MOTION OF A VORTEX NEAR A FREE-SURFACE

The early motion of a single vortex suddenly placed near a free surface is studied analytically. The general initial/boundary-value problem is solved in terms of a Taylor expansion in time. The vortex position and the surface elevation are determined to third order. We find a precise distinction between subcritical (weak) and supercritical (strong) vortices. All vortices start with retrograde horizontal motion. After a short time, subcritical vortices tend to turn and continue their motion in the prograde direction. Supercritical vortices cannot turn, but will continue their retrograde motion. They will accumulate a surface mound until surface breaking eventually occurs.