Transition from weak to strong cascade in MHD turbulence

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 $k^{-2}$ at large scales and as $k^{-5/3}$ 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.