Dynamics of decaying two-dimensional magnetohydrodynamic turbulence

High-resolution numerical studies of decaying two-dimensional magnetohydrodynamic turbulence were performed with up to 1024² collocation points in general periodic systems using various initial states, but restricting consideration to weak velocity-magnetic field correlation ρ. The global evolution is self-similar with constant kinetic to magnetic energy ratio E^V/E^M, macro- and microscale Reynolds numbers, and correlation ρ, while the total energy decays as E(t)∝(t+t₀)^-1. As in three dimensions, dissipative small-scale turbulence adjusts in such a way as to make the energy dissipation rate ɛ independent of the collisional dissipation coefficients. Normalized energy spectra are also invariant. The spectral index in the inertial range is, in general, close to 3/2 in agreement with Kraichnan's Alfvén wave argument E_k =DB^1/2ɛ^1/2k^-3/2, B=(E^M)^1/2, D≂1.8±0.2, but may be close to 5/3 in transient states, in which turbulence is concentrated in regions of weak magnetic field. In the dissipation range, intermittency gives rise to a modified dissipation scale l_eff =(l²λ)^1/3, with l=Kolmogorov scale and λ=Taylor microscale. This reflects the intermittency of the dissipation process, which is consistent with the picture of current microsheets of thickness l and width and spacing λ.