Numerical simulations with a finite-difference method have revealed that a Lamb dipole when placed in a viscous fluid moves along a straight line with decreasing velocity and increasing radius. The relationship between vorticity and streamfunction, which initially is linear, becomes more and more sinh-like as the dipole decays. Some other initial dipolar vorticity distributions (like two oppositely signed monopolar vortices) were found to evolve to a dipolar structure with Lamb-like characteristics.

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 we describe results of a study of the two-dimensional motion of a distributed monopolar vortex in a viscous incompressible fluid in a bounded rectangular domain with free-slip and no-slip boundary conditions. In the case of free-slip walls the motion of the vortex center can be satisfactorily modelled by a single point vortex in an inviscid fluid. Comparison of the results of both models reveals a good quantitative agreement for the trajectories of the vortex centers and of the period of one revolution around the center of the domain, for moderate viscous effects (Reϭ1000 and more͒. In a domain with no-slip walls the distributed monopolar vortex moves to the center of the domain along a curved but not smooth trajectory due to the interaction of the monopole and the wall-induced vorticity.