Vortices

We use Jacobi coordinates and Nambu brackets to derive a new representation of the motion of three vortices which, unlinke all previous reductions, introduces no singularities into the system. We use this to study the scattering of dipoles by stationary vortices.

A complete English translation of Walter Gröbli’s 1877 Ph.D. Thesis, together with some notes on the process. The work considers the dynamics of point vortices in a two-dimensional inviscid incompressible fluid and derives a number of exact solutions in the cases of three, four and $2n$ vortices with certain restriction on the vortices’ circulation and the symmetry of the initial configuration.

We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$

We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as leapfrogging orbits. …

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary …