Coalescence and Breakup-Induced Oscillations in the Evolution of the Raindrop Size Distribution

Abstract

Models or the coalescence/breakup process yield drop number distributions that approach equilibrium but the number density often is not a monotonic function of time. In some cases, the small-raindrop portion of the distribution rapidly attains high concentration levels before settling back toward an equilibrium position. An eigenanalysis of the coalescence/breakup equation is performed to gain an understanding of the solution behavior near equilibrium. The analysis reveals that the departure of the solution from equilibrium can be expressed as a linear combination of basis functions of the form eλj where Re(λj) < 0 so that the equilibrium drop distribution is asymptotically stable. The exponential basis functions feature a wide range of decay rates, and since Im (λj) ≠ 0 in some cases, the functions provide evidence of oscillations in the drop spectrum. It is shown that one particular damped oscillation can combine with a rapidly decaying transient to describe very well the nonmonotonic behavior characteristic of model-generated drop spectra. While the physical mechanism behind the oscillation is not yet understood, the initial reversal in the small-drop peak may be explained as rapid response due to filament breakup followed by a slower response due to coalescence. A particular sequence of observed raindrop distributions is found to exhibit a reversal in the spectral peak similar to that produced by the model.