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. © 1997 American Institute of Physics.

In this paper the strain rate in evolutions of elliptical vortices in inviscid two-dimensional flows is considered. Previous work ͓Vosbeek et al., Phys. Fluids 9, 3315 ͑1997͔͒ has revealed that there exists a relationship between the ͑in͒stability of an elliptical vortex of uniform vorticity ͑Kirchhoff vortex͒ and the spatial distribution of the strain rate. It is examined here how the strain distribution evolves in time for unstable Kirchhoff vortices. Furthermore, it is shown that there also exists a relationship between strain and ͑in͒stability of a vortex consisting of nested elliptical patches representing a more general vorticity distribution.

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