Transport and turbulence modeling of solar wind fluctuations

Magnetohydrodynamic (MHD) activity, including waves and turbulence, has been a focus of attention in solar wind research for several decades, owing to the wealth of available relevant spacecraft observations. Characterizations of the turbulence have generally been based on incompressible homogeneous turbulence theory. However, recent observations show that the fluctuations undergo systematic temporal evolution, suggesting couplings to large‐scale plasma and magnetic field inhomogeneities. Here we present in detail, and further develop, a theory of transport of small‐scale solar wind MHD turbulence, the preliminary results of which have been recently reported (Zhou and Matthaeus, Geophysical Research Letters, 16 , 755, 1989). Large‐scale plasma velocity and magnetic fields are specified, and small‐scale incompressible turbulence evolves in response to the associated inhomogeneities, as well as in accordance with modeled local nonlinear couplings. Dynamical equations based on a two length scale expansion are derived, from which the evolution of various wave number spectra may be computed, including magnetic and kinetic energies, cross helicity, induced electric field, and the corresponding helicities. Several simple analytic solutions predict, with increasing heliocentric distance, a decrease of the preponderance of outward traveling type Alfvénic fluctuations and a lowering of the small‐scale kinetic to magnetic energy ratio of small scale. Both of these are consistent with Helios and Voyager observations. The theory provides a basis for further computations that may be compared with statistical features of solar wind observations.