Meridional circulation in turbulent protoplanetary disks

Context. 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.
Aims: This paper aims at examining whether such large-scale flows exist in turbulent protoplanetary disks.
Methods: 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.
Results: 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 α disk models are suggested by the simulations and should be the focus of future work.
Conclusions: 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 of the central star cannot be accounted for by that process as suggested by recent models based on viscous disk theory.