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

TL;DR

This paper investigates the flow structure of steady periodic waves with constant vorticity in dielectric fluids under normal electric fields, revealing how electric potential variations influence stagnation points and recirculation zones.

Contribution

It introduces a novel conformal mapping and pseudo-spectral numerical approach to analyze the coupling of electric fields and vorticity in fluid flows.

Findings

Flow can have zero, two, or three stagnation points depending on voltage potential.

Recirculation zones are detailed alongside stagnation points.

Number of pressure maxima relates to saddle points.

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. The coupling of electric fields and vorticity is of significant research interest. In this paper, we study the flow structure of steady periodic travelling 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. Besides, we show that the number of local maxima of the pressure on the bottom boundary is intrinsically connected to the saddle points.