Collapse and Burst of generalized Surface Quasi-Geostrophic point Vortices

Abstract

We consider the generalized Surface Quasi-Geostrophic point vortices dynamics, and identify a sufficient condition implying existence of bursts out of (and collapses into) any given initial configuration of vortices. The condition is related to the stability of the linearized dynamics around three vortices evolving in a self-similar fashion.

15 pages