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 (nondissipative) 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.

Cascades and transitions in turbulent flows

“…Anisotropic versions have been examined in [364][365][366] and have been extended to high Prandtl number regimes in [367] and to Hall MHD in [368] (see [369] for a review). It is important to note that in (201) both field increments and single point quantities, b r = b • r, appear.…”

Magnetic fields from Multiplicative Chaos

“…A quantitative picture of the properties of anisotropic cascade emerged with the seminal papers by Goldreich & Sridhar (1995); Ng & Bhattacharjee (1996), at the heart of which lies the concept of critical balance. This picture keeps being refined, with additional ingredients such as dynamical alignment (Boldyrev 2006;Mallet & Schekochihin 2017) and thanks to important on-going efforts to tackle the problem by means of numerical simulations; for reviews see for example Verma (2004); Pouquet (2015); Rincon (2019); Moffatt & Dormy (2019). Our work relies on results derived by members of the hydrodynamics community, who themselves adapted ideas developed in the mathematics community.…”