Unsteady hydroplaning and motion of a profile with trailing vortices

In the present paper we consider in the Sedov formulation the problems of unsteady motion of a profile with trailing vortices, rebounding, and non-self-similar hydroplaning contact. The basic integral equation for determining the vortex distribution density is reduced to the Abel equation by solving an auxiliary system of ordinary differential equations. The rebounding limit is determined for a flat plate.