Continuous growth of droplet size variance due to condensation in turbulent clouds

TL;DR

This study combines a stochastic model and direct numerical simulations to demonstrate that turbulence causes the variance of droplet sizes in clouds to grow over time as t^{1/2}, leading to broad spectra relevant for rain formation.

Contribution

It reveals the quantitative relationship between turbulence scales and droplet size variance growth, validated by simulations, advancing understanding of cloud microphysics.

Findings

Droplet size variance increases as t^{1/2} over time.

Growth rate depends on turbulence scale separation and integral scales.

Simulations produce broad droplet spectra consistent with rain formation timescales.

Abstract

We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate proportional to the large-to-small turbulent scale separation and to the turbulence integral scales but independent of the mean turbulent dissipation. Direct numerical simulations confirm this result and produce realistically broad droplet size spectra over time intervals of 20 minutes, comparable with the time of rain formation.