Theory of vortex crystal formation in two-dimensional turbulence

Abstract

Experiments on pure electron plasmas have found that the decay of two-dimensional (2D) turbulence can lead to spontaneous formation of “vortex crystals,” which are symmetric arrays of strong vortices within a background of weaker vorticity. This paper presents a theory of these novel equilibrium states of 2D turbulence. The paper consists of two parts. In the first part, we show that the vortex crystals are well described as “regional” maximum fluid entropy (RMFE) states, which are equilibrium states reached through ergodic mixing of the background by the strong vortices. In the second part, a theory is advanced that allows us to predict from the initial conditions the approximate number of the strong vortices in the final state.