Simulations of Incompressible Magnetohydrodynamic Turbulence

We simulate incompressible MHD turbulence in the presence of a strongbackground magnetic field. Our major conclusions are: 1) MHD turbulence is mostconveniently described in terms of counter propagating shear Alfven and slowwaves. Shear Alfven waves control the cascade dynamics. Slow waves play apassive role and adopt the spectrum set by the shear Alfven waves, as does apassive scalar. 2) MHD turbulence is anisotropic with energy cascading morerapidly along k_perp than along k_parallel, where k_perp and k_parallel referto wavevector components perpendicular and parallel to the local magneticfield. Anisotropy increases with increasing k_perp. 3) MHD turbulence isgenerically strong in the sense that the waves which comprise it suffer orderunity distortions on timescales comparable to their periods. Nevertheless,turbulent fluctuations are small deep inside the inertial range compared to thebackground field. 4) Decaying MHD turbulence is unstable to an increase of theimbalance between the flux of waves propagating in opposite directions alongthe magnetic field. 5) Items 1-4 lend support to the model of strong MHDturbulence by Goldreich & Sridhar (GS). Results from our simulations are alsoconsistent with the GS prediction gamma=2/3. The sole notable discrepancy isthat 1D power law spectra, E(k_perp) ~ k_perp^{-alpha}, determined from oursimulations exhibit alpha ~ 3/2, whereas the GS model predicts alpha = 5/3.Comment: 56 pages, 30 figures, submitted to ApJ 59 pages, 31 figures, accepted to Ap