Interactions of eddies and waves in magnetohydrodynamic turbulence

Direct numerical simulations of three-dimensional magnetohydrodynamic turbulence at a Taylor Reynolds number of 1100 on a grid of $1536^3$ points are reported (arXiv:0707.3620 astro-ph, submitted to {\it Phys. Rev. Lett.}). The flow is incompressible and decaying in time, and the initial condition is a superposition of large scale ABC flows for wavenumbers $k \le 4$ and random noise at small scales with a $k^{-3}$ spectrum, with negligible correlation between velocity and the magnetic field ($\rho_C\sim 10^{-4}$) and equal kinetic and magnetic energies; finally, no uniform magnetic field is imposed. At peak of dissipation, the resulting 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 Alfv\'en waves and leading to a $\sim k^{-3/2}$ 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, and several parameters may play a role, such as $\rho_C$ 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 Alfv\'en waves.