Theory of vortex crystal formation in two-dimensional turbulence

Experiments on pure electron plasmas have found that the decay of two-dimen sional (2D) turbulence can lead to spontaneous formation of "vortex crystal s," which are symmetric arrays of strong vortices within a background of we aker vorticity. This paper presents a theory of these novel equilibrium sta tes of 2D turbulence. The paper consists of two parts. In the first part, w e show that the vortex crystals are well described as "regional" maximum fl uid entropy (RMFE) states, which are equilibrium states reached through erg odic 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 t he approximate number of the strong vortices in the final state. (C) 2000 A merican Institute of Physics. [S1070-664X(00)90705-5].