THE EROSION OF CUMULUS TOWERS

Abstract

A differential equation is formulated for the rate of rise of isolated buoyant elements in the atmosphere, based in part on analogy with the work of Davies and Taylor (1950) who studied the ascent of air bubbles in liquid. The equation involves a drag force which is proportional to the ascent velocity squared and which depends upon a linear dimension of the buoyant element, such as the radius of curvature of its upper surface. To eliminate this dimension from the differential equation, a law for the erosion, or rate of decrease in size of these buoyant air bubbles has been proposed. The basic assumptions are that the elements erode sufficiently slowly so that the flow around them is nearly the same as if they were in equilibrium, and that they retain their shape. From combination of the erosion law and the equation of motion, an erosion parameter, E, is derived, which to the extent that the laws are valid should be constant for all isolated cloudy bubbles, regardless of air mass or location. The erosion constant has been expressed in terms of the bubble's upward velocity, acceleration, and its buoyancy. The theory is thus subject to test in the case of cumulus towers, by simple measurements from time-lapse motion pictures and an environmental temperature sounding. Observations of twelve relatively isolated cumulus bubbles, selected from both the trade-wind region and middle latitudes, show that E is indeed constant within the limits of measurement. A case of the aggregation of several small bubbles into a larger one is also studied, and the applicability to it of the same erosion and drag laws is established. The interaction of bubbles with one another, and with the environment to form large cumulus clouds, is discussed qualitatively.