Ventilation Coefficients for Falling Ice Crystals in the Atmosphere at Low–Intermediate Reynolds Numbers

Wusheng Ji Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin

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Pao K. Wang Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin

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Abstract

The ventilation coefficients for columnar, hexagonal plate, and broad branch ice crystals falling in air are computed by first solving numerically the convective diffusion equation for water vapor density to obtain its profile around these ice crystals and then determining the total vapor flux on the surface of the crystal. The ratio of this flux to the flux on a stationary crystal gives the ventilation coefficient. The local flow velocity profiles around the falling crystals necessary for specifying the convective term in the convective diffusion equation were obtained previously by numerically solving the unsteady Navier–Stokes equations subject to appropriate crystal-shaped boundary conditions. Ventilation coefficients obtained in this way are illustrated as a function of the Schmidt and Reynolds numbers and are also fitted by empirical expressions. Applications of these ventilation coefficients are discussed.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton Street, Madison, WI 53706.

Email: pao@windy.meteor.wisc.edu

Abstract

The ventilation coefficients for columnar, hexagonal plate, and broad branch ice crystals falling in air are computed by first solving numerically the convective diffusion equation for water vapor density to obtain its profile around these ice crystals and then determining the total vapor flux on the surface of the crystal. The ratio of this flux to the flux on a stationary crystal gives the ventilation coefficient. The local flow velocity profiles around the falling crystals necessary for specifying the convective term in the convective diffusion equation were obtained previously by numerically solving the unsteady Navier–Stokes equations subject to appropriate crystal-shaped boundary conditions. Ventilation coefficients obtained in this way are illustrated as a function of the Schmidt and Reynolds numbers and are also fitted by empirical expressions. Applications of these ventilation coefficients are discussed.

Corresponding author address: Dr. Pao K. Wang, Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, 1225 W. Dayton Street, Madison, WI 53706.

Email: pao@windy.meteor.wisc.edu

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