Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment

Abstract

We investigate the effect of turbulence on the combined condensational and collisional growth of cloud droplets by means of high resolution direct numerical simulations of turbulence and a superparticle approximation for droplet dynamics and collisions. The droplets are subject to turbulence as well as gravity, and their collision and coalescence efficiencies are taken to be unity. We solve the thermodynamic equations governing temperature, water-vapor mixing ratio, and the resulting supersaturation fields together with the Navier-Stokes equation. We find that the droplet size distribution broadens with increasing Reynolds number and/or mean energy dissipation rate. Turbulence affects the condensational growth directly through supersaturation fluctuations, and it influences collisional growth indirectly through condensation. Our simulations show for the first time that, in the absence of updraft cooling, supersaturation fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (non-turbulent) condensational growth, which leads to a growing mean droplet size, but a narrower droplet size distribution. Our findings, instead, show that condensational growth facilitates collisional growth by broadening the size distribution in the tails at an early stage of rain formation. With increasing Reynolds numbers, evaporation becomes stronger. This counteracts the broadening effect due to condensation at late stages of rain formation. Our conclusions are consistent with results of laboratory experiments and field observations, and show that supersaturation fluctuations are important for precipitation.

Key parameters for droplet evaporation and mixing at the cloud edge

“…As a consequence, nearby droplets may have experienced quite different growth histories. The droplets of a cloudy parcel that is mixed with dry air evaporate at different rates, so that the droplet size distribution broadens (Lanotte et al ., 2009; Sardina et al ., 2015; 2018; Li et al ., 2020). Cloud‐resolving simulations (Hoffmann and Feingold, 2019) show that this mechanism can have a strong effect on droplet number densities in turbulent clouds.…”

Diffusion of turbulence following both stable and unstable step stratification perturbations

“…The constant κ and d χ are the thermal and water vapor diffusivity, respectively. This is a very consolidated basic model that is often used as a representation of the Eulerian equations for turbulent fields to which the liquid water component can be added as a Lagrangian set of N pointlike droplets ( [15][16][17][18][19][20][21] ).…”

Coagulation of inertial particles in supersonic turbulence

“…Comparing with the super-particle algorithm widely used in planet formation (Zsom & Dullemond 2008;Johansen et al 2012), our algorithm provides better collision statistics (Li et al 2017). We refer to (Li et al 2017) for a detailed comparison of the super-particle algorithm used in Johansen et al (2012) and Li et al (2017Li et al ( , 2018Li et al ( , 2020.…”