Cloud-droplet growth due to supersaturation fluctuations in stratiform clouds

Abstract

Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets being modeled as Lagrangian particles. The supersaturation field is calculated directly by simulating the temperature and water vapor fields instead of being treated as a passive scalar. Thermodynamic feedbacks to the fields due to condensation are also included for completeness. We find that the width of droplet size distributions increases with time, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower size distributions. Nevertheless, in agreement with earlier Lagrangian stochastic models of the condensational growth, the standard deviation of the surface area of droplets increases as t 1/2 . Also, for the first time, we explicitly demonstrate that the time evolution of the size distribution is sensitive to the Reynolds number, but insensitive to the mean energy dissipation rate. This is shown to be due to the fact that temperature fluctuations and water vapor mixing ratio fluctuations increases with increasing Reynolds number, therefore the resulting supersaturation fluctuations are enhanced with increasing Reynolds number. Our simulations may explain the broadening of the size distribution in stratiform clouds qualitatively, where the mean updraft velocity is almost zero.

Condensational and Collisional Growth of Cloud Droplets in a Turbulent Environment

“…The equations governing the Eulerian fields and condensation are the same as the standard ones (Vaillancourt et al 2002), and their implementation is described in Li et al (2018c). For the collision-coalescence dynamics we use the superparticle method, which is validated in Li et al (2017).…”

“…is the fluctuation of the water-vapor mixing ratio (Lamb and Verlinde 2011;Kumar et al 2014), with q v,env = 0.01 kg kg −1 ; see also Li et al (2018c). This follows the common approach (Vaillancourt et al 2002) in that it uses the Boussinesq approximation to describe the term Be z in Equations (2), assuming that density variations are negligible except when multiplied by the gravitational acceleration; see for example Mehaddi et al (2018).…”

“…Both T and q v are affected by droplets via the condensation rate C d (Vaillancourt et al 2001;Li et al 2018c),…”

“…However, they did not study the dependency of the droplet-size distribution upon the Reynolds number. Indeed, several works (Lanotte et al 2009;Sardina et al 2015;Siewert et al 2017;Li et al 2018c) suggested that condensational growth is sensitive to the Reynolds number. Collisional growth, however, is mainly affected by the mean energy dissipation rate (Ayala et al 2008;Chen et al 2016;Li et al 2018a).…”

“…For the dynamics of the local temperature and the local water-vapor mixing ratio we use the same model as Vaillancourt et al (2002), Saito and Gotoh (2018), and Chen et al (2018b), save for updraft cooling (see below). Details of our implementation are given in Li et al (2018c). The droplet dynamics in our simulations is coupled to the turbulence through Stokes force.…”