MHD Turbulence: A Biased Review

This review puts the developments of the last few years in the context of the canonical time line (Kolmogorov to Iroshnikov-Kraichnan to Goldreich-Sridhar to Boldyrev). It is argued that Beresnyak's objection that Boldyrev's alignment theory violates the RMHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrev's scalings, recovered in this interpretation, are thus an example of a physical theory of intermittency in a turbulent system. Emergence of aligned structures brings in reconnection physics, so the theory of MHD turbulence intertwines with the physics of tearing and current-sheet disruption. Recent work on this by Loureiro, Mallet et al. is reviewed and it is argued that we finally have a reasonably complete picture of MHD cascade all the way to the dissipation scale. This picture appears to reconcile Beresnyak's Kolmogorov scaling of the dissipation cutoff with Boldyrev's aligned cascade. These ideas also enable some progress in understanding saturated MHD dynamo, argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart. On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require adjustment - and a scheme for it is proposed - to take account of the part that a spontaneously emergent 2D condensate plays in mediating the Alfven-wave cascade. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed, concerning imbalanced MHD turbulence (for which a new theory is proposed), residual energy, subviscous and decaying regimes of MHD turbulence (where reconnection again features prominently). Finally, it is argued that the natural direction of research is now away from MHD and into kinetic territory.