Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics

The nature of the interactions between different scales in magnetohydrodynamic ( MHD) turbulence is important for the understanding of the behaviour of magnetized astrophysical, geophysical and industrial flows in a turbulent state. In this paper, we review some recent results in the study of locality of interactions in turbulent flows and we address some of the questions that arise. We examine the cascade of ideal invariants in turbulent MHD flows by examining the transfer functions. We show new results indicating that the nonlocal behaviour of the energy transfer in MHD is the result of a correlation between the velocity and magnetic fields. This nonlocality disappears if we randomize the phases of the two fields keeping the hydrodynamic and magnetic helicities fixed. The cascade of magnetic helicity is also investigated, with special focus on the fate of the small-scale helicity and its coupling with the large-scale flow. These results have implications for dynamo action, in particular for the commonly used distinction between large- and small-scale dynamos. The long-range interactions that exist in MHD flows also raise the question of the existence of universality in MHD, both in the kinematic dynamo regime as well as in the turbulent steady state.