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.