When air flows over terrain where the surface temperature varies with position, non-adiabatic heat will be added or subtracted. We consider the time-dependent disturbances induced in a uniform basic current as the result of differential heating on a flat rotating earth.
The problem of obtaining a plausible mathematical-physical description of the heating function is then discussed. A method which was proposed in a previous paper, Stern and Malkus (1953), is re-examined and restated, to clarify the underlying assumptions and the point of departure from the classical theory of the eddy conduction of heat.
With this description of the heating function, it is shown that the mean motions may be specified in terms of an “equivalent mountain.” This depends, in general, on the Coriolis parameter as well as the surface temperature, undisturbed wind speed, and the eddy conductivity of the heated region. The theory is applied to the small-scale sea-breeze problem, and it is shown that, by retaining the linearized advective term in the momentum equation, it is possible to explain the frequently observed phase relation between the diurnal temperature wave and the sea breeze without introducing friction. Additional derived relations for the hodograph suggest tests by means of future observations.