Ideal magnetofluid turbulence in two dimensions

Abstract: "A continuum model of coherent structures in two-dimensional magnetohydrodynamic turbulence is developed. These structures are macroscopic states which persist amongst the turbulent microscopic fluctuations, typically as magnetic islands with flow. They are modeled as statistical equilibrium states for the ideal (nondissipative) dynamics, which conserves energy and families of cross-helicity and flux integrals. The model predicts that an ideal magnetofluid will evolve into a turbulent relaxed state having steady mean magnetic and velocity fields, and Gaussian local fluctuations in these fields. Excellent qualitative and quantitative agreement is found with the results of direct numerical simulations. A rigorous justification of the theory is also provided, in the sense that the continuum model is derived from a lattice model in a fixed-volume, small-spacing limit. This construction uses the discrete Fourier transform to link the discretization of x-space with the truncation of k-space. The lattice model is defined by the most probable distribution on the discretized phase space that respects the approximated dynamical constraints. A concentration property shows that this distribution is equivalent to the microcanonical distribution in the continuum limit."