A Lagrangian approach to droplet condensation in atmospheric clouds

Abstract

The condensation of microdroplets in model systems, reminiscent of atmospheric clouds, is investigated numerically and analytically. Droplets have been followed through a synthetic turbulent flow field composed of 200 random Fourier modes, with wave numbers ranging from the integral scales [O(102 m)] to the Kolmogorov scales [O(10−3 m)]. As the influence of all turbulence scales is investigated, direct numerical simulation is not practicable, making kinematic simulation the only viable alternative. Two fully Lagrangian droplet growth models are proposed: a one-way coupled model in which only adiabatic cooling of a rising air parcel is considered, and a two-way coupled model which also accounts for the effects of local vapor depletion and latent heat release. The simulations with the simplified model show that the droplet size distribution becomes broader in the course of time and resembles a Gaussian distribution. This result is supported by a theoretical analysis which relates the droplet surface-area distribution to the dispersion of droplets in the turbulent flow. Although the droplet growth is stabilized by vapor depletion and latent heat release in the two-way coupled model, the calculated droplet size distributions are still very broad. The present results may provide an explanation for the rapid growth of droplets in the coalescence stage of rain formation, as broad size distributions are likely to lead to enhanced collision rates between droplets.