Effect of turbulence and condensation on drop‐size distribution in cloud

Equations are developed to represent the rate of change of the number of drops of a given size in a cloud owing to condensation and to coalescence respectively. Numerical computation from these equations shows that condensation has a much greater effect than coalescence on drop‐size distribution in clouds with small average drop size, with small liquid‐water content or with a large degree of super‐saturation. With the assumption that drop‐size distribution in a cloud is governed by rate of condensation on the drops in the cloud and rate of turbulent diffusion of the drops out of the cloud it is then shown that the fractional volume of water comprised by drops smaller than a specified size is expressible in terms of an Incomplete Gamma function. In this Incomplete Gamma function the argument is 1·5 and the upper limit to the integral varies as the square of the drop size and is also proportional to a quantity which depends upon the degree of turbulence and upon parameters connected with the rate of condensation. It is shown that this theoretical formula approximates closely to a simpler formula already established empirically and that reasonable values for the coefficient of turbulence and the condensation parameters lead to a mean drop size which agrees closely with measured values.