STATISTICAL PROPERTIES OF 2-DIMENSIONAL MAGNETOHYDRODYNAMIC TURBULENCE

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, δ<0.2, while fourth-order correlation functions exhibit a stronger effect δ≃0.35, consistent with the numerically observed Reynolds-number dependence of the flatness factor F ∝ R λ1/2. 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 ∈ is roughly consistent with a log-normal distribution at larger ∈ but shows a different behavior at small ∈. © 1990 American Institute of Physics.