Scale Interactions in Magnetohydrodynamic Turbulence

This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present-day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, die damping of velocity fluctuations by the Lorentz force, and the development of anisotropies can be characterized at different scales. In this context we consider three different configurations often studied in the literature: mechanically forced turbulence, freely decaying turbulence, and turbulence in the presence of a uniform magnetic field. Each configuration is of interest for different geophysical and astrophysical applications. Local and nonlocal transfers are discussed for each case. Whereas the transfer between scales of solely kinetic or solely magnetic energy is local, transfers between kinetic and magnetic fields are observed to be local or nonlocal depending on the configuration. Scale interactions in the cascade of magnetic helicity are also reviewed. Based on die results, the validity of several usual assumptions in hydrodynamic turbulence, such as isotropy of the small scales or universality, is discussed.