No abstract

No abstract

SUMMARYThe 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.

SUMhfARYIn a previous paper (Smith 1955), the problem of the resultant theoretical velocity field that arises from the diurnal variation of heating of a land mass with an initially stationary air mass was considered. The present paper considers the same problem with an initial overall velocity. Henceforth the first paper (Smith 1955) will be referred to as Part I.The same heat function is used as in Part I for the time and horizontal variations, but the vertical variation is amended for closer approximation to the different circumstances. The difficulty of the boundary condition at infinite height is overcome by associating the solutions with those of Pt. I.The resulting surface temperatures and vertical velocities at different times are shown in tables and graph.

The above three papers were read on 16 November 1955 DR. JOANNE S. MALxcus (partly communicated) : The papers of Smith (1955) and Pearce (1955) in the July issue of the Quarterly Journal are significant milestones in the investigation of air motions caused by differential heating. The sea-breeze problem, not long ago regarded as enormously diffcult and complex, has made rapid strides in the years since the war. While it would be naive to declare that any problem in meteorology has been ' solved,' at least in this one many of the important theoretical questions have been framed, and physical models now stand available for critical observational test. T o aid in deriving the greatest value from these recent contributions, a few remarks will be made here comparing the two approaches, both with one another and with previous treatments. (a) The relation between the work of Smith (1955) and that of M a l k~ and Stern (Z953)The latter authors studied the flow over a heated island with a prevailing wind and mnsidered only the quasi-steady situation expected near the time of maximum land-sea temperature excess, Smith treats the time-dependent evolution of the motions when the air mass is initially at rest. Actually, it is readily shown that each of these situations is described by a special case of a more general differential equation. This equation is derived by including a term u, 3/3x with the accelerational terms in Smith's equations of motion and modif9ng his definition of the heating function, H, to read : 37 3 7 . 37, H ( x , y , z , t ) = -+ U , -+ w -at 3X 32where uo is the prevailing geostrophic wind. The x-axis is chosen along uo and ug does not vary in space or time; r0 and 7 are reciprocals of the undisturbed and disturbed potential temperature