  We present full 2 Pi global 3-D stratified MHD simulations of accretion
disks. We interpret our results in the context of proto-planetary disks. We
investigate the turbulence driven by the magneto-rotational instability (MRI)
using the PLUTO Godunov code in spherical coordinates with the accurate and
robust HLLD Riemann solver. We follow the turbulence for more than 1500 orbits
at the innermost radius of the domain to measure the overall strength of
turbulent motions and the detailed accretion flow pattern. We find that regions
within two scale heights of the midplane have a turbulent Mach number of about
0.1 and a magnetic pressure two to three orders of magnitude less than the gas
pressure, while outside three scale heights the magnetic pressure equals or
exceeds the gas pressure and the turbulence is transonic, leading to large
density fluctuations. The strongest large-scale density disturbances are spiral
density waves, and the strongest of these waves has m=5. No clear meridional
circulation appears in the calculations because fluctuating radial pressure
gradients lead to changes in the orbital frequency, comparable in importance to
the stress gradients that drive the meridional flows in viscous models. The net
mass flow rate is well-reproduced by a viscous model using the mean stress
distribution taken from the MHD calculation. The strength of the mean turbulent
magnetic field is inversely proportional to the radius, so the fields are
approximately force-free on the largest scales. Consequently the accretion
stress falls off as the inverse square of the radius.

Earth and Planetary Astrophysics