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Cloud Droplet Coalescence: Statistical Foundations and a One-Dimensional Sedimentation Model1

Michael WarshawThe RAND Corporation, Santa Monica, Calif.

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Abstract

A derivation of the coalescence equation is given, stressing the statistical nature of the model and the questionable assumptions that are necessary to ensure its validity. It is concluded that the equation is probably adequate for real clouds, but inadequate when applied to small-volume coalescence experiments in the laboratory. The equation is then extended to include a sedimentation term and results are presented for droplet coalescence up to a radius of 50 μ. Significant numbers of larger droplets are produced in shorter times than those reported by other writers.

The distribution of droplets as a function of altitude both within and below a 500-m cloud is also given. After approximately 350 sec there appear to be more large droplets directly below the cloud base than within the cloud proper. An argument for the reasonableness of this result follows.

Lastly, some early results and cautionary statements about the use of “continuous collection” models above 50 μ are given.

Abstract

A derivation of the coalescence equation is given, stressing the statistical nature of the model and the questionable assumptions that are necessary to ensure its validity. It is concluded that the equation is probably adequate for real clouds, but inadequate when applied to small-volume coalescence experiments in the laboratory. The equation is then extended to include a sedimentation term and results are presented for droplet coalescence up to a radius of 50 μ. Significant numbers of larger droplets are produced in shorter times than those reported by other writers.

The distribution of droplets as a function of altitude both within and below a 500-m cloud is also given. After approximately 350 sec there appear to be more large droplets directly below the cloud base than within the cloud proper. An argument for the reasonableness of this result follows.

Lastly, some early results and cautionary statements about the use of “continuous collection” models above 50 μ are given.

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