Mass Conservation Considerations in Analytic Representation of Raindrop Fragment Distributions

Abstract Model formulation of drop breakup requires a set of analytic functions to describe the size distribution of water fragments that result from the collision of two raindrops of arbitrary diameter. The set of fragment distribution functions derived by Low and List in 1982 has provided the foundation for most of the recent modeling studies of raindrop collision. The formulas provide reasonably accurate approximations to histogram representations of laboratory data but produce distributions of drop fragments whose masses do not sum to the masses of the colliding drops. To correct the problem, new analytic expressions are derived using least squares fits with constraints on the total water mass content of the fragments and on the number of fragments produced by collision. Introduction of the mass conservation constraint reveals that, for drop collisions in which the mass of the larger colliding drop greatly exceeds that of the smaller drop, a certain feature is missing from both the histograms and the ...