How turbulence enhances coalescence of settling particles with applications to rain in clouds

S. Ghosh, J. Dáila, J. C R Hunt, A. Srdic, H. J S Fernando, P. R. Jonas

    Research output: Contribution to journalArticlepeer-review


    From theoretical, numerical and experimental studies of small inertial particles with density e ual to β(>1) times that of the fluid, it is shown that such particles are 'centrifuged' out of vortices and eddies in turbulence. Thus, in the presence of gravitational acceleration g, their average sedimentation velocity VT in a size range just below a critical radius acr is increased significantly by up to about 80%. We show that in fully developed turbulence, acr is determined by the circulation Tk of the smallest Kolmogorov micro-scale eddies, but is approximately independent of the rate of turbulent energy dissipation e, because Tk is about e ual to the kinematic viscosity v. It is shown that acr varies approximately like n23g-1/ 3(β-1)-1/2 and is about 20 μm (±2 mm) for water droplets in most types of cloud. New calculations are presented to show how this phenomena causes higher collision rates between these 'large' droplets and those that are smaller than acr, leading to rapid growth rates of droplets above this critical radius. Calculations of the resulting droplet size spectra in cloud turbulence are in good agreement with experimental data. The analysis, which explains why cloud droplets can grow rapidly from 20 to 80 mm irrespective of the level of cloud turbulence is also applicable where acr-1 mm for typical sand/mud particles. This mechanism, associated with une ual droplet/particle sizes is not dependant on higher particle concentration around vortices and the results differ uantitatively and physically from theories based on this hypothesis. © 2005 The Royal Society.
    Original languageEnglish
    Pages (from-to)3059-3088
    Number of pages29
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Issue number2062
    Publication statusPublished - 8 Oct 2005


    • Clouds
    • Coalescence
    • Droplets
    • Turbulence


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