Turbulent Mixing in the Outer Solar Nebula

The effects of turbulence on the mixing of gases and dust in the outer solar nebula are examined using three-dimensional MHD calculations in the shearing-box approximation with vertical stratification. The turbulence is driven by the magnetorotational instability. The magnetic and hydrodynamic stresses in the turbulence correspond to an accretion time at the midplane about equal to the lifetimes of T Tauri disks, while accretion in the surface layers is 30 times faster. The mixing resulting from the turbulence is also fastest in the surface layers. The mixing rate is similar to the rate of radial exchange of orbital angular momentum, so that the Schmidt number is near unity. The vertical spreading of a trace species is well matched by solutions of a damped wave equation when the flow is horizontally averaged. The damped wave description can be used to inexpensively treat mixing in one-dimensional chemical models. However, even in calculations reaching a statistical steady state, the concentration at any given time varies substantially over horizontal planes, due to fluctuations in the rate and direction of the transport. In addition to mixing species that are formed under widely varying conditions, the turbulence intermittently forces the nebula away from local chemical equilibrium. The different transport rates in the surface layers and interior may affect estimates of the grain evolution and molecular abundances during the formation of the solar system.