We investigate the locality or nonlocality of the energy transfer and the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field $\mathbf{B}$ at various intensities. The results are based on a detailed analysis of three-dimensional numerical flows at moderate Reynolds numbers. The energy transfer functions, as well as the global and partial fluxes, are examined by means of different geometrical wave number shells. On the one hand, the transfer functions of the two conserved Elsässer energies $E^{+}$ and $E^{-}$ are found local in both the directions parallel ($k_{\Vert }$ direction) and perpendicular ($k_{\perp }$ direction) to the magnetic guide field, whatever the $\mathbf{B}$ strength. On the other hand, from the flux analysis, the interactions between the two counterpropagating Elsässer waves become nonlocal. Indeed, as the $\mathbf{B}$ intensity is increased, local interactions are strongly decreased and the interactions with small $k_{\Vert }$ modes dominate the cascade. Most of the energy flux in the $k_{\perp }$ direction is due to modes in the plane at $k_{\Vert }=0$, while the weaker cascade in the $k_{\Vert }$ direction is due to the modes with $k_{\Vert }=1$. The stronger magnetized flows tend thus to get closer to the weak turbulence limit, where three-wave resonant interactions are dominant. Hence, the transition from the strong to the weak turbulence regime occurs by reducing the number of effective modes in the energy cascade.

• Received 6 August 2007

DOI:https://doi.org/10.1103/PhysRevE.76.056313