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The Capacitance of Rosette Ice Crystals

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  • 1 Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin
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Abstract

The capacitances of seven bullet rosette ice crystals are computed based on the classical electrostatic analogy theory of diffusional growth. The rosettes simulated have 2, 3, 4, 6, 8, 12, and 16 lobes using mathematical formulas published previously. The Laplace equation for the water vapor density distribution around a stationary rosette is solved explicitly by the finite element method. The total flux of vapor toward the rosette surface and the vapor density on the surface determine the capacitance. The capacitances of these rosettes are smaller than that of spheres of equal radii but greater than columnar ice crystals of the same maximum dimensions. They can be greater or smaller than that of circular plates, depending on the number of lobes. Since many previous estimates of rosette growth rates were based on the assumption that their capacitances are the same as spheres of equal radii, the present finding implies that some of the previous rosette growth rates may be overestimated. The overestimation becomes less important if the rosettes have more lobes. Empirical power equations are given to fit the relations between the capacitance and the number of lobes, surface area, and volume of rosettes. Possible implications of rosette capacitance on the atmospheric heating by cirrus clouds are also 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 capacitances of seven bullet rosette ice crystals are computed based on the classical electrostatic analogy theory of diffusional growth. The rosettes simulated have 2, 3, 4, 6, 8, 12, and 16 lobes using mathematical formulas published previously. The Laplace equation for the water vapor density distribution around a stationary rosette is solved explicitly by the finite element method. The total flux of vapor toward the rosette surface and the vapor density on the surface determine the capacitance. The capacitances of these rosettes are smaller than that of spheres of equal radii but greater than columnar ice crystals of the same maximum dimensions. They can be greater or smaller than that of circular plates, depending on the number of lobes. Since many previous estimates of rosette growth rates were based on the assumption that their capacitances are the same as spheres of equal radii, the present finding implies that some of the previous rosette growth rates may be overestimated. The overestimation becomes less important if the rosettes have more lobes. Empirical power equations are given to fit the relations between the capacitance and the number of lobes, surface area, and volume of rosettes. Possible implications of rosette capacitance on the atmospheric heating by cirrus clouds are also 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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