Criteria for hard excitation of electrohydrodynamic instability of the free surface of a conducting fluid

The nonlinear dynamics of the free surface of a liquid metal in a strong vertical electric field is considered. It is shown for the case of a horizontally bounded geometry that a fairly large-amplitude perturbation can remove the system from equilibrium, even if the initial surface is stable in the linear approximation. An analysis of possible equilibrium configurations of the charged equipotential surface enables us to estimate the threshold values of the surface perturbation amplitude and of the perturbed electric field strength required for the electrohydrodynamic instability to occur.