The Effect of Initial Droplet Size Spectra on Its Evolution During Turbulent Condensational Growth

We study condensational growth of droplets in the presence of turbulent mixing, which is relevant during entrainment of dry air into clouds. The aim here is to understand the role of the initial shape of the droplet size spectra on the final droplet spectra, at the end of turbulent mixing of the air parcel. Using numerical computations, we model the growth of droplets by resolving each droplet, evolving their size (radius) and temperature. The ambient atmosphere can be modeled as being either well-mixed (homogeneous) or inhomogeneous. In the well-mixed model, all droplets interact with the same ambient temperature field and vapor density. In the inhomogeneous model, the droplets interact with the local values of temperature and vapor density. To simulate cloud entrainment, we initially partion the domain into a dry and a wet region. The wet region contains droplets, along with supersaturated vapor. The dry region contains only subsaturated vapor. A 2D synthetic turbulence field has been imposed on the droplet, vapor and temperature field. We observe that if the initial droplet size spectra contains significant number of large droplets, then there is little difference between the final droplet spectra predicted by the well-mixed and inhomogeneous models. This occurs because the large droplets release vapor relatively quickly in subsaturated conditions, and immediately saturate the dry air into which they gets mixed, thus “freezing” the rest of the size spectra. Our theoretical analysis predicts that, for a given turbulence eddy turnover rate, a family of droplet size spectra exists whose evolution will be well predicted by the “well-mixed” models. Comparison of the results from the analysis and simulations are made.