Waves in the lee of a mountain with elliptical contours

Abstract

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 l2=gB/V2 is assumed to be constant throughout the atmosphere, and in the second l2 is assumed to fall off exponentially with height, in each case with (V’’/V ) = q2 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 l2 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 l2 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.