Analysis of Model-Produced Raindrop Size Distributions in the Small-Drop Range

Abstract

Current models of drop coalescence and breakup generate raindrop size distributions that evolve toward an equilibrium whose form features a pronounced peak in the small-drop range. It has been known for some time that the peak can be attributed to filament-type breakup, but the particular aspects of filament breakup responsible for the peak have not been identified. To explain the development of the peak, an investigation is carried out to determine the role of specific components of current breakup formulations in producing a relative maximum in the drop number density at a particular drop size. Both physical and artificial causes are considered. From existing laboratory data, it is found that when two drops collide, the maximum number of fragments produced by filament-type breakup occurs when the diameter of the smaller colliding drop lies within a narrow range. The resulting number of satellite drops produced by the collisions has a maximum within a correspondingly narrow size range. It is the restricted range in which the satellite peaks occur for individual drop size pairs that gives rise to the small-drop peak found in model-generated drop size distributions that account for collisions between all possible drop size pairs. Evidence is presented to show that the peak in the satellite number is associated with a peak in the Weber number for low-energy collisions and with the fact that in high-energy collisions filament breakup occurs only when the collisions are off-center. Artificial factors that tend to produce peaks in the small-drop range are found to be present in the model formulation but are shown to be inconsequential with regard to the existence and position of the peak found in the solutions. The difficulties of model verification with regard to the small-drop range are discussed, and requirements for gathering suitable observational data are outlined.