THE FLOW OF A STABLE ATMOSPHERE OVER A HEATED ISLAND, PART II

Abstract

In Part I, the convective motions produced by the flow of a stable air stream over a small flat island were studied when the distribution of heating as a function of the coordinates was assumed. In Part II, the mechanism of the heating is examined. It is found that the heat source obeys an eddy-conduction equation and is established by turbulent eddying in the mixed ground layer. The streamline displacement may be divided into two components, one obeying the equation for air flow over a mountain ridge and the other obeying a heat-conduction equation, the latter component being important only in the near vicinity of the island. An “equivalent mountain” corresponding to the heated island may be specified analytically; it depends only upon the temperature distribution along the surface, the wind speed, the eddy conductivity in the ground layer, and the undisturbed stability. Its amplitude is related to the maximum streamline displacement. The “equivalent mountain” for Nantucket Island is calculated for two extreme observational cases. The complete streamline picture is constructed for several examples of an air stream whose properties remain unaltered to great heights. The basic current possessing a change in stability or wind speed at an upper level is also discussed, and the forecasting of lee waves is related to the development of the mixed ground layer via the height of the “equivalent mountain.” An expression for the sea breeze is also derived.