Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2019 / 4 / b

For an initially monodisperse cloud the relative settling speed vanishes, so there is no gravitational collection term in this model. Set $D=(S-1)/(F_k+F_d)$ and use $M=4\pi {\rho }_l{r}^3/3$. Condensational growth givesTaking upward height from cloud base as positive, the droplet speed relative to the ground is the updraft minus its downward terminal velocity:For a launch at $h_r(0)=0$,This assumes the prescribed uniform updraft and supersaturation persist along the trajectory, and that the Stokes-type radius-squared fall law remains applicable.