Direct Evidence of the Transition from Weak to Strong Magnetohydrodynamic Turbulence

One of the most important predictions in magnetohydrodynamics is that in the presence of a uniform magnetic field b_{0}e[over ^]_{∥} a transition from weak to strong wave turbulence should occur when going from large to small perpendicular scales. This transition is believed to be a universal property of several anisotropic turbulent systems. We present, for the first time, direct evidence of such a transition using a decaying three-dimensional direct numerical simulation of incompressible balanced magnetohydrodynamic turbulence with a grid resolution of 3072^{2}×256. From large to small scales, the change of regime is characterized by (i) a change of slope in the energy spectrum going from approximately -2 to -3/2, (ii) an increase of the ratio between the wave and nonlinear times, with a critical ratio of χ_{c}∼1/3, (iii) a modification of the isocontours of energy revealing a transition from a purely perpendicular cascade to a cascade compatible with the critical-balance-type phenomenology, and (iv) an absence followed by a dramatic increase of the communication between Alfvén modes. The changes happen at approximately the same transition scale and can be seen as manifest signatures of the transition from weak to strong wave turbulence. Furthermore, we observe a significant nonlocal three-wave coupling between strongly and weakly nonlinear modes resulting in an inverse transfer of energy from small to large scales.