Clustering of point vortices in a periodic box

TL;DR

This paper uses Monte Carlo simulations to analyze clustering behavior of point vortices in a periodic box, employing the L function to identify states of clustering and negative temperature.

Contribution

It introduces a simulation approach to study vortex clustering and applies the L function to characterize spatial organization in vortex systems.

Findings

Positive L indicates clustering and Onsager's negative temperature state.

Simulation results reveal conditions under which vortices cluster.

Clustering correlates with negative temperature states.

Abstract

The Monte Carlo simulation of $N$ point vortices with square periodic boundary conditions is performed where $N$ is order of 100. The clustering property is examined by computing the $L$ function familiar in the field of spatial ecology. The case of a positive value of $L$ corresponds to the state of clustering and the Onsager's negative temperature.