Turbulent Condensation of Droplets: Direct Simulation and a Stochastic Model

Abstract

The effect of turbulent mixing on droplet condensation is studied via direct numerical simulations of a population of droplets in a periodic box of homogeneous isotropic turbulence. Each droplet is tracked as a fluid particle whose radius grows by condensation of water vapor. Forcing of the small wavenumbers is used to sustain velocity, vapor, and temperature fluctuations. Temperature and vapor fluctuations lead to supersaturation fluctuations, which are responsible for broadening the droplet size distribution in qualitative agreement with in situ measurements. A model for the condensation of a population of cloud droplets in a homogeneous turbulent flow is presented. The model consists of a set of Langevin (stochastic) equations for the droplet area, supersaturation, and temperature surrounding the droplets. These equations yield corresponding ordinary differential equations for various moments and correlations. The statistics predicted by the model, for instance, the droplet area–supersaturation correlation, reproduce the simulations well.