MHD turbulence: a biased review

Abstract

This review of scaling theories of magnetohydrodynamic (MHD) turbulence aims to put the developments of the last few years in the context of the canonical time line (from Kolmogorov to Iroshnikov–Kraichnan to Goldreich–Sridhar to Boldyrev). It is argued that Beresnyak's (valid) objection that Boldyrev's alignment theory, at least in its original form, violates the Reduced-MHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, a version of which is recovered in this interpretation, and the concept of dynamic alignment (equivalently, local 3D anisotropy) are thus an example of a physical theory of intermittency in a turbulent system. The emergence of aligned structures naturally brings into play reconnection physics and thus the theory of MHD turbulence becomes intertwined with the physics of tearing, current-sheet disruption and plasmoid formation. Recent work on these subjects by Loureiro, Mallet et al. is reviewed and it is argued that we may, as a result, finally have a reasonably complete picture of the MHD turbulent cascade (forced, balanced, and in the presence of a strong mean field) all the way to the dissipation scale. This picture appears to reconcile Beresnyak's advocacy of the Kolmogorov scaling of the dissipation cutoff (as $\mathrm {Re}^{3/4}$ ) with Boldyrev's aligned cascade. It turns out also that these ideas open the door to some progress in understanding MHD turbulence without a mean field – MHD dynamo – whose saturated state is argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart (this is a new result). On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require some adjustment – and a new scheme for such an adjustment is proposed – to take account of the determining part that a spontaneously emergent 2D condensate plays in mediating the Alfvén-wave cascade from a weakly interacting state to a strongly turbulent (critically balanced) one. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed: imbalanced turbulence (for which a new, tentative theory is proposed), residual energy, MHD turbulence at subviscous scales, and decaying MHD turbulence (where there has been dramatic progress recently, and reconnection again turned out to feature prominently). Finally, it is argued that the natural direction of research is now away from the fluid MHD theory and into kinetic territory – and then, possibly, back again. The review lays no claim to objectivity or completeness, focusing on topics and views that the author finds most appealing at the present moment.

Scaling of the Hosking integral in decaying magnetically dominated turbulence

“…It agrees with the assumption of the relevant time scale being the Alfvén time; see . On the other hand, if there really are two distinct scales that evolve differently, the result cannot be self-similar; see also § 11.2.3 of Schekochihin (2022) for a discussion.…”

“…The term ‘magnetic helicity density correlation integral’ may be more appropriate but rather clumsy. Following Schekochihin (2022), we now refer to it as the Hosking integral. We use the term integral instead of invariant as long as we are not in the ideal limit.…”

Critical balance and scaling of strongly stratified turbulence at low Prandtl number

“…Critical balance argues that linear wave and nonlinear interaction time scales are comparable, , on a scale-by-scale basis throughout a local energy cascade, giving a prediction for the anisotropy of the turbulence as a function of scale. Originally applied in mean-field magnetohydrodynamic (MHD) turbulence (Goldreich & Sridhar 1995) (see also Schekochihin (2022) and references therein), critical balance successfully predicts power laws of the anisotropic energy spectra and associated transition scales in rotating turbulence and unity Prandtl-number strongly stratified turbulence (Nazarenko & Schekochihin 2011).…”

CFD for turbulence: from fundamentals to geophysics and astrophysics

“…The task of doing a complete review is daunting. For this reason, we refer the interested readers to the excellent monographs in the references [56][57][58], Chapter 12 of [30], and Section 11 of [2] for more details.…”