Dynamics of decaying two-dimensional magnetohydrodynamic turbulence

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Abstract
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+t 0)− 1. As in three dimensions, dissipative small‐scale turbulence adjusts in such a way as to make the energy dissipation rate ε 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 =D B 1 / 2ε1 / 2 k − 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 =(l 2λ)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.