The Role of Breakup and Coalescence in the Three-Peak Equilibrium Distribution of Raindrops

Abstract

Equilibrium raindrop size distributions with three peaks in number concentration (3PED) result from different breakup types and coalescences. Filament breakup produces drops in the small-drop peak of the 3PED and sheet breakup in the medium-drop peak, while disk breakup does not significantly affect the 3PED. Drops in the large-drop peak are produced by all types of interaction. A forty-dimensional phase space for number concentration, each dimension representing a different drop size, shows how equilibrium is approached and maintained. When reduced to seven dimensions, the complex processes of moving drops in and out of the peaks at equilibrium are clearly identified. Small drops are lost by coalescence, and filament breakup is the major sink of medium drops. The introduction of a measure for the difference between two spectra, the metric, shows that, starting from a Marshall–Palmer distribution with a rainrate of 54 mm h−1, the distribution moved farther away from the 3PED between 120 s and 350 s before approaching the 3PED continuously. A three-dimensional model, the diameter ranges under the peaks being the dimensions, shows that this occurs because many small drops are produced by filament breakup replacing the initial deficit of small drops with a surplus, which subsequently is depleted. There is no evidence for any oscillation of the raindrop spectra about its equilibrium value. It appears that a significant population of both 1 mm and 2 mm drops are needed before a 3PED can occur, but a 3PED can be safely assumed to develop once they are present.