Simulations of Incompressible Mhd Turbulence

We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows. 1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves. 2) MHD turbulence is anisotropic with energy cascading more rapidly along k⊥ than along k‖, where k⊥ and k‖ refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k⊥ such that excited modes are confined inside a cone bounded by k‖ ∝ k ⊥ where γ < 1. The opening angle of the cone, Θ(k⊥) ∝ k ⊥ , defines the scale dependent anisotropy. 3) The 1D inertial range energy spectrum is well fit by a power law, E(k⊥) ∝ k ⊥ , with α > 1. 4) MHD turbulence is generically strong in the sense that the waves which comprise it suffer 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 Θ(α−1)/(1−γ) ≪ 1. 5) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping’s shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/Θ(k⊥) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics. 6) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations. 7) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD Current Address, Department of Physics, UCLA, [email protected] Caltech 150-21, [email protected]