Theory of interaction between two plane vortices in a perfect fluid (Q1097783)

We consider the unsteady interaction between two vortices with arbitrary strengths, elliptic at the initial time, in an approximation of the smallness of the vortex dimensions in comparison with the distance between them. It is shown that the centers of the vortex regions move as point vortices of the same strength as distributed vortices, while the regions of vorticity themselves, remaining elliptic in shape, are periodically deformed and rotate nonuniformly around their centers. The dynamics of these motions is studied by means of a plane.