Theoretical Analysis of Entrainment-Mixing Process at Cloud Boundaries

We summarize results obtained in the series of the theoretical studies considering turbulent mixing near cloud boundaries. In most cases time evolution of microphysical parameters and of size distributions is investigated solving diffusion-evaporation equation describing time and spatial evolution of size distribution function within either closed mixing volume or in open region in the vicinity of the cloud-dry air interface. Non-dimensional parameters determining the time dependence of microphysical variables and final state are introduced and analyzed. It is shown that a) mixing always leads to droplet spectrum broadening, b) effective radius changes within the narrow interface zone at cloud edge and remains nearly constant within the cloud body; c) there is a sole non-dimensional parameter determining whether the cloud will grow by involving of dry air or evaporate as a result of mixing; d) mixing at cloud edge leads to formation of a humid shell with thickness of a few hundred meters. Theoretical results are compared with high frequency in-situ measurements.