Universal properties of three-dimensional magnetohydrodynamic turbulence: Do Alfv\'en waves matter?

We analyse the effects of the propagating Alfv\'en waves, arising due to non-zero mean magnetic fields, on the nonequilibrium steady states of three-dimensional (3d) homogeneous Magnetohydrodynamic (MHD) turbulence. In particular, the effects of Alfv\'en waves on the universal properties of 3dMHD turbulence are studied in a one-loop self-consistent mode-coupling approach. We calculate the kinetic- and magnetic energy-spectra. We find that {\em even} in the presence of a mean magnetic field the energy spectra are Kolmogorov-like, i.e., scale as $k^{-5/3}$ in the inertial range where $\bf k$ is a Fourier wavevector belonging to the inertial range. We also elucidate the multiscaling of the structure functions in a log-normal model by evaluating the relevant intermittency exponents, and our results suggest that the multiscaling deviations from the simple Kolmogorov scaling of the structure functions decrease with increasing strength of the mean magnetic field. Our results compare favourably with many existing numerical and observational results.Comment: To appear in JSTAT (2005