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 the mean updraft cooling, supersaturation-fluctuation-induced broadening of droplet size distributions enhances the collisional growth. This is contrary to classical (nonturbulent) 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.

We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high-resolution (1024(3)) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves toward a shape that is a reflection of the gas-density distribution, regardless of the initial distribution. That is, in case of isothermal, rotationally forced turbulence, the GSD tends to be a lognormal distribution. We also show that in hypersonic turbulence, decoupling of gas and dust becomes important and that this leads to an even further accelerated grain growth.

Condensational growth of cloud droplets due to supersaturation fluctuations is investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations (DNS) 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 increase 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.

Weinvestigate the effect of turbulence on the collisional growth of micrometer-sized droplets through highresolution numerical simulations with well-resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate ε, but only weakly on the Reynolds number. This can be explained through the « dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as ε1/2 even when coalescence is invoked. The size distribution exhibits power-law behavior with a slope of 23.7 from a maximum at approximately 10 up to about 40 mm. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is because turbulence enhances the collisional growth between similar-sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth.