Formation of regions with high energy and pressure gradients at the free surface of a liquid dielectric in a tangential electric field

The nonlinear dynamics of the free surface of an ideal incompressible non-conducting fluid with a high dielectric constant subjected to a strong horizontal electric field is simulated using the method of conformal transformations. It is shown that at initial stages of interaction of counter-propagating periodic waves of significant amplitude, there is a direct energy cascade leading to energy transfer to small scales. This results in the formation of regions with a steep wave front at the fluid surface, in which the dynamic pressure and the pressure exerted by the electric field undergo a discontinuity. It has been demonstrated that the formation of regions with high gradients of electric field and fluid velocity is accompanied by breaking of surface waves; the inclination angles of the boundary tend to 90$^\circ$C, and the surface curvature increases without bound.