The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.

The thermal plasma beta in the solar wind and the solar corona is of the order of and . Zank et al. developed 2D and slab turbulence transport model equations of the order of and using nearly incompressible (NI) theory. We solve the Zank et al. NI MHD coupled turbulence transport equations for the inhomogeneous solar wind from 1 to 75 au, and compare the numerical solutions to Voyager 2 observations. We find that (1) the 2D turbulent energies are larger than the slab energies throughout the heliosphere; (2) the 2D turbulent energies decrease more slowly than the slab turbulent energies within ∼4 au, while the slab energies increase and the 2D energies flatten in the outer heliosphere; (3) the 2D normalized cross-helicity decreases faster than the slab normalized cross-helicity within ∼4 au; (4) the 2D normalized residual energy is more magnetically dominated than the slab; (5) the variance of density fluctuations decreases more rapidly than within ∼10 au, and more slowly in the outer heliosphere; and (6) the observed variance in magnetic field fluctuations as a function of the thermal plasma beta is described by the two-component turbulence transport model. In summary, the NI MHD two-component Zank et al. turbulence transport model captures the behavior of the forward, backward, and total energies in the fluctuating Elsässer variables, the variance in the magnetic field, kinetic energy, and density fluctuations, the cross-helicities and residual energies, the thermal temperature and plasma beta, and the various correlation lengths.

A new model describing the transport and evolution of turbulence in the quiet solar corona is presented. In the low plasma beta environment, transverse photospheric convective fluid motions drive predominantly quasi-2D (nonpropagating) turbulence in the mixed-polarity “magnetic carpet,” together with a minority slab (Alfvénic) component. We use a simplified sub-Alfvénic flow velocity profile to solve transport equations describing the evolution and dissipation of turbulence from (including the Alfvén surface). Typical coronal base parameters are used, although one model uses correlation lengths derived observationally by Abramenko et al., and the other assumes values 10 times larger. The model predicts that (1) the majority quasi-2D turbulence evolves from a balanced state at the coronal base to an imbalanced state, with outward fluctuations dominating, at and beyond the Alfvén surface, i.e., inward turbulent fluctuations are dissipated preferentially; (2) the initially imbalanced slab component remains imbalanced throughout the solar corona, being dominated by outwardly propagating Alfvén waves, and wave reflection is weak; (3) quasi-2D turbulence becomes increasingly magnetized, and beyond , the kinetic energy is mainly in slab fluctuations; (4) there is no accumulation of inward energy at the Alfvén surface; (5) inertial range quasi-2D rather than slab fluctuations are preferentially dissipated within ; and (6) turbulent dissipation of quasi-2D fluctuations is sufficient to heat the corona to temperatures K within , consistent with observations that suggest that the fast solar wind is accelerated most efficiently between .

A primary goal of the Parker Solar Probe (PSP) Mission is to answer the outstanding question of how the solar corona plasma is heated to the high temperatures needed for the acceleration of the solar wind. Various heating mechanisms have been suggested, but one that is gaining increasing credence is associated with the dissipation of low frequency magnetohyrodynamic (MHD) turbulence. However, the MHD turbulence models come in several flavors: one in which outwardly propagating Alfvén waves experience reflection from the large-scale flow and density gradients associated with the solar corona, and the resulting counterpropagating Alfvén waves couple nonlinearly to produce quasi-2D turbulence that dissipates and heats the corona, thereby driving the solar wind. The second approach eschews a dominant outward flux of Alfvén waves but argues instead that quasi-2D turbulence dominates the lower coronal plasma and is generated in the constantly upwelling magnetic carpet, experiencing dissipation as it is advected through the corona and into the solar wind, yielding temperatures in the corona that exceed a million degrees. We review the two turbulence models, describe the modeling that has been done, and relate PSP observations to the basic predictions of both models. Although PSP measurements are made in the super-Alfvénic solar wind, the observations are close to the coronal region, thus providing a glimpse into the likely properties of coronal turbulence. Observations of low-frequency MHD turbulence by PSP in the super-Alfvénic solar wind allow us to place constraints on models of the turbulently heated solar corona that drive the supersonic solar wind.