The transport of low-frequency turbulence in astrophysical flows. II. Solutions for the super-Alfvénic solar wind

Zank et al. developed a turbulence transport model for low-frequency incompressible magnetohydrodynamic (MHD) turbulence in inhomogeneous flows in terms of the energy corresponding to forward and backward propagating modes, the residual energy, the correlation lengths corresponding to forward and backward propagating modes, and the correlation length of the residual energy. We apply the Zank et al. model to the super-Alfvénic solar wind i.e., $|U|\gg |V_A|$ and solve the coupled equations for two cases, the first being the heliosphere from 0.29 to 5 AU with and without the Alfvén velocity, and the second being the "entire" heliosphere from 0.29 to 100 AU in the absence of the Alfvén velocity. The model shows that (1) shear driving is responsible for the in situ generation of backward propagating modes, (2) the inclusion of the background magnetic field modifies the transport of turbulence in the inner heliosphere, (3) the correlation lengths of forward and backward propagating modes are almost equal beyond ∼30 AU, and (4) the fluctuating magnetic and kinetic energies in MHD turbulence are in approximate equipartition beyond ∼30 AU. A comparison of the model results with observations for the two cases shows that the model reproduces the observations quite well from 0.29 to 5 AU. The outer heliosphere ($>1$ AU) observations are well described by the model. The temporal and latitudinal dependence of the observations makes a detailed comparison difficult but the overall trends are well captured by the models. We conclude that the results are a reasonable validation of the Zank et al. model for the super-Alfvénic solar wind.