This Ph.D. thesis examines the challenging problem of how turbulence affects the growth of cloud droplets in warm clouds. Droplets grow by either condensation or collision. Without turbulence, the condensation process driven by a uniform supersaturation field is only efficient when droplets are smaller than 15 μm (radius). Gravitational collision becomes effective when the radius of droplets is larger than 50 μm. The size gap of 15–50 μm, in which neither condensation nor collision processes dominate droplet growth, has puzzled the cloud microphysics community for around 70 years. It is the key to explaining the rapid warm rain formation with a timescale of about 20 minutes. Turbulence has been proposed to bridge this size gap by enhancing droplet growth processes, and thereby, to explain rapid warm rain formation. Since cloud–climate interaction is one of the greatest uncertainties for climate models, the fundamental understanding of rapid warm rain formation may help improve climate models.

The condensational and collisional growth of cloud droplets in atmospheric turbulence is essentially the problem of turbulence-droplet interaction. However, turbulence alone is one of the unresolved and most challenging problems in classical physics. The turbulence–droplet interaction is even more difficult due to its strong nonlinearity and multi-scale properties in both time and space. In this thesis, Eulerian and Lagrangian models are developed and compared to tackle turbulence–droplet interactions. It is found that the Lagrangian superparticle model is computationally less demanding than the Eulerian Smoluchowski model.

The condensation process is then investigated by solving the hydrodynamic and thermodynamic equations using direct numerical simulations with droplets modeled as Lagrangian particles. With turbulence included, the droplet size distribution is found to broaden, which is contrary to the classical theory without supersaturation fluctuations, where condensational growth leads to progressively narrower droplet size distributions. Furthermore, the time evolution of droplet size distributions is observed to strongly depend on the Reynolds number and only weakly on the mean energy dissipation rate. Subsequently, the effect of turbulence on the collision process driven by both turbulence and gravity is explored. It is found that the droplet size distribution depends moderately on the mean energy dissipation rate, but is insensitive to the Reynolds number. Finally, the effect of turbulence on the combined condensational and collisional growth is investigated. In this case, the droplet size distribution is found to depend on both the Reynolds number and the mean energy dissipation rate. Considering small values of the mean energy dissipation rate and high Reynolds numbers in warm clouds, it is concluded that turbulence enhances the condensational growth with increasing Reynolds number, while the collision process is indirectly affected by turbulence through the condensation process. Therefore, turbulence facilitates warm rain formation by enhancing the condensation process, which predominantly depends on the Reynolds number.