\u00a0 \u00a0 \u00a0The recent achievement of the Parker Solar Probe, that of entering into the magnetically dominated
\nsolar corona [1], offers an unprecedented opportunity to test the various theoretical
\npredictions we have on how turbulence in the solar corona develops and evolves. The long-standing
\ncoronal heating problem [2,3] and the associated solar wind acceleration problem [4] are one of the
\nlast unsolved classical astrophysical problems, with plasma heating through wave turbulence being a
\nstrong contender for a solution. Turbulence, in its true sense a strongly nonlinear process, is yet to be
\nfully understood. However, in the case of a magnetized plasma, as the solar corona and solar wind,
\ndifferent phenomenological models exist, aimed at explaining some of the expected properties of
\nplasma turbulence and its generation mechanism [5,6]. In the \u2018Kolmogorovian\u2019 fashion, some of the
\nlaws of plasma turbulence are derived by dimensional analysis under a series of assumptions. The
\nphenomenological models have at their core the Els\u00e4sser formulation [7] of the conservation laws
\ndescribing the evolution of plasma at the largest scales, the magnetohydrodynamic equations. These
\nequations, at their simplest homogeneous and incompressible form, tell us that fluctuations in such a
\nplasma are waves propagating either parallel or anti-parallel to the local magnetic field, called Alfv\u00e9n
\nwaves. Additionally, it is clear that the only wave interactions that couple nonlinearly, and thus are
\nable to generate turbulence, are collisions among counter-propagating Alfv\u00e9n waves [8,9]. This simple
\nobservation is still at the basis of much of the available theoretical and numerical models of how
\nturbulence is generated and maintained in the solar corona. In the specific case of the solar corona,
\nthe picture is the following: at the photospheric level, the convective motions continually excite waves
\npropagating away from the Sun and into the solar corona along the magnetic field lines [10]. These
\nwaves encounter a varying wave speed along their propagation direction, leading to wave reflections.
\nThe outward-propagating waves and the reflected, Sunward-propagating waves are mutually
\ndeformed as they pass through each other, which leads to a turbulent cascade, bringing down the
\nwave energy to scales where it can be dissipated into heat. Models of the solar corona and solar wind
\nbased on this phenomenology are the incompressible or reduced-MHD models [11,12,13]. Within the
\nframe of such models, the new observations immediately lead to some never-before verifiable
\nquestions: what happens to the turbulent cascade at the critical Alfv\u00e9n point, where the Sunward propagating
\nwaves are stationary in the frame of the Sun, due to the solar wind speed being equal to
\nthe propagation speed of the waves? Does it \u2018turn off\u2019? The current theoretical models seem to
\ndisagree in what concerns the nature of turbulence around this critical point [14]. On the other hand,
\ntheoretical models yield different predictions of energy spectra parallel and perpendicular to the
\nmean magnetic field, with some supporting the long-held principle of critical balance between
\nnonlinear and linear timescales, while others resulting in similar spectra along and across the magnetic
\nfield, violating critical balance [15,16].<\/p>\n
A different theoretical approach, allowing for `nearly-incompressible` dynamics based on the first
\norders of the compressible magnetohydrodynamic equations expanded in terms of compressibility as
\na small parameter, yields that the turbulent dynamics in a strongly magnetized plasma as the solar
\ncorona are not mediated by waves, but basically evolve quasi-two dimensionally in planes
\nperpendicular to the magnetic field [14,16]. Waves propagating through this 2D turbulence are
\nthemselves deformed and acquire spectral characteristics of the background turbulence. Such models
\npredict that turbulence is unaffected by the existence of a critical Alfv\u00e9n point for plasma beta regimes
\nencountered in the corona and solar wind.<\/p>\n
Recently, the assumptions of incompressibility and\/or inhomogeneity became partly or fully
\nrelaxed through various theoretical works, leading to a much more complex picture of turbulence
\nevolution in the solar corona. In this full magnetohydrodynamic picture, the Alfv\u00e9n wave is no longer
\nthe unique mode, magnetosonic waves being also present. A multitude of nonlinear couplings are
\nallowed in this case in addition to the counterpropagating Alfv\u00e9n wave collisions, which is further
\nenriched by allowing the plasma to be inhomogeneous in the planes perpendicular to the magnetic
\nfield [17]. For example, the parametric decay of Alfv\u00e9n waves, leading to density and velocity
\nperturbations along the magnetic field, was shown to greatly increase the reflection rate of Alfv\u00e9n
\nwaves, leading to a stronger nonlinear cascade and heating than in the incompressible models [18,19].
