A Three-dimensional Model for the Evolution of Magnetohydrodynamic Turbulence in the Outer Heliosphere

We present a time-dependent, three-dimensional single-fluid model for the transport of magnetohydrodynamic (MHD) turbulence that is self-consistently evolving with a dynamic large-scale solar wind in the outer heliosphere. The emphasis is on the region beyond the termination shock, where the solar wind expands subsonically, as well as sub-Alfvénically and nonradially. In extension of earlier work, we refine the treatment of turbulence by considering, in addition to the Elsässer energies, a nonconstant energy difference (or residual energy) and by allowing each of these quantities its own characteristic correlation length scale. While the nonlinear effects in the equations for the Elsässer energies and their length scales are implemented using familiar von Kármán–Howarth style modeling of homogeneous MHD turbulence, the energy difference, which is not conserved in the absence of dissipation, and its length scale are modeled using distinct approaches. We also clarify the impact of the choice of measurement direction for correlation functions associated with two-dimensional fluctuations in transport models. Finally, we illustrate and study the solutions of the resulting six-equation model in detail.