Air parcel random walk and droplet spectra broadening in clouds

We study the effect of turbulent flow on the droplet growth in a cloud during the condensational phase. Using the air parcel model, we describe analytically how the distribution of droplets over sizes evolves at the different stages of parcel movement. We show that turbulent random walk superimposed on an accelerated ascent of the parcel make the relative width of droplet distribution to grow initially as $t^{1/2}$ and then decay as $t^{-3/2}$.