Collisions of Small Drops in a Turbulent Flow. Part III: Relative Droplet Fluxes and Swept Volumes

Abstract Swept volumes of cloud droplets with radii below 20 μm are calculated under conditions typical of atmospheric cloud turbulence characterized by enormous values of Reynolds numbers, high turbulent intermittency, and characteristic values of the dissipation rate. To perform the calculations, the motion equation for small droplets proposed by Maxey is generalized for Stokes numbers St > 0.1, which allows one to simulate relative droplet motion even for very high turbulence intensities typical of deep cumulus clouds. Analytical considerations show that droplet motion is fully determined by turbulent shears and the Lagrangian accelerations. A new statistical representation of a turbulent flow has been proposed based on the results of the scale analysis of turbulence characteristics and those related to the droplet motion. According to the method proposed, statistical properties of turbulent flow are represented by a set of noncorrelated samples of turbulent shears and Lagrangian accelerations. Each sa...

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