A review of the possible role of constraints in MHD turbulence

Abstract

A review of some of the issues that have arisen over the years concerning the energy distribution among scales for magnetohydrodynamics (MHD) turbulence is given here. A variety of tools are employed to that effect, and a central role is played by taking into consideration the ideal (non-dissipative) invariants, namely the total energy, the magnetic helicity and the cross-correlations between the velocity and the magnetic field (concentrating on the three-dimensional case). These concepts, based mostly on theory, models and direct numerical simulations, are briefly put in the context of observations, in particular the solar wind, and some of the remaining open questions are delineated as well. New results on ideal MHD dynamics in three dimensions on equivalent grids of up to $6144^3$ points using the Taylor-Green flow generalized to MHD are also mentioned.