A statistical equilibrium model of coherent structures in magnetohydrodynamics
journal contributionposted on 01.01.1994, 00:00 by Richard Jordan
Abstract: "A statistical equilibrium theory is developed which characterizes the large-scale coherent structures that emerge during the course of the evolution of an ideal two-dimensional magnetofluid. Macrostates are defined to be 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-Liebler 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 evolution equations of the magnetohydrodynamic system. The predictions of the statistical equilibrium model are found to be in excellent qualitative and quantitative agreement with recent high resolution numerical simulations of turbulence in slightly dissipative two-dimensional magnetofluids."