We simulate incompressible, MHD turbulence using a pseudo-spectral code. Ourmajor conclusions are as follows.
1) MHD turbulence is most conveniently described in terms of counter propagatingshear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slowwaves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascadescomposed entirely of shear Alfvén waves do not generate a significant measureof slow waves.
2) MHD turbulence is anisotropic with energy cascading more rapidly along k⊥ thanalong k∥, where k⊥ and k∥ refer to wavevector components perpendicular and parallelto the local magnetic field. Anisotropy increases with increasing k⊥ such that excitedmodes are confined inside a cone bounded by k∥ ∝ kγ⊥ where γ less than 1. The openingangle of the cone, θ(k⊥) ∝ k-(1-γ)⊥, defines the scale dependent anisotropy.
3) MHD turbulence is generically strong in the sense that the waves which comprise itsuffer order unity distortions on timescales comparable to their periods. Nevertheless,turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ2 (k⊥)≪1.
4) MHD cascades are best understood geometrically. Wave packets suffer distortionsas they move along magnetic field lines perturbed by counter propagating waves.Field lines perturbed by unidirectional waves map planes perpendicular to the localfield into each other. Shear Alfvén waves are responsible for the mapping's shear andslow waves for its dilatation. The amplitude of the former exceeds that of the latterby 1/θ(k⊥) which accounts for dominance of the shear Alfvén waves in controllingthe cascade dynamics.
5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as thevelocity and magnetic field perturbations.
6) Decaying MHD turbulence is unstable to an increase of the imbalance betweenthe flux of waves propagating in opposite directions along the magnetic field. ForcedMHD turbulence displays order unity fluctuations with respect to the balanced stateif excited at low k by δ(t) correlated forcing. It appears to be statistically stable tothe unlimited growth of imbalance.
7) Gradients of the dynamic variables are focused into sheets aligned with the magneticfield whose thickness is comparable to the dissipation scale. Sheets formed byoppositely directed waves are uncorrelated. We suspect that these are vortex sheetswhich the mean magnetic field prevents from rolling up.
8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth byGoldreich and Sridhar (1995, 1997). Results from our simulations are also consistentwith the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D powerlaw spectra, E(k⊥) ∝ k-∝⊥, determined from our simulations exhibit ∝ ≈ 3/2, whereasthe GS model predicts ∝ = 5/3.
