Momentum

A simple, but general, horizontal momentum budget for inviscid (cid:143) ow is developed to understand how the vertical (cid:143) ux of horizontal momentum varies with height in a mountain-forced trapped lee-wave train. Taking a sinusoidal form for the wave (cid:142) eld, from the analytical solution for a two-layer Scorer-parameter atmosphere, the constant Bernoulli functional on a streamline is used to diagnose the momentum (cid:143) ux. It is shown that in an inviscid, steady wave train the magnitude of the momentum (cid:143) ux decreases with height as a sinusoidal function. The present theory clearly shows how this pro(cid:142) le of momentum (cid:143) ux with height is a direct consequence of the exact balance between the vertical derivative of momentum (cid:143) ux and the dynamic pressure difference across the mountain in steady state. The simple analytic pro(cid:142) le of (cid:143) ux with height shows a remarkable qualitative similarity with numerical-model results from idealized case-studies of (cid:143) ow over an isolated mountain ridge.