter sweep on the intensity of the electric field is carried out in order to study its role in the appearance of stagnation points. We find that for elevation solitary waves the location of stagnation points does not change significantly with variations of the electric field. For depression solitary waves, on the other hand, the electric field acts as a catalyser that makes possible the appearance of stagnation points - in the sense that in its absence there is no stagnation point.