Self-similar vortex configurations: Collapse, expansion, and rigid-vortex motion

The motion of point vortices that preserves the initial geometry of the vortex arrangement is an important class of vortex motion associated with N-vortex systems, referred to as the self-similar motion. While the self-similar motion of three-point vortices is well understood, larger vortex systems still need to be explored. Here, we use simple concepts from linear algebra to numerically investigate the distribution of initial conditions that lead to the self-similar motion of point vortices.