. Compendium of meteorology. Meteorology. 424 DYNAMICS OF THE ATMOSPHERE envelope which encloses all points in the x, t plane cov- ered by two or more characteristics. The meaning of such an envelope depends almost entirely on the physi-. A X Fig. 2.—The characteristics of a compression wave. cal nature of the problem and of the quantity u. The envelope has meaning if it is possible to have two values of M at a point. Usually the assumptions involved in deriving equations (1) and (2) are violated before the envelope is formed by the characteristics. If the region in which equations (1) and (2)
. Compendium of meteorology. Meteorology. 424 DYNAMICS OF THE ATMOSPHERE envelope which encloses all points in the x, t plane cov- ered by two or more characteristics. The meaning of such an envelope depends almost entirely on the physi-. A X Fig. 2.—The characteristics of a compression wave. cal nature of the problem and of the quantity u. The envelope has meaning if it is possible to have two values of M at a point. Usually the assumptions involved in deriving equations (1) and (2) are violated before the envelope is formed by the characteristics. If the region in which equations (1) and (2) cannot be used is very small and motion inside it is not important, it is assumed to be so thin that it can be drawn as a line in the x, t plane and it is called a jump. It is so called because there are jumps in values of ii and w on going across such a line. Such an assumption can be made in gas dynamics where the jump is called a shock, in hydraulics where it is called a hydraulic jump, in flow under an inversion where it is called a pressure jump, and to a certain extent in flow in a planetary jet stream where the jump is called a block. FLOW UNDER AN INVERSION Statement of the Problem. The changes in height of an inversion and the flow beneath an inversion are of great interest to synoptic meteorologists. The frontal contour charts of the Canadian Weather Service [6] bring home the fact that motions of the frontal surface are important even far behind its intersection with the ground. The behavior of low-level winds during and just after the passage of a surface cold front in the Western Plains is usually a topic of discussion among forecasters. Finally, the forecasters in tropical areas are interested in the variation of the winds below the trade wind inversion. It is the writer's opinion that a mathe- matical theory of flow under an inversion will help to describe these phenomena and perhaps will eventually lead to quantitative forecasting techniques. Several phenomen
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