Eddy diffusion and settling speed in blown snow

In an analysis of observations of snow density taken in the Arctic, Sommerfeld and Businger have shown that the ratio of eddy diffusivity for blowing snow is almost an order of magnitude larger than the eddy viscosity derived from the wind profile. In this paper an attempt has been made to explain how this eddy diffusivity could be so large. It has been shown that for fall velocities greater than the standard deviation of the vertical wind component the average snow density is mainly determined by the upward-moving snow particles. From a combination of this result with a simple generalization of Prandtl's mixing length concept an effective eddy diffusivity has been derived which indeed may become as large as that observed. The effect of turbulence on the average settling speed of snow particles has also been analyzed. The average settling speed is considerably reduced by turbulence when the average wind speed is greater than 20 m/sec. The reduction becomes particularly significant if the settling speed in calm air is small (e.g., 50 cm/sec), in which case it is sufficient to give a reasonable description of the Antarctic data reported by Mellor and Radok.