UNIVERSAL STATISTICS OF POINT VORTEX TURBULENCE: THE DOUBLY-PERIODIC DOMAIN

etc15 Tracking Number 438

A new solution technique is used to obtain a statistical description of the motion of $N$ point vortices, evolving in the usual two-dimensional doubly-periodic domain, in the limit $N \to \infty$. In contrast to previous approaches such as \cite{joyce:73}, a mean-field approximation is not used, meaning that the theory can describe the full (divergent) stationary energy spectrum associated with the vortex motion. An explicit formula for this energy spectrum is obtained, which is compared with direct numerical simulations with $N=50$ vortices, and excellent agreement is found across a range of vortex interaction energies (Hamiltonian of the point vortex system). The implications for understanding related non-equilibrium systems such as 2D classical turbulence and superfluid turbulence are discussed.