The Collisional Problem of Cloud Droplets Moving in a Turbulent Environment–Part II: Turbulent Collision Efficiencies

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Abstract
The collision efficiencies for small cloud drops moving under the influence of gravity in a viscous, incompressible, turbulent medium are obtained for drop radii of 10 µm < R1 < 50 µm and droplet/drop ratios of 0 < R2/R1 < 1. For the scales of motion considered, the 2/3 Kolmogorov law defines the cloud's turbulent flow structure, which is assumed to be locally homogeneous and isotropic. Two levels of the rate of energy dissipation per unit mass, e = 1 and c = 10 cm2 s−3, representing typical values for the initial stages of cloud development, are considered. The turbulent collision efficiencies are calculated numerically as outlined in Part I of this study (Almeida, 1976). When compared to the nonturbulent (still-air) collision efficiency values, these turbulent collision efficiencies show remarkable differences. For drop radii of R1 > 40 µm the differences are negligible. However, for smaller drop radii the turbulent collision efficiencies are much larger than the still-air efficiencies. Implications of these increased collision efficiencies in the theoretical condensation/still-air collection growth problem are discussed. It is shown, for example, that a drop with a radius of R1 = 15 µm in a turbulent environment collides more efficiently than does a drop with a radius of R1 = 25 µm in still air. Tables are presented with the numerical values of both turbulent and nonturbulent linear collision efficiency functions.

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