The Collection Kernel for Two Falling Cloud Drops Subjected to Random Perturbations in a Turbulent Air Flow: A Stochastic Model

Abstract

A stochastic model is presented to compute the collection kernel of cloud drops affected by turbulent air fluctuations. The model is based on stochastic differential equations with ?white noise? terms representing the random turbulent displacements. The size of the random displacements is characterized by the turbulent diffusion coefficient. The associated initial boundary value problem for the partial differential equation of the Fokker-Planck type is solved numerically using finite-difference methods. For small perturbations, the collection kernel computed with the stochastic model agrees extremely well with the (deterministic) analytic expression for the collection kernel valid for non-turbulent air. The results indicate that turbulent fluctuations enhance the probability of collisions. This is particularly evident for droplets of radii less than or equal to 50 ?m.