Statistical properties of two-dimensional magnetohydrodynamic turbulence

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Abstract
The statistical properties of two‐dimensional (2‐D) magnetohydrodynamic (MHD) turbulence are studied by means of high‐resolution numerical simulations. As a theoretical point of reference, the β model of intermittent turbulence is adapted to the MHD case. Comparison of simulation results for energy spectra with the β‐model predictions shows intermittency corrections to be small, δF∝R1/2λ. An argument is given that this scaling valid for Rλ∼102 is, however, not characteristic of the asymptotic regime Rλ→∞, where a constant value of F is to be expected. The probability distributions of the field difference δv(x,t), δB(x,t) are Gaussian for large separation x or t, approaching an approximately exponential distribution for x, t→0. This behavior can be understood by a simple probabilistic argument. The probability distribution of the local energy dissipation rate ε is roughly consistent with a log‐normal distribution at larger ε but shows a different behavior at small ε.