The transition from weak to strong turbulence when passing from large to small scales in magnetohydrodynamic (MHD) turbulence with guide field is a cornerstone of anisotropic turbulence theory. We present the first check of this transition, using the Shell-RMHD, which combines a shell model of perpendicular nonlinear coupling and linear propagation along the guide field. This model allows us to reach Reynolds numbers around ${10}^6$. We obtain surprisingly good agreement with the theoretical predictions, with a reduced perpendicular energy spectrum scaling as $k_{\perp }^{-2}$ at large scales and as $k_{\perp }^{-5/3}$ at small scales, where critical balance between nonlinear and propagation time is reached. However, even in the strong regime, a high level of excitation is found in the weak coupling region of Fourier space, which is due to the rich frequency spectrum of large eddies. A corollary is that the reduced parallel spectral slope is not a definite test of the spectral anisotropy, contrary to standard belief.

• Received 23 January 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.025004