The propagation of groups of internal gravity waves in a shear flow

The propagation in a shear flow of travelling internal gravity waves of short wavelength is investigated by the W.K.B. approximation. This implies that the Richardson number is large. It is shown that a wave group moves with the local group velocity defined in terms of the dominant wavenumber, the absolute frequency and horizontal components of wavenumber being constant. The wave energy carried by a wave packet varies, being proportional to the frequency relative to a frame moving with the local mean wind. A wave packet, on this approximation, can never pass through a critical level at which its horizontal phase velocity is equal to the mean wind, nor is it reflected there.

These results imply restrictions on the propagation of internal gravity waves from the troposphere to the upper atmosphere.