Free-surface signature of unsteady, two-dimensional vortex flows

The inviscid interaction of two-dimensional vortex flows with a free surface is studied numerically using a combined vortex/boundary integral technique. The vorticity is modelled as point vortices, vortex sheets and finite area vortex regions. Two problems are studied in considerable detail, the head-on collision of a vortex pair with a free surface and the large-amplitude Kelvin-Helmholtz instability of a submerged shear layer. The interaction is controlled by a Froude number and by the geometric parameters describing the initial vortex configuration. In the large-Froude-number limit, the surface motion follows the vortical flow, but depends only weakly on the actual value of the Froude number. For low Froude numbers, the free surface remains almost flat, and the disturbances caused by the vortical flow decrease rapidly with Froude number.