Renormalized Onsager functions and merging of vortex clusters

Abstract

This paper is devoted to an heuristic discussion of the merging mechanism between two clusters of point vortices, supported by some numerical simulations. A concept of renormalized Onsager function is introduced, elaboration of the solutions of the mean field equation. It is used to understand the shape of the single cluster observed as a result of the merging process. Potential implications for the inverse cascade 2D turbulence are discussed.