Stationary States of Two-Dimensional Turbulence

Abstract

A class of exact statistical equilibria for the Navier-Stokes equation not including viscosity in two dimensions is noted and the corresponding fluctuation spectrum calculated. These solutions may account for the phenomena recently observed in numerical simulations of two-dimensional turbulence by Deem and Zabusky, including the existence of two distinct regimes of turbulence and the relaxation of one of these towards equipartition of vorticity.