# Renormalized Onsager functions and merging of vortex clusters

## TL;DR

This paper numerically studies how vortex clusters merge, introduces a renormalized Onsager function to analyze their shapes, and discusses implications for 2D turbulence inverse cascade.

## Contribution

It introduces the renormalized Onsager function to better understand vortex cluster shapes after merging, advancing the analysis of vortex dynamics.

## Key findings

- Vortex clusters merge through a specific mechanism.
- Renormalized Onsager functions describe the shape of merged clusters.
- Implications for inverse cascade in 2D turbulence are discussed.

## Abstract

In this letter we numerically investigate the merging mechanism between two clusters of point vortices. We introduce a concept of renormalized Onsager function, an elaboration of the solutions of the mean field equation, and use it to understand the shape of the single cluster observed as a result of the merging process. We finally discuss the potential implications for the inverse cascade 2D turbulence.