Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence

A comprehensive picture of three-dimensional (3D) isotropic magnetohydrodynamic (MHD) turbulence is presented based on the first 5123-mode numerical simulations performed. Both temporal and spatial scaling properties are studied. For finite magnetic helicity H the energy decay is governed by the constancy of H and the decrease of the ratio of kinetic and magnetic energy Γ=EK/EM. A simple model consistent with a series of simulation runs predicts the asymptotic decay laws E∼t−1/2, EK∼t−1. For nonhelical MHD turbulence, H≃0, the energy decays faster, E∼t−1. The energy spectrum follows a k−5/3 law, clearly steeper than k−3/2 previously found in 2D MHD turbulence. The scaling exponents of the structure functions are consistent with a modified She–Leveque model ζpMHD=p/9+1−(1/3)p/3, which corresponds to a basic Kolmogorov scaling and sheet-like dissipative structures. The difference between the 3D and the 2D behavior can be related to the eddy dynamics in 3D and 2D hydrodynamic turbulence.