Flow structure beneath periodic waves with constant vorticity under normal electric fields

Abstract

Waves with constant vorticity and electrohydrodynamics flows are two topics in fluid dynamics that have attracted much attention from scientists for both the mathematical challenge and their industrial applications. Coupling of electric fields and vorticity is of significant research interest. In this paper, we study the flow structure of steady periodic traveling waves with constant vorticity on a dielectric fluid under the effect of normal electric fields. Through the conformal mapping technique combined with pseudo-spectral numerical methods, we develop an approach that allows us to conclude that the flow can have zero, two, or three stagnation points according to variations in the voltage potential. We describe in detail the recirculation zones that emerge together with the stagnation points. In addition, we show that the number of local maxima of the pressure on the bottom boundary is intrinsically connected to the saddle points.