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.

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

“…Flamarion et al [5] showed that the appearance of stagnation points beneath periodic travelling waves can occur at small vorticity with the help of electric fields. Besides, it was shown that the position of all the stagnation points changed significantly with variations in the electric field.…”

“…However, very few works have focused on the features of a velocity field associated with free surface waves in EHD flows. To our knowledge, the only study in this direction is the one carried out by Flamarion et al [5] in which the authors show that normal electric field acts as a mechanism that helps the appearance of stagnation points beneath periodic waves with constant vorticity. Stagnation points can be understood as points in the fluid domain that travels at the same speed as the wave.…”

Large-Amplitude Steady Solitary Water Waves with Constant Vorticity

“…However, there is as of yet no proof that any of the solutions we construct are truly overturning. The pressure beneath solitary waves with constant vorticity has recently been studied [28], as well as their nonlinear stability [11].…”

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

“…When ν is non-zero (and γ = 0), equation( 10) admits elevation solitary wave solutions when 0 ≤ B < B c and depression solitary wave solutions when B > B c . When electric forces are present, solitary waves of equation (10) do not have a closed form. We consider a solitary wave solution of (10) denoted by Θ = Θ(ξ − Cτ ) propagating with speed C. It immediately follows that η 0 (ξ, τ ) = Θ(ξ − Cτ ).…”

“…However, very few works have focused on the features of a velocity field associated with free surface waves in EHD flows. To our knowledge, the only study in this direction is the one carried out by Flamarion et al [10]. In this work the authors considered the full Euler equations to show that normal electric field acts as a mechanism that helps the appearance of stagnation points beneath periodic waves with constant vorticity.…”