Nonlinear wave dynamics under the presence of a strong horizontal electric field and a bathymetry

In this letter, we explore free-surface flow of an ideal dielectric liquid subjected to a strong tangential electric field in the presence of variable bottom topographies. Analytically, we demonstrate that nonlinear waves of arbitrary shape can propagate at a critical speed without distortion, provided they are in resonance with a moving localized obstacle at the bottom. Numerical solutions of the full model for various obstacle types yield two key results: (i) For localized obstacles, a wave forms above the obstacle, then splits into symmetric waves traveling in opposite directions at the same speed and a stationary disturbance formed due to electric field inhomogeneities. (ii) Periodic spatial bathymetries induce periodic motion in both space and time. Additionally, considering traveling solitary waves, we show that a small dispersive tail arises when they interact with the bathymetry.