The 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 [4] are one of the
last unsolved classical astrophysical problems, with plasma heating through wave turbulence being a
strong contender for a solution. Turbulence, in its true sense a strongly nonlinear process, is yet to be
fully understood. However, in the case of a magnetized plasma, as the solar corona and solar wind,
different phenomenological models exist, aimed at explaining some of the expected properties of
plasma turbulence and its generation mechanism [5,6]. In the ‘Kolmogorovian’ fashion, some of the
laws of plasma turbulence are derived by dimensional analysis under a series of assumptions. The
phenomenological models have at their core the Elsässer formulation [7] of the conservation laws
describing the evolution of plasma at the largest scales, the magnetohydrodynamic equations. These
equations, at their simplest homogeneous and incompressible form, tell us that fluctuations in such a
plasma are waves propagating either parallel or anti-parallel to the local magnetic field, called Alfvén
waves. Additionally, it is clear that the only wave interactions that couple nonlinearly, and thus are
able to generate turbulence, are collisions among counter-propagating Alfvén waves [8,9]. This simple
observation is still at the basis of much of the available theoretical and numerical models of how
turbulence is generated and maintained in the solar corona. In the specific case of the solar corona,
the picture is the following: at the photospheric level, the convective motions continually excite waves
propagating away from the Sun and into the solar corona along the magnetic field lines [10]. These
waves encounter a varying wave speed along their propagation direction, leading to wave reflections.
The outward-propagating waves and the reflected, Sunward-propagating waves are mutually
deformed as they pass through each other, which leads to a turbulent cascade, bringing down the
wave energy to scales where it can be dissipated into heat. Models of the solar corona and solar wind
based on this phenomenology are the incompressible or reduced-MHD models [11,12,13]. Within the
frame of such models, the new observations immediately lead to some never-before verifiable
questions: what happens to the turbulent cascade at the critical Alfvén point, where the Sunward propagating
waves are stationary in the frame of the Sun, due to the solar wind speed being equal to
the propagation speed of the waves? Does it ‘turn off’? The current theoretical models seem to
disagree in what concerns the nature of turbulence around this critical point [14]. On the other hand,
theoretical models yield different predictions of energy spectra parallel and perpendicular to the
mean magnetic field, with some supporting the long-held principle of critical balance between
nonlinear and linear timescales, while others resulting in similar spectra along and across the magnetic
field, violating critical balance [15,16].
A different theoretical approach, allowing for `nearly-incompressible` dynamics based on the first
orders of the compressible magnetohydrodynamic equations expanded in terms of compressibility as
a small parameter, yields that the turbulent dynamics in a strongly magnetized plasma as the solar
corona are not mediated by waves, but basically evolve quasi-two dimensionally in planes
perpendicular to the magnetic field [14,16]. Waves propagating through this 2D turbulence are
themselves deformed and acquire spectral characteristics of the background turbulence. Such models
predict that turbulence is unaffected by the existence of a critical Alfvén point for plasma beta regimes
encountered in the corona and solar wind.
Recently, the assumptions of incompressibility and/or inhomogeneity became partly or fully
relaxed through various theoretical works, leading to a much more complex picture of turbulence
evolution in the solar corona. In this full magnetohydrodynamic picture, the Alfvén wave is no longer
the unique mode, magnetosonic waves being also present. A multitude of nonlinear couplings are
allowed in this case in addition to the counterpropagating Alfvén wave collisions, which is further
enriched by allowing the plasma to be inhomogeneous in the planes perpendicular to the magnetic
field [17]. For example, the parametric decay of Alfvén waves, leading to density and velocity
perturbations along the magnetic field, was shown to greatly increase the reflection rate of Alfvén
waves, leading to a stronger nonlinear cascade and heating than in the incompressible models [18,19].
Additionally, by allowing for the existence of magnetic flux tubes with different physical properties,
new wave types appear, such as surface and body modes, propagating along the flux tubes. Some of
these surface waves can lead to a nonlinear cascade of wave energy and turbulence already through
unidirectional propagation; that is, without the need of collisions of counterpropagating waves
[20,21]. Stemming from the many-fold increase in complexity of the inhomogeneous and fully
compressible models, no simple analytical predictions can be made, as in the case of the previously
presented theoretical models. However, direct numerical simulations allow us to extract some
statistical parameters of the fluctuation fields that can be compared to the in-situ measurements of
Parker Solar Probe.
Clearly, we are at a crucial moment for the different theoretical models of solar coronal and solar
wind turbulence, as they need to undergo stringent verifications based on the most recent data we
have from the Parker Solar Probe. This meeting would constitute an ideal occasion for the clash of the
available theoretical models, both among them and with the final challenge, that of in-situ evidence.
It is also an ideal setting to find observables that cannot be explained on the basis of the available
models, therefore stimulating the development of new theoretical models which incorporate
additional physics and help better explain the nature of solar wind turbulence.
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