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Journal of Statistical Physics

, Volume 87, Issue 3–4, pp 661–695 | Cite as

Ideal magnetofluid turbulence in two dimensions

  • Richard Jordan
  • Bruce Turkington
Articles

Abstract

A continuum model of coherent structures in two-dimensional magnetohydro-dynamic turbulence is developed. These structures are macroscopic states which persist among the turbulent microscopic fluctuations, typically as magnetic islands with flow. They are modeled as statistical equilibrium states for the non-dissipative 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 magnetic and velocity fields, and Gaussian 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 fixed-volume, small-spacing limit. This construction uses the discrete Fourier transform to link the discretization ofx-space with the truncation ofk-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.

Key Words

Magnetohydrodynamics turbulence coherent structure statistical equilibrium maximum entropy discrete Fourier transform 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Richard Jordan
    • 1
  • Bruce Turkington
    • 2
  1. 1.Center for Nonlinear Analysis, Department of MathematicsCarnegie Mellon UniversityPittsburgh
  2. 2.Department of Mathematics and StatisticsUniversity of MassachusettsAmherst

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