Point Vortex Dynamics Influenced by the Surface Motion

We study a coupled system of differential equations, which models the dynamics of fluid with a free surface and a point vortex in the body of the fluid. For long surface waves of small amplitude, the effects of the interaction between the waves and the point vortex are modeled within the framework of the Boussinesq regime. It turns out that the solitary waves on the surface are not destroyed by the interaction with the vortex, and, as a matter of fact, the solitary waves remain practically unaffected for a significant range of the vortex strength. As a result, a further simplification of the model is proposed, where the vortex motion under solitons propagating on the surface is determined from a system of decoupled ordinary differential equations.