Interaction of a Vortex Pair with a Free Surface.

The trailing vortices generated by the control planes of submarines give rise to surface signatures in the form of scars and striations. Two counter-rotating vortices were generated in a novel experimental system and their interaction with the free surface was investigated. In addition, the governing equations have been solved through the use of the boundary-element method for a representative Frounde number. The results have been expressed in terms of the depth of submergence of the vortices, their mutual induction velocity, and the initial vortex separation. It has been shown that the free surface begins to deform when the vortices are at a distance of about one initial vortex separation from the free surface. The height of the maximum deformation is attained at a normalized time of about 0.1, when the vortices are at a distance of about 0.5b sub 0 from the free surface. The elevated part of the surface is bounded by two scars, whose motion is slaved to that of the vortices. Theses