A Theory of AIr Drainage

The equation of motion is derived for a compressible fluid cooling at the bottom by contact with a radiating surface of uniform slope and large extent. During the early stages the drainage velocity is found to vary periodically about an equilibrium value. The equilibrium value is proportional to the net outgoing radiation from the ground, and is inversely proportional to the height to which cooling extends and to the slope of the ground. The rate at which equilibrium is attained depends upon the assumed form of the frictional force. In the absence of detailed observations of drainage velocities, it is concluded tentatively that the assumption of a frictional force which is proportional to the square of the velocity gives fairly realistic results.