Diffusion of Small Particles in a Nonuniform Atmosphere

The downward motion of small particles in an isothermal turbulence-free atmosphere has been studied for the case of variable diffusion coefficient, utilizing two models. In the first of these, the diffusion coefficient has been taken as an exponential function of altitude, while in the second the variation has been assumed parabolic. Analytic solutions have been obtained for one dimension and three dimensions for both models. The calculations, which have been restricted to the exponential case, show the development of a profile of constant shape which moves with the same velocity, independent of the mass of the particles. These results, which are derivable from our solution, are in agreement with the numerical work of Banister and Davis. It is also shown that the qualitative nature of the results for late time is independent of the initial distribution.