Poisson Statistics in Distributions of Coalescing Droplets

Abstract

The statistical behavior of a collection of cloud droplets distributed by volume and possibly also with position in space is discussed by the use of master functions. Elementary considerations show that Poisson statistics are correct for the number of droplets in small ranges of volume or other parameters, and are a good approximation for extended ranges. A theorem is proved concerning the reduction in degree of correlation as droplet collection proceeds. A single numerical example of mathematical rather than physical interest is given.