Collapse and Burst of generalized Surface Quasi-Geostrophic point Vortices

TL;DR

This paper investigates the dynamics of generalized Surface Quasi-Geostrophic point vortices, establishing conditions for vortex bursts and collapses based on linear stability analysis around self-similar three-vortex configurations.

Contribution

It introduces a sufficient condition linking vortex stability to the occurrence of bursts and collapses in generalized Surface Quasi-Geostrophic vortex systems.

Findings

Identified a stability criterion for vortex bursts and collapses.

Linked vortex behavior to linearized dynamics stability.

Provided insights into vortex evolution in geophysical fluid models.

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.