Dipole dynamics in the point vortex model

At the very heart of turbulent fluid flows are many interacting vortices that produce a chaotic and seemingly unpredictable velocity field. Gaining new insight into the complex motion of vortices and how they can lead to topological changes of flows is of fundamental importance in our strive to understand turbulence. Our aim is form an understanding of vortex interactions by investigating the dynamics of point vortex dipoles interacting with a hierarchy of vortex structures using the idealized point vortex model. Motivated by its close analogy to the dynamics of quantum vortices in Bose-Einstein condensates, we present new results on dipole size evolution, stability properties of vortex clusters, and the role of dipole-cluster interactions in turbulent mixing in 2D quantum turbulence. In particular, we discover a mechanism of rapid cluster disintegration analogous to a time-reversed self-similar vortex collapse solution.Comment: 57 pages (40 pages + appendix), 22 figure