Dynamics of electrified liquid metal surface using shallow water model

A shallow water model that incorporates surface tension and electric field effects is developed to investigate the dynamics of an electrified liquid surface. The computational model is verified against the Zakharov-Kuznetsov equation and is applied to study the growth and damping of the electrified liquid surface. A linear wave analysis is performed under a shallow water theory assuming an analytic solution of the electric field, similar to the Tonks-Frenkel instability. The electrified liquid surface grows or dampens based on the balance of the electric field, surface tension, and gravitational forces. The numerical results obtained from the electrified shallow water solver are in good agreement with the theoretical analysis.