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A statistical equilibrium model of coherent structures in magnetohydrodynamics

A statistical equilibrium theory is developed to characterize the large-scale coherent structures in a turbulent two-dimensional magnetofluid. Macrostates are defined as local joint probability distributions, or Young measures, on the values of the fluctuating magnetic field and velocity field at each point in the spatial domain. The most probable macrostate is found by maximizing a Kullback entropy functional subject to constraints dictated by the conserved integrals of the ideal dynamics. This maximum entropy macrostate is, for each point in the spatial domain, a Gaussian probability distribution, whose local mean is an exact stationary solution of the equations of ideal magnetohydrodynamics. The predictions of the model are in excellent qualitative and quantitative agreement with recent high resolution numerical simulations of turbulence in slightly dissipative two-dimensional magneto fluids.