A Three-Dimensional MHD Simulation of the Solar Corona and Solar Wind with Turbulence Transport and Heating

We present results from a fully three-dimensional magnetohydrodynamic model of the solar corona and solar wind with transport of turbulence and turbulent heating. The model is based on Reynolds-averaged solar wind equations coupled with transport equations for turbulence energy, cross helicity and correlation scale. The model employs separate energy equations for protons and electrons and takes into account the effects of electron heat conduction, Coulomb collisions, radiative cooling, Reynolds stresses, eddy viscosity, and turbulent heating of protons and electrons. The computational domain extends from the coronal base to 5 AU and consists of two regions: the coronal region, 1-30 solar radii, and the solar wind region, from 30 solar radii to 5 AU. Steady-state solutions in both regions are constructed by time relaxation. Inner boundary conditions are specified using either a tilted-dipole approximation or synoptic solar magnetograms. A scaling factor for magnetograms and the strength of solar dipole are adjusted by comparison with Ulysses observations. Except for electron temperature, the model shows reasonable agreement with Ulysses data during its first and third fast latitude transits. We also derive a formula for the loss of angular momentum caused by the outflowing plasma. The formula takes into account the effects of turbulence. The simulation results show that turbulence can notably affect the Sun's loss of angular momentum.