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 (${3072}^2\times 1024$) 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 $C_{\mathrm{KA}}=3.27\pm 0.07$ for Alfvénic turbulence and $C_K=4.2\pm 0.2$ for full MHD turbulence, which is higher than the hydrodynamic value of 1.64. This larger $C_K$ indicates inefficient energy transfer in MHD turbulence, which is in agreement with diffuse locality.

• Received 30 November 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.075001