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Statistics and Parameterizations of the Effect of Turbulence on the Geometric Collision Kernel of Cloud Droplets

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  • 1 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada
  • | 2 Recherche en Prévision Numérique, Meteorological Service of Canada, Dorval, Quebec, Canada
  • | 3 Department of Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada
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Abstract

Collision statistics of cloud droplets in turbulent flow have been calculated for 12 droplet size combinations in four flow fields with levels of the eddy dissipation rate of turbulent kinetic energy ranging from 95 to 1535 cm2 s−3. The flow fields were generated by using a direct numerical simulation technique and large numbers of droplets were explicitly tracked through the flow field for each experiment. The effect of turbulence on the collision kernel increases with both increasing radius ratio and eddy dissipation rate. These increases range from fairly modest values to almost 10 times the gravitational geometric collision kernel. The two physical processes responsible for these increases are the radial relative velocities and the preferential concentration or clustering of the droplets. The radial relative velocities increased by up to 3 times the corresponding gravitational value and the greatest increase in the clustering, as measured by the radial distribution function, is 4.5 times the value for a random distribution as for the gravitational case. Parameterizations have been developed for the effect of turbulence on the radial relative velocities and the clustering of the droplets. These models reduce the average root-mean-squared errors in the existing velocity parameterization of Saffman and Turner and Wang et al. by 32% and the clustering parameterization of Zhou et al. by up to 58%.

Corresponding author address: Dr. Charmaine Franklin, Bureau of Meteorology Research Centre, GPO Box 1289K, Melbourne, Victoria 3001, Australia. Email: c.franklin@bom.gov.au

Abstract

Collision statistics of cloud droplets in turbulent flow have been calculated for 12 droplet size combinations in four flow fields with levels of the eddy dissipation rate of turbulent kinetic energy ranging from 95 to 1535 cm2 s−3. The flow fields were generated by using a direct numerical simulation technique and large numbers of droplets were explicitly tracked through the flow field for each experiment. The effect of turbulence on the collision kernel increases with both increasing radius ratio and eddy dissipation rate. These increases range from fairly modest values to almost 10 times the gravitational geometric collision kernel. The two physical processes responsible for these increases are the radial relative velocities and the preferential concentration or clustering of the droplets. The radial relative velocities increased by up to 3 times the corresponding gravitational value and the greatest increase in the clustering, as measured by the radial distribution function, is 4.5 times the value for a random distribution as for the gravitational case. Parameterizations have been developed for the effect of turbulence on the radial relative velocities and the clustering of the droplets. These models reduce the average root-mean-squared errors in the existing velocity parameterization of Saffman and Turner and Wang et al. by 32% and the clustering parameterization of Zhou et al. by up to 58%.

Corresponding author address: Dr. Charmaine Franklin, Bureau of Meteorology Research Centre, GPO Box 1289K, Melbourne, Victoria 3001, Australia. Email: c.franklin@bom.gov.au

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