A Numerical Model for the Equilibrium Shape of Electrified Raindrops

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  • 1 Department of atmospheric Sciences, University of Illinois at Urbana-Champaign, Urbana. Illinois
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Abstract

The model Beard Chuang, using the differential form of Laplace's formula, has been extended to raindrop shapes under the influence of vertical electric fields and drop charges. A finite volume method was used with a boundary-fitted coordinate system to calculate the shape-dependent electric field. The distorted shape was obtained by numerical integration from the upper to lower pole by iteration to achieve the appropriate drop volume and force balance using shape-dependent stresses.

The model prediction of the critical electric field for instability is within a few percent of previous models for a stationary drop, but stability was found to be considerably enhanced for raindrops because of the counteracting aerodynamic distortion. The predicted critical fields for larger raindrops, however, are about 2 kV cm−1 higher than found in the wind tunnel measurements of Richards and Dawson. Model raindrop shapes in a strong, electric field show a pronounced extension of the upper pole, and a flattened base caused by the increased fall speed from vertical stretching. The resultant triangular drop profiles are similar to wind tunnel observations.

The shape of highly charged raindrops have a pronounced oblate distortion caused by the charge enhancement of existing distortion and the fall speed reduction of the aerodynamic asymmetry. The shapes for upward and downward electric forces differ because of the altered fall speed. For the maximum field and charge expected in thunderstorms, a downward force increases the aerodynamic distortion thereby counteracting the electric stretching so that axis ratios are nearly the same as in the absence of electric stresses. In contrast, an upward electric force decreases the aerodynamic distortion, resulting in an enhanced vertical stretching to the extent that large raindrops can become unstable.

Abstract

The model Beard Chuang, using the differential form of Laplace's formula, has been extended to raindrop shapes under the influence of vertical electric fields and drop charges. A finite volume method was used with a boundary-fitted coordinate system to calculate the shape-dependent electric field. The distorted shape was obtained by numerical integration from the upper to lower pole by iteration to achieve the appropriate drop volume and force balance using shape-dependent stresses.

The model prediction of the critical electric field for instability is within a few percent of previous models for a stationary drop, but stability was found to be considerably enhanced for raindrops because of the counteracting aerodynamic distortion. The predicted critical fields for larger raindrops, however, are about 2 kV cm−1 higher than found in the wind tunnel measurements of Richards and Dawson. Model raindrop shapes in a strong, electric field show a pronounced extension of the upper pole, and a flattened base caused by the increased fall speed from vertical stretching. The resultant triangular drop profiles are similar to wind tunnel observations.

The shape of highly charged raindrops have a pronounced oblate distortion caused by the charge enhancement of existing distortion and the fall speed reduction of the aerodynamic asymmetry. The shapes for upward and downward electric forces differ because of the altered fall speed. For the maximum field and charge expected in thunderstorms, a downward force increases the aerodynamic distortion thereby counteracting the electric stretching so that axis ratios are nearly the same as in the absence of electric stresses. In contrast, an upward electric force decreases the aerodynamic distortion, resulting in an enhanced vertical stretching to the extent that large raindrops can become unstable.

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