\nAdditionally, by allowing for the existence of magnetic flux tubes with different physical properties,
\nnew wave types appear, such as surface and body modes, propagating along the flux tubes. Some of
\nthese surface waves can lead to a nonlinear cascade of wave energy and turbulence already through
\nunidirectional propagation; that is, without the need of collisions of counterpropagating waves
\n[20,21]. Stemming from the many-fold increase in complexity of the inhomogeneous and fully
\ncompressible models, no simple analytical predictions can be made, as in the case of the previously
\npresented theoretical models. However, direct numerical simulations allow us to extract some
\nstatistical parameters of the fluctuation fields that can be compared to the in-situ measurements of
\nParker Solar Probe.<\/p>\n
Clearly, we are at a crucial moment for the different theoretical models of solar coronal and solar
\nwind turbulence, as they need to undergo stringent verifications based on the most recent data we
\nhave from the Parker Solar Probe. This meeting would constitute an ideal occasion for the clash of the
\navailable theoretical models, both among them and with the final challenge, that of in-situ evidence.
\nIt is also an ideal setting to find observables that cannot be explained on the basis of the available
\nmodels, therefore stimulating the development of new theoretical models which incorporate
\nadditional physics and help better explain the nature of solar wind turbulence.<\/p>\n
1. Kasper, J. C. et al.; Physical Review Letters, Volume 127, Issue 25, article id.255101, 2021
\n2. Van Doorsselaere, T. et al.; Space Science Reviews, Volume 216, Issue 8, article id.140, 2020
\n3. Viall, N. M. et al.; Space Physics and Aeronomy, GMS Vol. 258, AGU, 2021
\n4. Viall, N. M. et al.; JGR: Space Physics, Volume 125, Issue 7, article id. e26005, 2020
\n5. Beresnyak, A.; LRCA, Volume 5, Issue 1, article id. 2, 59 pp, 2019
\n6. Schekochihin, A.; eprint arXiv:2010.00699, 2020
\n7. Els\u00e4sser, W.; Physical Review, vol. 79, Issue 1, pp. 183-183, 1950
\n8. Iroshnikov, P. S.; Astronomicheskii Zhurnal, Vol. 40, p.742, 1963
\n9. Kraichnan, R. H.; Physics of Fluids, Volume 8, Issue 7, p.1385-1387, 1965
\n10. Tomczyk, S. et al.; Science, Volume 317, Issue 5842, pp. 1192-, 2007
\n11. Matthaeus, W. H. et al.; ApJ, Volume 523, Issue 1, pp. L93-L96, 1999
\n12. van Ballegooijen, A. A. et al.; ApJ, Volume 821, Issue 2, article id. 106, 19 pp., 2016
\n13. Chandran, B. et al.; JPP, Volume 85, Issue 4, article id. 905850409, 2019
\n14. Adhikari, L. et al.; ApJ, Volume 876, Issue 1, article id. 26, 2019
\n15. Telloni, D. et al.; ApJ, Volume 887, Issue 2, article id. 160, 2019
\n16. Zank, G. P. et al.; ApJ, Volume 900, Issue 2, id.115, 2020
\n17. Magyar, N. et al; ApJ, Volume 873, Issue 1, article id. 56, 2019
\n18. Shoda, M. et al; ApJL, Volume 880, Issue 1, article id. L2, 2019
\n19. Matsumoto, T.; MNRAS, Volume 500, Issue 4, pp.4779-4787, 2021
\n20. Magyar, N. et al.; ApJ, Volume 882, Issue 1, article id. 50, 2019
\n21. Magyar, N. et al.; ApJ, Volume 907, Issue 1, id.55, 2021<\/p>\n","protected":false},"excerpt":{"rendered":"
\u00a0 \u00a0 \u00a0The recent achievement of the Parker Solar Probe, that of entering into the magnetically dominated solar corona [1], offers an unprecedented opportunity to test the various theoretical predictions we have on how turbulence in the solar corona develops and evolves. The long-standing coronal heating problem [2,3] and the associated solar wind acceleration problem […]<\/p>\n","protected":false},"author":46,"featured_media":0,"parent":73,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-40","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/pages\/40","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/users\/46"}],"replies":[{"embeddable":true,"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":6,"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/pages\/40\/revisions"}],"predecessor-version":[{"id":48,"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/pages\/40\/revisions\/48"}],"up":[{"embeddable":true,"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/pages\/73"}],"wp:attachment":[{"href":"https:\/\/teams.issibern.ch\/turbulencesolarcorona\/wp-json\/wp\/v2\/media?parent=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}