Energy transfers in forced MHD turbulence

The energy cascade in magnetohydrodynamics is studied using high resolution direct numerical simulations of forced isotropic turbulence. The magnetic Prandtl number is unity and the large scale forcing is a function of the velocity that injects a constant rate of energy without generating a mean flow. A shell decomposition of the velocity and magnetic fields is proposed and is extended to the Elsasser variables. The analysis of energy exchanges between these shell variables shows that the velocity and magnetic energy cascades are mainly local and forward, though non-local energy transfer does exist between the large, forced, velocity scales and the small magnetic structures. The possibility of splitting the shell-to-shell energy transfer into forward and backward contributions is also discussed.