Waves in the lee of an isolated hill

Abstract

Abstract A two‐dimensional ridge produces a system of lee waves parallel to it, in a suitable airstream. Synthesizing an isolated hill by superposition of ridges inclined at various angles but intersecting in a point, and representing this by an integral, the interference pattern of the lee‐wave systems of the component ridges has been computed. An isolated hill produces a lee‐wave pattern very similar to that produced by a ship moving across the surface of deep water. It is confined within a wedge‐shaped region, the corner of the wedge being vertical and through the hill top. The half‐angle of the wedge depends upon the airstream characteristics but is typically about 15°. The waves decrease in amplitude downstream like x −½ . If an oval hill lies across the airstream an appreciale lee‐wave system will be produced but it is greatly reduced in amplitude if the major axis of the hill is turned through 30° or more from the normal to the airstream. The discussion is restricted, on account of its complexity, to airstreams composed of only two layers, in each of which the parameter l is independent of height.