Analytic characterization of stability islands on two point vortex systems

TL;DR

This paper investigates the stability islands in two point vortex systems by analyzing passive particle dynamics, providing analytical expressions for their boundaries and characterizing their morphology.

Contribution

It offers a detailed analytical and computational characterization of stability islands in two vortex systems, a fundamental scenario in fluid dynamics.

Findings

Computed perimeter and area of stability islands

Derived analytical expressions for island boundaries

Highlighted the morphology of stability regions

Abstract

In a system of point vortices, there exist regions of stability around each vortex, even if the system is chaotic. These regions are usually called stability islands and they have a morphology that is hard to characterise. We study and characterise them in two point vortex systems in the infinite two-dimensional plane -- the simplest scenario -- by studying the dynamics of passive particles in these environments. We present computations for the perimeter and area of these islands and highlight the analytical expressions that define their boundary.