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Register a new userMHD Turbulence: A Biased Review
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Alexander Schekochihin
Publication date
2020
fields
Physics
and research's language is
English
Authors
Alexander A. Schekochihin
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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 Beresnyaks objection that Boldyrevs alignment theory violates the RMHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrevs 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 Beresnyaks Kolmogorov scaling of the dissipation cutoff with Boldyrevs 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.
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Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.
The rate of magnetic field diffusion plays an essential role in several astrophysical plasma processes. It has been demonstrated that the omnipresent turbulence in astrophysical media induces fast magnetic reconnection, which consequently leads to large-scale magnetic flux diffusion at a rate independent of the plasma microphysics. This process is called ``reconnection diffusion (RD) and allows for the diffusion of fields which are dynamically important. The current theory describing RD is based on incompressible magnetohydrodynamic (MHD) turbulence. In this work, we have tested quantitatively the predictions of the RD theory when magnetic forces are dominant in the turbulence dynamics (Alfv{e}nic Mach number $M_A < 1$). We employed the textsc{Pencil Code} to perform numerical simulations of forced MHD turbulence, extracting the values of the diffusion coefficient $eta_{RD}$ using the Test-Field method. Our results are consistent with the RD theory ($eta_{RD} sim M_A^{3}$ for $M_A < 1$) when turbulence approaches the incompressible limit (sonic Mach number $M_S lesssim 0.02$), while for larger $M_S$ the diffusion is faster ($eta_{RD} sim M_A^{2}$). This work shows for the first time simulations of compressible MHD turbulence with the suppression of the cascade in the direction parallel to the mean magnetic field, which is consistent with incompressible weak turbulence theory. We also verified that in our simulations the energy cascading time does not follow the scaling with $M_A$ predicted for the weak regime, in contradiction with the RD theory assumption. Our results generally support and expand the RD theory predictions.
We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD turbulence, we study the high Reynolds number magnetohydrodynamic turbulence for helicity injection at a scale that is much smaller than the scale of energy injection. In a short range of scales larger than the forcing scale of magnetic helicity, a bottleneck-like effect appears, which results in a local reduction of the spectral slope. The slope changes in a domain with a high level of relative magnetic helicity, which determines that part of the magnetic energy related to the helical modes at a given scale. If the relative helicity approaches unity, the spectral slope tends to $-3/2$. We show that this energy pileup is caused by an inverse cascade of magnetic energy associated with the magnetic helicity. This negative energy flux is the contribution of the pure magnetic-to-magnetic energy transfer, which vanishes in the non-helical limit. In the context of astrophysical dynamos, our results indicate that a large-scale dynamo can be affected by the magnetic helicity generated at small scales. The kinetic helicity, in particular, is not involved in the process at all. An interesting finding is that an inverse cascade of magnetic energy can be provided by a small-scale source of magnetic helicity fluctuations without a mean injection of magnetic helicity.
The current understanding of MHD turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $lambdasim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $lambda$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the sub-inertial, reconnection interval of MHD turbulence, with the Fourier energy spectrum $E(k_perp)propto k_perp^{-5/2}$, where $k_perp$ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas ($Pm$), where the reconnection scale is found to be $lambda/Lsim S_L^{-4/7}Pm^{-2/7}$.
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.
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