Terminal Velocity Adjustment for Cloud and Precipitation Drops Aloft

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  • 1 Laboratory for Atmospheric Research, University of Illinois at Urbana-Champaign and Illinois State Water Survey, Urbana 61801
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Abstract

The velocities of cloud and precipitation drops aloft are obtained from the sea level velocity by multiplication with an adjustment factor. For cloud drops (1–40 µm diameter) the adjustment factor is found from the Stokes-Cunningham equation, and depends upon the Knudsen number and dynamic viscosity. For larger drops (40 µm–6 mm diameter) the adjustment factor is obtained from a semi-empirical fit to the data of Beard (1976) and depends upon the drop diameter, air density and dynamic viscosity. The adjustment factor for each size range is reduced to a simple function of drop size, air temperature and pressure. The velocities aloft using the adjustment method are found to be within 1% of the more precise values of Beard (1976) for reasonable atmospheric conditions. Polynomial formulas are included for calculating the sea level velocities.

Abstract

The velocities of cloud and precipitation drops aloft are obtained from the sea level velocity by multiplication with an adjustment factor. For cloud drops (1–40 µm diameter) the adjustment factor is found from the Stokes-Cunningham equation, and depends upon the Knudsen number and dynamic viscosity. For larger drops (40 µm–6 mm diameter) the adjustment factor is obtained from a semi-empirical fit to the data of Beard (1976) and depends upon the drop diameter, air density and dynamic viscosity. The adjustment factor for each size range is reduced to a simple function of drop size, air temperature and pressure. The velocities aloft using the adjustment method are found to be within 1% of the more precise values of Beard (1976) for reasonable atmospheric conditions. Polynomial formulas are included for calculating the sea level velocities.

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