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 origin, structure, and propagation characteristics of a switchback are compelling questions posed by Parker Solar Probe (PSP) observations of velocity spikes and magnetic field reversals. By assuming interchange reconnection between coronal loop and open magnetic field, we show that this results in the generation of upward (into the heliosphere) and downward complex structures propagating at the fast magnetosonic speed (i.e., the Alfvén speed in the low plasma beta corona) that can have an arbitrary radial magnetic field deflection, including “S-shaped.” We derive the evolution equation for the switchback radial magnetic field as it propagates through the inhomogeneous supersonic solar corona. An analytic solution for arbitrary initial conditions is used to investigate the properties of a switchback propagating from launch ∼6 to ∼35 R _⊙ where PSP observed switchbacks during its first encounter. We provide a detailed comparison to an example event, showing that the magnetic field and plasma solutions are in accord with PSP observations. For a simple single switchback, the model predicts either a single or a double-humped structure; the former corresponding to PSP observing either the main body or the flanks of the switchback. The clustering of switchbacks and their sometimes complicated structure may be due to the formation of multiple closely spaced switchbacks created by interchange reconnection with numerous open and loop magnetic field lines over a short period. We show that their evolution yields a complex, aggregated group of switchbacks that includes “sheaths” with large-amplitude radial magnetic field and velocity fluctuations.

The New Horizons Solar Wind Around Pluto (NH SWAP) instrument has provided the first direct observations of interstellar and He pickup ions (PUIs) at distances between ∼11.26 and 38 au in the solar wind. The observations demonstrate that the distant solar wind beyond the hydrogen ionization cavity is indeed mediated by PUIs. The creation of PUIs modifies the underlying low-frequency turbulence field responsible for their own scattering. The dissipation of these low-frequency fluctuations serves to heat the solar wind plasma, and accounts for the observed non-adiabatic solar wind temperature profile and a possible slow temperature increase beyond ∼30 au. We develop a very general theoretical model that incorporates PUIs, solar wind thermal plasma, the interplanetary magnetic field, and low-frequency turbulence to describe the evolution of the large-scale solar wind, PUIs, and turbulence from 1–84 au, the structure of the perpendicular heliospheric termination shock, and the transmission of turbulence into the inner heliosheath, extending the classical models of Holzer and Isenberg. A detailed comparison of the theoretical model solutions and observations derived from the Voyager 2 and NH SWAP data sets shows excellent agreement between the two for reasonable physical parameters.

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 .