Turbulence-Cloud Droplet Interaction in Cloud Microphysics Simulator

Statistical theory by Chandrakar et al. (2016, Proc. Natl. Acad. Sci. USA, 113, 14243-14248) is carefully studied and used to validate ``Cloud Microphysics Simulator (CMS)", a DNS model which computes the evolution of the cloud droplets and turbulence based on the microscopic dynamics (Saito and Gotoh, New J. Phys., 20, 023001, 2018). The theory is originally proposed to explain the broadening of cloud droplet size-distribution (droplet spectrum) obtained from 'PI-chamber', a laboratory cloud chamber, and is constructed in terms of Langevin equation for supersaturation fluctuation. The standard deviation of the squared droplet radius is expressed as a function of a characteristic system time which is defined by the harmonic mean of the phase relaxation time of the droplets and the turbulent mixing time, and was found to agree with the experimental data from PI-chamber.

In order to examine the validity of the CMS, we compare the CMS simulation results with the theory, and find that the standard deviation of the squared droplet radius by the CMS is consistent with the theoretical prediction and behaves very similarly to that found in the PI-chamber. Furthermore, careful analysis of the DNS data shows that 1. Turbulent mixing time in the theory is slightly longer by about 25% than the large-eddy turnover time of turbulence, 2. The diffusion coefficient appearing in the standard deviation of the squared droplet radius should be expressed in terms of the Lagrangian autocorrelation time of the supersaturation. When the above points are accounted in the theory, the agreement between the theoretical prediction and the CMS results becomes very satisfactory.

In addition to the above findings, we obtained the analytical expression for the droplet spectrum in steady state by deriving the Fokker-Planck equation for the size distribution. The aerosol effects are introduced as the zero flux boundary condition at R²=0, where R is a droplet radius. This is mathematically equivalent to the case of the Brownian motion under the presence of wall. It is found that the analytical size distribution is proportional to R*exp(-c R² ), where c is a constant, and agrees well with our DNS results for both cases with or without aerosol effects, and qualitatively with the PI-chamber results as well.