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The effect upon a stable atmosphere of a heat source (5–10 km width), which is a specified function of the coordinates, is investigated theoretically. A two-dimensional problem is chosen, with the x-coordinate in the direction of the mean undisturbed surface wind U, and the z-direction vertical. The heat source, a finite-width pulse in x, has maximum amplitude at the ground (z = 0) and decays with height. A steady state, in which the heat supplied by the source is continuously carried away downstream, is assumed, and the equations of motion are linearized by the method of perturbations. By Fourier analysis of the pulse function, the perturbation equations are made separable, and solutions for the streamline flow are obtained. It is shown that “lee waves,” i.e., extended downstream oscillations in the streamlines, occur only if the undisturbed wind or stability undergoes a change in the vertical. The results of the analysis are compared with observations made over Nantucket Island, a flat sandy strip about 5 km in width.
Malkus et al. (Sun,) studied this question.