A Numerical Simulation of the Gravitational Coagulation Process for Cloud Droplets

Abstract

The stochastic collection process of a large drop capturing a spectrum of randomly positioned small droplets is investigated by Monte Carlo simulation, and sample growth statistics from 32 independent trials are analyzed and compared to the values obtained from integrating the growth equation. It is found that the sample mean drop mass is compatible with that predicted by the growth equation. However, the sample mean radius is significantly less than the value resulting from continuous growth at the end of 1000 sec. The large-drop growth rate in a polydisperse cloud with an empirical spectrum is compared with that in a monodisperse cloud with the same liquid water content and the same mean volume radius. The growth rate is shown to be considerably smaller in the monodisperse cloud even though it is represented by droplets with a size that is larger than three-fourths of the droplets in the polydisperse spectrum. The problem of cloud spectrum evolution is investigated using the kinetic equation with a set of the empirical Khrgian and Mazin spectra as initial conditions. It seems that for clouds with the same liquid water content the magnitude of R_av is crucial in determining the rate of the coagulation growth. Computation was also made with an initial normal distribution spectrum. An “expected” spectrum of large droplets computed from a version of the kinetic equation for the large size end is compared with random sampling results, and substantial differences between them are found.