Turbulence and cloud droplets in cumulus clouds

Abstract

In this paper, we report on the successful and seamless simulation of turbulence and the evolution of cloud droplets to raindrops over 10 minutes from microscopic viewpoints by using direct numerical simulation. Included processes are condensation–evaporation, collision–coalescence of droplets with hydrodynamic interaction, Reynolds number dependent drag, and turbulent flow within a parcel that is ascending within a self-consistently determined updraft inside a cumulus cloud. We found that the altitude and the updraft velocity of the parcel, the mean supersaturation, and the liquid water content are insensitive to the turbulence intensity, and that when the turbulence intensity increases, the droplet number density swiftly decreases while the spectral width of droplets rapidly increases. This study marks the first time the evolution of the mass density distribution function has been successfully calculated from microscopic computations. The turbulence accelerated to form a second peak in the mass density distribution function, leading to the raindrop formation, and the radius of the largest drop was over 300 μ m at the end of the simulation. We also found that cloud droplets modify the turbulence in a way that is unlike the Kolmogorov–Obukhov–Corrsin theory. For example, the temperature and water vapor spectra at low wavenumbers become shallower than ${k}^{-5/3}$ in the inertial-convective range, and decrease slower than exponentially in the diffusive range. This spectra modification is explained by nonlinear interactions between turbulent mixing and the evaporation–condensation process associated with large numbers of droplets.

Keywords

• turbulence
• cloud droplets
• turbulence spectra