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 512(3)-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 Gamma =E-K/E-M. A simple model consistent with a series of simulation runs predicts the asymptotic decay laws E similar tot(-1/2), E(K)similar tot(-1). For nonhelical MHD turbulence, H similar or equal to0, the energy decays faster, E similar to 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 zeta (MHD)(p)=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. (C) 2000 American Institute of Physics. [S1070-664X(00)05312-X].