A conceptual model for entrainment in cumulus clouds

Abstract

Cumulus clouds are generally modeled as a plume, and the model works well up until the cloud base is encountered, beyond which the continuously entraining model does not appear appropriate. Although it has been known for a long time that cumulus clouds have very little lateral entrainment, the reason for it is not evident. An expression for the mean streamwise velocity profile as a Gaussian multiplied by a fourth-order polynomial factor is hereby proposed such that the mass and momentum fluxes are decoupled. This model suggests that cumulus clouds differ from other shear flows in that the former need not interact with the ambient for some downstream distance. The proposed model replicates a number of characteristics of cumulus clouds like a conserved mass flux with varying momentum flux, and may therefore be employed to describe them, in a time-averaged sense, beyond the cloud base.