The Effect of Turbulence on the Collision Rates of Small Cloud Drops

A. S. Koziol Atmospheric Environment Service, Dorval, Quebec, Canada

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H. G. Leighton Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

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Abstract

The significance of the influence of turbulence on collisions and coalescence of small cloud droplets is still an outstanding problem. In particular, the growth of droplets in the radius range 10 to 15 µm is not well understood. The present research examines whether or not turbulence affects the growth rate of such small drops by simulating trajectories of two hydrodynamically interacting droplets in a turbulent field. The trajectories were calculated with a model based on linear Stokes hydrodynamics. Turbulence was modeled in the form of random Fourier modes with both the space and time spectra prescribed. Both spectra were characterized by Kolmogorov scaling. The space spectrum was modeled in the inertial and dissipation subranges. On the basis of scale analysis, only small-scale time variations were allowed, and the so-called Eulerian–Lagrangian time spectrum was applied. The results show that most collision rates increase moderately in a turbulent flow characterized by rates of energy dissipation of the order of 1, 10, and 100 cm2 s−3.

Abstract

The significance of the influence of turbulence on collisions and coalescence of small cloud droplets is still an outstanding problem. In particular, the growth of droplets in the radius range 10 to 15 µm is not well understood. The present research examines whether or not turbulence affects the growth rate of such small drops by simulating trajectories of two hydrodynamically interacting droplets in a turbulent field. The trajectories were calculated with a model based on linear Stokes hydrodynamics. Turbulence was modeled in the form of random Fourier modes with both the space and time spectra prescribed. Both spectra were characterized by Kolmogorov scaling. The space spectrum was modeled in the inertial and dissipation subranges. On the basis of scale analysis, only small-scale time variations were allowed, and the so-called Eulerian–Lagrangian time spectrum was applied. The results show that most collision rates increase moderately in a turbulent flow characterized by rates of energy dissipation of the order of 1, 10, and 100 cm2 s−3.

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