Cloud droplet collisions in turbulent environment: Collision statistics and parameterization

The purpose of this paper is to quantify the influence of turbulence in collision statistics by separately studying the impacts of computational domain sizes, eddy dissipation rates (EDRs), and droplet sizes and eventually to develop an accurate parameterization of collision kernels. Direct numerical simulations (DNS) were performed with a relatively wide range of EDRs and Taylor microscale Reynolds numbers R_λ. EDR measures the turbulence intensity levels. DNS model studies have simulated homogeneous turbulence in a small domain in the cloud's adiabatic core. Clouds clearly have much larger scales than current DNS can simulate. For this reason, it is emphasized that R_λ obtained from current DNS is fundamentally only a measure of the computational domain size for a given EDR and cannot completely describe the physical properties of cloud turbulence. Results show that the collision statistics are independent of the domain sizes and hence of the computational R_λ for droplet sizes no bigger than 25 μm as long as the droplet separation distance, which is on the order of the Kolmogorov scale in real clouds, is resolved. Instead, they are found to be highly correlated with EDRs and droplet sizes, and this correlation is used to formulate an improved parameterization scheme. The new scheme well represents the turbulent geometric collision kernel with a relative uncertainty of 14%. A comparison between different parameterizations is made, and the formulas proposed here are shown to improve the fit to the collision statistics.