Energy spectra stemming from interactions of Alfvén waves and turbulent eddies

Direct numerical simulations of three-dimensional magnetohydrodynamic turbulence at a Taylor Reynolds number of 1100 on a grid of 15363 points are reported (arXiv:0707.3620 astro-ph, submitted to Phys. Rev. Lett.). The flow is incompressible and decaying in time, and the initial condition is a superposition of large scale ABC Beltrami flows for wavenumbers k ≤ 4 and random noise at small scales with a k-3 spectrum, with negligible correlation between the velocity and the magnetic field (ρC~ 10-4) and equal kinetic and magnetic energies; finally, no uniform magnetic field is imposed. At peak of dissipation, current and vorticity sheets have formed within which strong correlations between the velocity and the magnetic field are found. Dissipation of energy appears independent of Reynolds number, and the energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectrum compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfvén waves and leading to a ~ k-3/2 law; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k\perp-2 spectrum, the perpendicular direction referring to the local quasi-uniform magnetic field. Whether such results are universal is not clear, for example because of the importance of nonlocal interactions between widely separated scales in MHD. Several parameters may play a role, such as ρC or the amount of magnetic helicity in the flow. Thus, high-resolution parametric studies are needed in order to understand in detail the interactions of turbulent eddies and Alfvén waves.