Numerical Study of Free-Surface Electro-Hydrodynamic Wave Turbulence

Direct numerical simulation of the three-dimensional chaotic motion of a dielectric liquid with a free surface under the action of an external horizontal electric field is carried out. The numerical model takes into account the effects of surface tension, viscosity, and external isotropic random forcing acting at large scales. A transition from dispersive capillary wave turbulence to quasi-isotropic non-dispersive EHD surface turbulence with an increase in the external electric field strength is numerically observed for the first time. At the regime of developed EHD wave turbulence, the total electrical energy is found to be much greater than the energy of capillary waves, i.e., electro-hydrodynamic effects play a dominant role. At the same time, anisotropic effects are detected that lead to the generation of capillary wave packets traveling perpendicular to the external field direction. Despite the revealed anisotropy, the calculated spectrum of EHD wave turbulence is in very good agreement with the analytical spectrum obtained on the basis of dimensional analysis of weak turbulence spectra.