Reversals in Evolving Raindrop Size Distributions Due to the Effects of Coalescence and Breakup

Abstract

Numerical solutions of the coalescence/breakup equation often produce drop size distributions that move away from equilibrium before turning back. In particular, distributions evolving from Marshall?Palmer form rapidly overshoot their equilibrium position, reverse direction, and then settle slowly toward equilibrium. To explain such reversals in the changing drop distribution, an analysis has been performed using a simple model that contains only three drop-size categories. From several basic properties of the coalescence/breakup process, it is shown that the distribution is forced to develop an excess (deficit) of both large and small drops balanced by a deficit (excess) of medium-sized drops. The ratio of excess water mass in the small-drop category to that in the large-drop category approaches a constant value as the distribution approaches equilibrium. In an effort to achieve this proportion, a reversal occurs in some part of the drop distribution.