Turbulent Mixing in the Outer Solar Nebula

The effects of turbulence on the mixing of gases and dust in the outer Solarnebula are examined using 3-D MHD calculations in the shearing-boxapproximation with vertical stratification. The turbulence is driven by themagneto-rotational instability. The magnetic and hydrodynamic stresses in theturbulence correspond to an accretion time at the midplane about equal to thelifetimes of T Tauri disks, while accretion in the surface layers is thirtytimes faster. The mixing resulting from the turbulence is also fastest in thesurface layers. The mixing rate is similar to the rate of radial exchange oforbital angular momentum, so that the Schmidt number is near unity. Thevertical spreading of a trace species is well-matched by solutions of a dampedwave equation when the flow is horizontally-averaged. The damped wavedescription can be used to inexpensively treat mixing in 1-D chemical models.However, even in calculations reaching a statistical steady state, theconcentration at any given time varies substantially over horizontal planes,due to fluctuations in the rate and direction of the transport. In addition tomixing species that are formed under widely varying conditions, the turbulenceintermittently forces the nebula away from local chemical equilibrium. Thedifferent transport rates in the surface layers and interior may affectestimates of the grain evolution and molecular abundances during the formationof the Solar system.Comment: To appear in the Astrophysical Journal; 20 pages, 9 figure