This dissertation describes processes of entrainment and turbulent mixing between a cloud and its environment, and the impact entrainment has on the spectrum of cloud droplets. An approach to locally predict homogeneity of the subgrid-scale turbulent mixing in large-eddy simulations of shallow clouds was presented.

Processes of entrainment and turbulent mixing are widely observed in boundary layer clouds and change clouds properties. The impact of entrainment and mixing on the cloud microphysics is the main subject of the dissertation. Entrainment leads to a reduction of the liquid water content, but its effect on the droplet spectrum is poorly understood. The key issue is whether the evaporation due to mixing results in a reduction of only the droplet size (as in the homogeneous mixing), both the number of droplets and their sizes (as in the inhomogeneous mixing), or only the number of droplets (as in the extremely inhomogeneous mixing). The homogeneity of mixing depends on the relative magnitude of the time scales for droplet evaporation and for turbulent homogenization. Homogeneous mixing takes place when the turbulent homogenization time scale is much smaller than the droplet evaporation time scale because all droplets are then exposed to the same conditions during evaporation. In the opposite limit, when the turbulent homogenization time scale is much longer than the droplet evaporation time scale, extremely inhomogeneous mixing is thought to occur, with some droplets evaporating completely and the rest not experiencing any evaporation at all.

The dissertation contains a short theoretical description of the process of cloud droplet evaporation due to turbulent mixing and characteristic times scales for droplet evaporation and for turbulent homogenization. In addition, the characteristic scale (width) of cloud filaments that decrease during turbulent stirring is introduced. The description is used to develop a new parameterization of subgrid-scale mixing in large eddy simulations (LES) with double-moment bulk microphysics scheme. The new scheme allows to predict the two time scales that determine the subgrid-scale mixing scenario: the time scale of turbulent homogenization and the time scale of cloud droplet evaporation. The scheme was added to the numerical model EULAG that features the 2-moment microphysical scheme. The model was applied in simulations of shallow convection observed during the Barbados Oceanographic and Meteorological Experiment (BOMEX) and cumulus under stratocumulus observed over the North Sea during Intensive Observation Period at Cabauw Tower (IMPACT, part of the European Integrated Project on Aerosol Cloud Climate and Air Quality Interactions, EUCAARI). The results of simulations are discussed in the dissertation.