Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant under the action of strong tangential electric field is investigated in the present work. The equations of boundary motion admit an exact solution in the form of nonlinear waves of arbitrary shape propagating without distortion along the surface of liquid in the direction of (or against the direction of) the external field. The velocity of periodic waves is greater than velocity of linear one and depends on problem parameters: fluid depth, wave amplitude and wavelength. It is obtained an explicit solution of the problem for the weakly nonlinear waves; in accordance with it, the rise to velocity is proportional to square of wave amplitude. Numerical analysis of exact expression for strongly nonlinear waves has shown that speed of waves propagation increases unlimitedly in the situation where amplitude is close to the fluid depth, i.e. when the surface touches the bottom. Despite the fact that nonlinear waves can separately propagate without distortion, the interaction of counter-propagating waves can result in deformation of the boundary. Numerical modeling methods based on using of dynamic conformal transforms of the region occupied by the fluid into parametric strip of auxiliary variables were chosen for the study of interaction of the oppositely traveling waves. The simulations show that nonlinear waves are actually deformed in result of their collisions; herewith the effect of nonlinearity is inversely proportional to the liquid depth, i.e. deformation increases with depth decreasing.

This work was supported by the Ministry of Education and Science of the Russian Federation (state contract no. 0389-2014-0006); by the RFBR (project nos. 16-38-60002, 16-08-00228, 17-08-00430); by the Presidium of UB, RAS (project no. 15-8-2-8); and by and the Presidential Programs of Grants in Science (project no. SP-132.2016.1).