Spectral Slope and Kolmogorov Constant of MHD Turbulence

The spectral slope of strong MHD turbulence has recently been a matter of controversy. While the Goldreich-Sridhar model predicts a -5/3 slope, shallower slopes have been observed in numerics. We argue that earlier numerics were affected by driving due to a diffuse locality of energy transfer. Our highest-resolution simulation (30722x1024) exhibited the asymptotic -5/3 scaling. We also discover that the dynamic alignment, proposed in models with -3/2 slope, saturates and cannot modify the asymptotic, high Reynolds number slope. From the observed -5/3 scaling we measure the Kolmogorov constant CKA=3.27±0.07 for Alfvenic turbulence and CK=4.2±0.2 for full MHD turbulence, which is higher than the hydrodynamic value of 1.64. This larger CK indicates inefficient energy transfer in MHD turbulence, which is in agreement with diffuse locality.