Production and damping of turbulence by particles in the solar nebula

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Abstract
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 model, our current model includes local generation, transport, and dissipation of turbulence. In particular, our derivation of the equation governing the kinetic energy of turbulence explicitly includes the damping of turbulence by particle drag. We have also included the kinetic pressure of the particles in both models, analogous to the turbulent pressure of the gas phase, and refined certain dimensionless constants of the flow. We present numerical results for particles 60 cm in radius. Both the switch to the one‐equation model and the inclusion of turbulence damping by particles tend to increase particle concentrations at the midplane of the nebula, but the particle pressure and the improved flow constants both decrease the particle concentration there. These effects nearly offset one another, supporting our previous conclusion that settling of particles to the midplane of the solar nebula is self‐limiting, so that direct accretion of planetesimals by gravitational instability is inhibited.

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