Wave breaking on the surface of a dielectric liquid in a horizontal electric field

Abstract

The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of capillarity and gravity are not taken into account, it is shown that nonlinear surface waves have a tendency to break. In result of the collapse of the surface waves, the curvature of the boundary and the gradient of the local electric field undergo infinite discontinuity on the surface of the liquid. The angles of the boundary inclination remain small. The characteristic collapse time of a surface wave traveling in a given direction is calculated versus the dielectric constant of the liquid. It is shown that the time of the singularity formation increases infinitely at small and high values of the dielectric constant. The first case corresponds to the transition of the system to the neutral stability regime (the jump in electrostatic pressure at the boundary turns into zero). At high values of the dielectric constant of the liquid, the collapse time also increases. This effect is associated with the realization of a special regime of fluid motion, in which the propagation of nonlinear surface waves of an arbitrary configuration occurs without distortions. For the liquids with relative permittivity close to five, the wave breaking time reaches a minimum, i.e., the collapse of the surface waves for such liquids occurs most intensively.