  Based on the viscous disk theory, a number of recent studies have suggested
there is large scale meridional circulation in protoplanetary disks. Such a
flow could account for the presence of crystalline silicates, including
calcium- and aluminum-rich inclusions (CAIs), at large distances from the sun.
This paper aims at examining whether such large-scale flows exist in turbulent
protoplanetary disks. High-resolution global hydrodynamical and
magnetohydrodynamical (MHD) numerical simulations of turbulent protoplanetary
disks were used to infer the properties of the flow in such disks. By
performing hydrodynamic simulations using explicit viscosity, we demonstrate
that our numerical setup does not suffer from any numerical artifact. The
aforementioned meridional circulation is easily recovered in viscous and
laminar disks and is quickly established. In MHD simulations, the
magnetorotational instability drives turbulence in the disks. Averaging out the
turbulent fluctuations on a long timescale, the results fail to show any
large-scale meridional circulation. A detailed analysis of the simulations show
that this lack of meridional circulation is due to the turbulent stress tensor
having a vertical profile different from the viscous stress tensor. A simple
model is provided that successfully accounts for the structure of the flow in
the bulk of the disk. In addition to those results, possible deviations from
standard vertically averaged alpha disk models are suggested by the simulations
and should be the focus of future work. Global MHD numerical simulations of
fully ionized and turbulent protoplanetary disks are not consistent with the
existence of a large-scale meridional flow. As a consequence, the presence of
crystalline silicates at large distance for the central star cannot be
accounted for by that process as suggested by recent models based on viscous
disk theory.
