Modelling the Effect of Turbulence on the Collision of Cloud Droplets

Abstract

From an analysis of scales in the cloud droplet collision problem, the authors infer that a trajectory model that is to be capable of predicting collisions between droplets of all possible sizes should be of second-order, that is should explicitly model particle acceleration. But for collisions between large droplets (radius about 50 µm or larger), which are still much smaller than raindroplets, a first-order model is appropriate. The relative motion of large droplets are studied with a first-order, two particle trajectory model. Turbulence is found to be unimportant (relative to differential gravitational settling) if the (large) droplet sizes are sufficiently distinct. Zeroth-order two-particle models, of the type hitherto applied to be problem, deteriorate in accuracy as the influence of turbulence on the droplet separation increases, that is, for large σv/v?, where σv is the turbulent velocity scale and v? is the droplet still-air terminal velocity. Under no circumstance is a single-particle model applicable.