Collapse and Turbulence of Electro-Hydrodynamic Water Waves

This work numerically investigates the fully nonlinear evolution of the free surface of a deep non-conducting liquid in a strong tangential electric field based on the method of dynamic conformal transformations. Direct numerical simulation revealed two possible scenarios for the evolution of nonlinear surface electro-hydrodynamic waves: collapse at finite time (in the non-viscous case) and turbulence generated by strongly nonlinear shock-like waves (taking into account both dissipation and pumping of energy). In the process of wave breaking, regions with a steep wave front arise, in which the curvature of the boundary increases infinitely. The inclusion of viscosity prevents the formation of singularities, and the system transfers to a strongly turbulent mode of motion. The spectrum of surface disturbances is very well described by the Kuznetsov spectrum k−4, which corresponds to the second-order singularities in the liquid boundary. The measured probability density functions demonstrate a high level of intermittency in the turbulent regime, i.e., extreme events such as shocks play a dominant role in the evolution of the system. The results of calculations such as the turbulence spectrum, type of surface singularity, and the presence of intermittency are in good qualitative agreement with recent experiments carried out by Ricard and Falcon for a ferrofluid in a magnetic field.