Collapse interactions of finite-sized two-dimensional vortices

The point vortex model predicts that a certain configuration of three point vortices leads to a collapse of these vortices to one point. Numerical simulations have been performed to investigate the effect of a finite vortex size on this two-dimensional collapse interaction. The paper presents results obtained with contour dynamics simulations of patches of uniform vorticity, and results obtained with finite difference simulations of vortices with continuous properties. In addition, the effect of viscosity and the presence of impermeable domain boundaries are investigated. The results show that the motion of finite-sized vortices is quite similar to the motion of point vortices as long as the mutual distance between the vortices is larger than their size. When the vortices are closer together their shapes start to deform and the subsequent evolution is different from that of the point vortices, and an actual collapse to one vortex does not take place.