Gravity capillary waves generated by a moving pressure distribution in the presence of constant vorticity and dissipation

Two-dimensional nonlinear free-surface flows due to a pressure distribution moving at a constant velocity at the surface of a fluid of infinite depth are considered. The effects of the gravity and of the surface tension are included in the dynamic boundary condition. The vorticity in the fluid is assumed to be constant. The dissipation is modelled by a quasi potential approximation. The problem is solved numerically by a boundary integral equation method and numerical solutions are presented. The results unify previous findings for irrotational gravity capillary waves, waves in the presence of constant vorticity and free surface flows with dissipation.