Some analytical calculations on the effect of turbulence on the settling and growth of cloud droplets

Abstract

Recent research on the interaction of inertial particles with turbulent vortices show that inertial bias causes particles to settle faster in turbulence than in still air as a consequence of particle accumulation in downward fluid velocity regions [Hainaux et al., 2000; Davila and Hunt 2001; Fevrier et al., 2000]. To date, these effects have not been included in models of droplet collection growth. In addition earlier models have also neglected the dependence of the collection growth on the radius of the smaller collected drops assuming that the collected drops are stationary. We have considered all these effects and have still been able to solve the collection equation analytically and the earlier Baker[1993] results are retrievable as a special case when these effects are turned off. The results presented in this study are in closed form and are therefore extremely attractive for precipitation parametrizations in large scale models.