A simple perturbation model for the electrostatic shape of falling drops

Abstract

Use of a consistent first-order perturbation equation and spherical harmonics helped to reconcile apparent inconsistencies in the cosine series method. The electric stress was included in the first-order model using a sphere in a uniform vertical field, with the effect of a net charge approximated by a reduction in surface tension for a spherical drop. The perturbation drop shapes for electric distortion were found to be appreciably altered by coupling between shape and fall speed. A simple axis ratio formula, valid for small perturbation, was based on the principal shape coefficient, containing terms for the aerodynamic distortion, electric field and charge: α = 1 - (0.198 We-0.281 X2)FQ. This equation, when coupled with a shape-drag relation, yielded a cubic equation for axis ratio. Our results indicate detectable shape changes in thunderstorms - produced directly by strong electric fields, but modified considerably by changes in fall speed, with and without charges. -from Authors