Effects of Turbulence on the Collision-Coalescence Growth of Cloud Droplets

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One of the mechanisms by which rain is formed is the collision and coalescence of cloud droplets. This is usually called the warm rain mechanism, to distinguish it from the process of diffusional growth, which is important for the formation of precipitation in clouds colder than 0 degrees C containing a mixture of ice crystals and supercooled water droplets. It has long been speculated that turbulent air motions may increase the rate of droplet collisions and hence speed up the formation of precipitation. Two effects are attributed to turbulence that would tend to increase the rate of droplet collisions: (1) an inertial effect whereby collisions are caused by the inability of a drop to move with the airflow out of the path of an approaching larger drop; (2) an accumulation effect, whereby persistent vortices in the turbulent flow create regions of higher drop concentration, in which the rate of collisions will be increased. This project analyzes these effects by computing the movement of drops in turbulent air by direct numerical simulation (DNS). One objective is to quantify and parameterize the combined effects of turbulence, droplet inertia, and gravitational settling on the droplet collision kernel, a quantity that describes the probability that a larger drop will overtake and collide with a smaller drop in unit time, given that they are both present in unit concentration. Another objective is to apply the new parameterization in solving the stochastic coalescence equation, which describes the evolution of a droplet spectrum as the drops interact and collide with each other, to determine the extent to which turbulence shortens the time for precipitation-sized drops (about 0.1 mm) to form. The project requires the collaboration of a specialist in computational fluid dynamics and a cloud physicist. Basically, it brings to bear on cloud physics techniques that have been developed for the analysis of multiphase flows in engineering. The result will be a more accurate parameterization of rain formation by the warm rain process, which could help to explain discrepancies that seem to exist between current theory (which does not include turbulence) and the observed times for precipitation formation.