On two-dimensional magnetohydrodynamic turbulence

Numerical studies of decaying two-dimensional (2D) magnetohydrodynamic (MHD ) turbulence are presented. Results concern mainly the decay laws of integr al quantities and the scaling properties of spectra and structure functions . The self-similarity of the decay is characterized by the invariance of th e ratios of resistive and viscous dissipation rates, kinetic and magnetic e nergies, and mean parallel and perpendicular velocities. The energy decay r ate is primarily determined by the conservation of the mean-square magnetic potential, but the process is somewhat retarded at intermediate times by c urrent density condensation in the magnetic eddies. In contrast to the 3D c ase, the energy spectrum agrees with the Iroshnikov-Kraichnan (IK) law E(k) similar tok(-3/2), but is modified by a strong anomalous bottleneck effect. Structure functions of the Elsasser fields satisfy the property of extende d self-similarity, which provides accurate values of the relative scaling e xponents. Also the structure functions themselves show clear scaling proper ties, particularly at the highest Reynolds numbers studied. The scaling exp onent zeta (2) is consistent with the IK spectrum, but zeta (3) and zeta (4 ) remain distinctly below unity, which is surprising in view of an exact re lation suggesting zeta (3)=1. Finally, the role of the tearing mode in 2D M HD turbulence is revisited. (C) 2001 American Institute of Physics.