Wave propagation in a stratified shear flow

Abstract

The linearized initial-value problem for a two-dimensional, unbounded, exponentially stratified, plane Couette flow is considered. The solution is used to evaluate the evolution of wave-packet perturbations to the mean flow for all Richardson numbers J > ¼, demonstrating that a consistent wave-packet approach to wave propagation in these flows is possible for all J > ¼. It is found that the vertical influence of a wave-packet perturbation is limited to a distance of order (J − ¼)½/k0, where k0 is the magnitude of the initial central wave vector. These results are used to clarify the J [gsim ] ¼ conclusions of an earlier treatment by Booker & Bretherton.