Production and damping of turbulence by particles in the solar nebula

We have developed a "one-equation" model for the turbulent boundary layer. surrounding the midplane of the solar nebula and compared it with the "zero -equation" (Prandtl) model used in our previous work. Unlike the Prandtl mo del, our current model includes local generation, transport, and dissipatio n of turbulence. In particular, our derivation of the equation governing th e kinetic energy of turbulence explicitly includes the damping of turbulenc e by particle drag. We have also included the kinetic pressure of the parti cles in both models, analogous to the turbulent pressure of the gas phase, and refined certain dimensionless constants of the flow. We present numeric al results for particles 60 cm in radius. Both the switch to the one-equati on model and the inclusion of turbulence damping by particles tend to incre ase particle concentrations at the midplane of the nebula, but the particle pressure and the improved flow constants both decrease the particle concen tration there. These effects nearly offset one another, supporting our prev ious conclusion that settling of particles to the midplane of the solar neb ula is self-limiting, so that direct accretion of planetesimals by gravitat ional instability is inhibited.