Numerical Investigation of Collision-Induced Breakup of Raindrops. Part II: Parameterizations of Coalescence Efficiencies and Fragment Size Distributions

Abstract

Results of numerically investigated binary collisions of 32 drop pairs presented in Part I of this study are used to parameterize coalescence efficiencies and size distributions of breakup fragments of large raindrops. In contrast to the well-known results of Low and List, it is shown that coalescence efficiencies Ec can be described best by means of the Weber number We yielding Ec = exp(?1.15We). The fragment size distributions gained from our numerical investigations were parameterized by fitting normal, lognormal, and delta distributions and relating the parameters of the distribution functions to physical quantities relevant for the breakup event. Thus, this parameterization has formally a substantial similarity to the one of Low and List, although no reference is made to breakup modes such as filament, disk, and sheet. Additionally, mass conservation is guaranteed in the present approach. The parameterizations from Low and List, as well as the new parameterizations, are applied to compute a stationary size distribution (SSD) from solving the kinetic coagulation?breakup equation until a time-independent state is reached. Although with the parameterizations of Low and List, the SSD shows an often-reported three-peak structure, with the new parameterizations the second peak vanishes completely.