Scale-locality of energy transfer in magnetohydrodynamic turbulence.

We investigate scale-locality of energy cascade in magnetohydrodynamic (MHD) turbulence at high kinetic and magnetic Reynolds numbers. There is a growing consensus that large-scale flow can transfer energy to the magnetic field at arbitrarily small scales in the inertial range (Alexakis et al. (2005,2007), Carati et al. (2006), Yousef et al. (2007), Schekochihin et al. (2008), etc.) However, we rigorously prove that such non-local transfer cannot occur, under very weak scaling conditions for velocity and magnetic-field increments accepted to hold in the inertial-inductive range of turbulent MHD flows. Our analysis shows that inter-scale fluxes of two conserved quantities, total energy and cross helicity, are dominated by local triadic interactions. Nonlocal triads make an asymptotically negligible contribution, decaying as a power of the scale-disparity. Furthermore, nonlocal-in-scale triads may dominate in field-line stretching, but energy conversion by stretching is primarily between velocity and magnetic-field modes at comparable scales. To verify our analytical results, we present data of forced MHD turbulence from a pseudospectral simulation on a grid of $1024^3$ points with phase-shift dealiasing.