The cascade behavior of turbulent magnetohydrodynamics with a strong background magnetic field is examined and compared with direct numerical solutions at high Reynolds number. Resonant interactions give rise to qualitatively different behavior for modes below a characteristic wave number k L defined in terms of the background field. Modes with parallel wave number above k L are passively driven by the longer wavelength modes, even when the majority of the energy is contained in the passive wave numbers. The passive modes do not cascade to higher parallel wave numbers, so the parallel wave number spectrum is not a power law and does not extend to dissipation scales. Energy is cascaded normally to small perpendicular scales, but more rapidly in the case of the passive modes, so an anisotropic spectrum develops from isotropic initial conditions. For a finite system with minimum wave number Ͼk L , the only dynamically controlling mode is the vertical average, or mean mode. The mean mode evolves with two-dimensional dynamics, forming coherent current structures which are mirrored by the passive modes. Because of the differential decay rates, the mean mode dominates at long times. Quantitative comparisons are made to numerical solutions of reduced magnetohydrodynamics. ͓S1063-651X͑98͒06406-X͔
Numerical solutions of decaying two-dimensional incompressible magnetohydrodynamic turbulence reach a long-lived self-similar state which is described in terms of a turbulent enstrophy cascade. The ratio of kinetic to magnetic enstrophy remains approximately constant, while the ratio of energies decreases steadily. Although the enstrophy is not an inviscid invariant, the rates of enstrophy production, dissipation, and conversion from magnetic to kinetic enstrophy are very evenly balanced, resulting in smooth power law decay. Energy spectra have a k−3/2 dependence at early times, but steepen to k−5/2. Local alignment of the intermediate and small-scale fields grows, but global correlation coefficients do not. The spatial kurtosis of current grows and is always greater than the vorticity kurtosis. Axisymmetric monopole patterns in the current (magnetic vortices) are dominant structures; they typically have a weaker concentric, nonmonotonic vorticity component. Fast reconnection or coalescence events occur on advective and Alfvén time scales between close vortices of like sign. Current sheets created during these coalescence events are local sites of enstrophy production, conversion, and dissipation. The number of vortices decreases until the fluid reaches a magnetic dipole as its nonlinear evolutionary end-state.
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