Waves in the lee of a mountain with elliptical contours

Abstract

This paper considers the flow over a mountain which has elliptical contours, for two types of undisturbed air stream. In the first case the static stability parameter l ² = gB /V ² is assumed to be constant throughout the atmosphere, and in the second l ² is assumed to fall off exponentially with height, in each case with ( V’’/V ) = q ² also being constant. On the basis of the wave equation derived in an earlier paper, a simpler method is developed to find approximations to the difficult Fourier integrals which arise. The results show that when l ² is constant the form of the waves is determined by the value of q. When q = 0 the waves lie in a strip in the lee of the highest part of the mountain, but when q is large enough the waves are contained in a wedge, and resemble ship waves. When l ² falls off exponentially the waves closely resemble ship waves for any value of q . The variation of the amplitude of the waves as various parameters are changed is discussed in detail.