Collapse interactions of finite-sized two-dimensional vortices

Abstract

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.

The strain rate in evolutions of (elliptical) vortices in inviscid two-dimensional flows

“…In the paper by Vosbeek et al, 3 this quantity has been used in studying the collapse interaction of three, initially circular, monopolar vortices of uniform vorticity. It was shown there that the strain induced by two vortices caused the third vortex to be torn apart completely.…”

Self-similar motion of three point vortices

“…Only as the three concentrated vortices approach one another very closely do they "discover" that they cannot collide as in three-vortex collapse, and a rapid, in some cases quite dramatic, departure from the three-vortex solution takes places. The study by Vosbeek et al 13 is a good starting point for this set of issues.…”

Acceleration of Contour Dynamics Simulations with a Hierarchical-Element Method

“…In this example, the same initial configuration is chosen as in [20,21], i.e. : where Ö is the radial distance to the centre of the vortex, Ê its radius, and its strength or circulation.…”

“…In the paper by Vosbeek et al [21], the point vortices are replaced by initially circular monopoles of finite size and several numerical simulations were carried out to study the influence of e.g. viscosity and the size of the monopoles on the interaction behaviour of the vortices.…”