A THEORY OF VORTEX MERGER

This paper discusses a 2D vortex merger for the particular case of a w eak point vortex and an extended vortex of nearly circular cross secti on. A Hamiltonian analysis describes the interaction of the point vort ex with surface waves on the extended vortex. Critical layers around t he extended vortex are introduced where ''point vortex-surface wave'' resonances occur. Vortex merger occurs only when there is an overlap o f neighboring critical layers. In this case the point vortex cascades through a sequence of resonances as it spirals in and merges with the extended vortex.