Ideal magnetofluid turbulence in two dimensions
نویسندگان
چکیده
A continuum model of coherent structures in two-dimensional magnetohydrodynamic turbulence is developed. These structures are macroscopic states which persist among the turbulent microscopic fluctuations, typically as magnetic islands with Ilow. They are modeled as statistical equilibrium states Ibr the nondissipative dynamics, which conserves energy and families of cross-helicity and flux integrals. The model predicts that from a given initial state an ideal magnetofluid will evolve into a final state having steady mean m~,gnetic and velocity fields, and Gat, ssian local fluctuations in these fields. Excellent qualitative and quantitative agreement is found with the known 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 fixedvolume, small-spacing limit. This construction uses the discrete Fourier trans[brm to link the discretization of x-space with the trunc~,tion of k-space. Under the ergodic hypothesis and a separation-of-scales hypothesis, the lattice model is defined by a mean-field approximation to the Gibbs measure on the discretized phase space. A concentration property shows that this measure is equivalent to the microcanonical measure in the continuum limit.
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تاریخ انتشار 2005