Momentum flux due to trapped lee Waves forced by mountains

A simple, but general, horizontal momentum budget for inviscid flow is developed to understand how the vertical flux of horizontal momentum varies with height in a mountain-forced trapped lee-wave train. Taking a sinusoidal form for the wave field, from the analytical solution for a two-layer Scorer-parameter atmosphere, the constant Bernoulli functional on a streamline is used to diagnose the momentum flux. It is shown that in an inviscid, steady wave train the magnitude of the momentum flux decreases with height as a sinusoidal function. The present theory clearly shows how this profile of momentum flux with height is a direct consequence of the exact balance between the vertical derivative of momentum flux and the dynamic pressure difference across the mountain in steady state. The simple analytic profile of flux with height shows a remarkable qualitative similarity with numerical-model results from idealized case-studies of flow over an isolated mountain ridge.