The Anisotropy of Magnetohydrodynamic Alfvénic Turbulence

We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudospectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling law k_∥~k^2/3_⊥ recently proposed by Goldreich & Sridhar. Here k_∥ (and k_⊥) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.