Wave turbulence of a liquid surface in an external tangential electric field

A direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field taking into account viscous forces has been performed. It has been shown that the interaction of counter-propagating nonlinear waves can generate a direct energy cascade. In the quasistationary energy dissipation regime, probability density functions for angles of inclination of the boundary tend to a Gaussian distribution and the shape of the boundary becomes complex and chaotic. The spectrum of the surface perturbations in this regime is described by a power law $k^{-5/2}$. The energy spectrum has the form $k^{-3/2}$, which coincides with the Iroshnikov-Kraichnan energy spectrum and indicates that the observed wave turbulence of the liquid surface and the weak magnetohydrodynamic turbulence of interacting Alfv\'en waves have a related nature.