Comments on the diffusion model of turbulent mixing

Several recent investigations of post--main-sequence stellar evolution have used a diffusion model of turbulent mixing, and each author has used a different variation. We justify the diffusion model in the framework of a statistical theory of turbulence and show that the difference between the two diffusion equations that have been proposed is related to an ambiguity in the definition of a Lagrangian hydrodynamical calculation by finite differences in the presence of turbulence. We present difference equations for solving the diffusion equation which theory and experience indicate are free of numerical difficulties. (AIP)