We investigate the transfer of energy from large scales to small scales in fully developed forced three-dimensional magnetohydrodynamics (MHD) turbulence by analyzing the results of direct numerical simulations in the absence of an externally imposed uniform magnetic field. Our results show that the transfer of kinetic energy from large scales to kinetic energy at smaller scales and the transfer of magnetic energy from large scales to magnetic energy at smaller scales are local, as is also found in the case of neutral fluids and in a way that is compatible with the Kolmogorov theory of turbulence. However, the transfer of energy from the velocity field to the magnetic field is a highly nonlocal process in Fourier space. Energy from the velocity field at large scales can be transferred directly into small-scale magnetic fields without the participation of intermediate scales. Some implications of our results to MHD turbulence modeling are also discussed.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

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.

We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami () forcing, creating helical flow. The Zeman scale at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy and helicity , and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of points, with Rossby and Reynolds numbers, respectively, equal to and . At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond by Kolmogorov spectra for and . Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at , a clear sign of recovery of three-dimensionality in the small scales.