Three Models for the Coalescence Growth of Cloud Drops

Daniel T. Gillespie Earth and Planetary Sciences Division, Naval Weapons Center, China Lake, Calif. 93555

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Abstract

In an attempt to resolve the confusion over the “stochastic completeness” of the stochastic coalescence equation, an analysis is made of an idealized cloud consisting of a number of large “drops” falling through very many small, equal-size “droplets” with a constant drop-droplet collection kernel. It is shown how three superficially equivalent physical interpretations of the drop-droplet collection kernel lead to three quite different models for the growth of the drops. The implications of and relationships between the models are drawn out in detail. The stochastic completeness controversy is apparently a consequence of a failure to distinguish clearly between two of these three conceptual approaches.

Abstract

In an attempt to resolve the confusion over the “stochastic completeness” of the stochastic coalescence equation, an analysis is made of an idealized cloud consisting of a number of large “drops” falling through very many small, equal-size “droplets” with a constant drop-droplet collection kernel. It is shown how three superficially equivalent physical interpretations of the drop-droplet collection kernel lead to three quite different models for the growth of the drops. The implications of and relationships between the models are drawn out in detail. The stochastic completeness controversy is apparently a consequence of a failure to distinguish clearly between two of these three conceptual approaches.

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