The interaction between a pair of counter rotating vortices and a free boundary

The inviscid, two-dimensional interaction between a pair of counter-rotating line vortices and a free surface has been studied. An analytical solution to the linearized small- disturbance problem has been thoroughly explored. It is found that in response to weak vortices, disturbances much like gravity waves are generated on the surface. Increasing the strength of the vortices suppresses the dispersive character of the surface waves and limits the range of available frequencies. For the full non-linear free surface boundary conditions numerical calculations were carried out for both strong and weak vortices. The former are little affected by the presence of the surface, rising to form a bubble-like disturbance and bursting through. Weaker vortices are deflected towards the trajectory that would be followed by vortices approaching a solid boundary. The results are in agreement with experimental observations. In particular the scarring phenomena--surface depressions whose axes are perpendicular to the flow plane--are seen in both the numerical and analytical results.