SPHERICAL VORTEX THEORY OF BUBBLE-LIKE MOTION IN CUMULUS CLOUDS

Abstract

The bubble concept is here put on a more quantitative basis by approximating the buoyant bubble in a cloud by a spherical vortex. The approximate solution of the equations of motion is made with the aid of ?Hill's Spherical Vortex? as described by Lamb (1932). In the solution as presented here, two arbitrary parameters representing the aerodynamic interaction and the mass exchange of the bubble with the surrounding air are introduced. Qualitative features of the motion are independent of the parameter values. The effects of entrainment on the motion are determined by a refined application of Stommel's method (1947, 1951) of computing entrainment. The solution of the problem, therefore, is given in terms of integrated differential equations which for given values of the arbitrary parameters, environmental potential temperature and specific humidity, and initial conditions yield the bubble velocity and potential temperature as a function of height. Specific applications of the solution are made to bubble motions in a saturated and an unsaturated environment.