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

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.

Stochastic Equations of Hydrodynamic Theory of Plasma

“…Equations ( 31) and ( 32) present new formulas for the value of the critical electric field strength. We also mention data from [130][131][132].…”

Trayectorias de partículas bajo ondas periódicas forzadas de pequeña amplitud en un canal poco profundo con vorticidad constante

“…La ventaja de usar modelos reducidos radica en el hecho de que resolver dichos modelos requiere costos computacionales más bajos que las ecuaciones de Euler y aún puede capturar estructuras complejas debajo de las ondas de agua, por ejemplo, en presencia de estructuras de vorticidad constante como los ojos de gato de Kelvin (Kelvin cat-eyes) [9,13,14,15]. Dicha estructura se caracteriza por la existencia de puntos de estancamiento (puntos críticos del sistema dinámico autónomo de trayectorias de partículas) y zonas de recirculación dentro del fluido [16,17,18].…”