The validity of the kinetic collection equation revisited
نویسندگان
چکیده
The kinetic collection equation (KCE) describes the evolution of the average droplet spectrum due to successive events of collision and coalescence. Fluctuations and non-zero correlations present in the stochastic coalescence process would imply that the size distributions may not be correctly modeled by the KCE. In this study we expand the known analytical studies of the coalescence equation with some numerical tools such as Monte Carlo simulations of the coalescence process. The validity time of the KCE was estimated by calculating the maximum of the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value. A good correspondence between the analytical and the numerical approaches was found for all the kernels. The expected values from analytical solutions of the KCE, were compared with true expected values of the stochastic collection equation (SCE) estimated with Gillespie’s Monte Carlo algorithm and analytical solutions of the SCE, after and before the breakdown time. The possible implications for cloud physics are discussed, in particular the possibility of application of these results to kernels modified by turbulence and electrical processes.
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Interactive comment on “The validity of the kinetic collection equation revisited” by L. Alfonso et al
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Interactive comment on “The validity of the kinetic collection equation revisited” by L. Alfonso et al
The paper is dedicated to the analysis of the properties of the kinetic collection equation (KCE) for several types of kernels allowing the analytical solution. The solution of the KCE is compared with a more precise solution of the stochastic collision equation. To estimate the validity of KCE, the stochastic collision equation is solved by the Monte Carlo method. The analysis of the behavior ...
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