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