Two Dimensional Diffusion of a Polydispersed Cloud

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Abstract
The two dimensional diffusion of a polydispersed cloud in the surface layers of the atmosphere is treated by integrating the monodispersed solution over a distribution of particle sizes. An analytic solution is constructed from consideration of the non-dimensional parameters upon which the value of the integrals depend. It is possible then to construct criteria for neglecting either the dispersion of particle terminal velocity or the diffusive action of turbulent eddies. The criteria are fully worked out for the case of a log normal distribution of mass versus terminal velocity. For this case, the criteria depend only on the logarithm of the ratios of the median terminal velocity to the diffusion velocity, and on the logarithmic standard deviation of the terminal velocity distribution.

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