Vertical Variation of the Steady-State Drop Spectrum in a One-Dimensional Rain Shaft

Abstract Past work has provided thorough analysis of the coalescence/breakup process in a “box model” setting in which the drop size distribution is assumed invariant with height. In this work, the analysis is extended to examine the coalescence/breakup process in a one-dimensional shaft model setting that allows vertical variation of the drop size distribution due to sedimentation. The objectives are to gain a better understanding of the rain process and to acquire the knowledge necessary to parameterize the shaft model solutions. When vertical variation is taken into account, the steady-state form of the model equation describes the rate of change in the drop size distribution with fall distance for a fixed input condition at the shaft top. This equation is formally quite similar to the box model equation describing temporal evolution of the drop spectrum, and many characteristics of the box model solutions carry over to the steady-state, shaft model solutions, but with fall distance replacing time as t...