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

Fausto Carlos de Almeida National Center for Atmospheric Research, Boulder, CO 80307

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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.

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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