Theoretical analysis of the entrainment-mixing process at cloud boundaries. Part I: Droplet size distributions and humidity within the interface zone

The problem of a complex entrainment-mixing process is analyzed by solving a diffusion-evaporation equation for an open region in the vicinity of the cloud-dry air interface. Upon normalization the problem is reduced to a one-parametric one, the governing parameter being the potential evaporation parameter R proportional to the ratio of saturation deficit in the dry air to the available liquid water content in the cloud air. As distinct from previous multiple studies analyzing mixing within closed adiabatic volumes, we consider a principally nonstationary problem that never leads to a homogeneous equilibrium state. It is shown that at R < -1 the cloud edge shifts toward the cloud; that is, the cloud dissipates due to mixing with dry air, and the cloud volume decreases. If R > -1, the cloud edge shifts outside; that is, the mixing leads to an increase in the cloud volume. The time evolution of droplet size distribution and its moments, as well as the relative humidity within the expanding cloud-dry air interface, are calculated and analyzed. It is shown that the values of the mean volume radii rapidly decrease within the interface zone in the direction away from the cloud, indicating significant changes in the cloud edge microstructure. Scattering diagrams plotted for the cloud edge agree well with high-frequency in situ measurements, corroborating the reliability of the proposed approach. It is shown that the humidity front moves toward dry air faster than the front of liquid water content. As a result, the mixing leads to formation of a humid air shell around the cloud. The widths of the interface zone and humid shell are evaluated.