A Theoretical Study of the Compensating Downward Motions Associated with Cumulus Clouds

An attempt is made to investigate theoretically the controlling influence of compensating downward motions on the development of cumulus clouds and the size of the cloudless areas associated with them. The model consists of two circular concentric air columns, the inside column corresponding to the updraft (cloud) region and the outside concentric annular column to the downward motion region. The combined cell is surrounded by the atmospheric at rest. The governing equations of both the updraft and the compensating downward motion are derived from the conservation equations of momentum, heat, moisture and mass. The differential equations are solved numerically to compute the vertical velocity, temperature, specific humidity and liquid water content in and out of the cloud as functions of height and time. Two experiments were performed with and without the effect of compensating downward motion. The main conclusions are the following: Without the effect of the compensating motion, the structure of the solitary updraft tends to a steady state. However, with the compensating motion, no tall cloud is maintained (unless there is a steady source of moisture at the cloud base), since the compensating downward motion acts as a “break.” Also, it was found that the most active cloud system develops when the ratio of the cloud area over the entire area (including the cloudless area associated with the updraft) is of the order of several per cent.