Theory of air flow over a heated land mass

The velocity field of a stable atmosphere over and around a heated land mass is found, as a function of both time and distance, by consideration of the equations of motion, continuity and added heat. A heat function is introduced, in the last of these, which is not only fairly simple mathematically but also bears a good resemblance to the atmospheric picture. Certain terms are neglected initially to simplify the mathematics of the problem but they are used later to check the validity of the results and it is found that, in general, the solution would have been negligibly affected by the inclusion of these terms. There is difficulty in using the boundary condition at infinite height but this is overcome by evaluating the problem by two methods. The numerical work was done on the EDSAC at Cambridge and some graphs of these results, using a normal type of ground temperature distribution and lapse rate, are shown.