Fully nonlinear capillary–gravity solitary waves under a tangential electric field, Part II: Dynamics

Abstract

The stability and dynamics of two-dimensional fully nonlinear capillary–gravity solitary waves are studied when a uniform electric field is applied in the direction parallel to the undisturbed free surface of a dielectric fluid. For simplicity, we assume that the permittivity of the gas above the fluid is much smaller, therefore the two-layer problem can be reduced to be a one-layer one. The existence of fully localized solitary waves in deep water has been thoroughly studied in our previous work (Tao and Guo, 2014) via weakly nonlinear normal form analysis and fully nonlinear numerical computation. In the present paper, the stability and dynamics of the obtained solitary waves are investigated based on the time-dependent conformal map technique. Similar to the nonelectric capillary–gravity solitary waves, all depression waves, together with elevation waves featuring two big troughs connected by a small dimple, are found to be stable. Furthermore, head-on and overtaking collisions between stable solitary waves are studied via a numerical time integration.