Mountain waves produced by a stratified shear flow with a boundary layer. Part III: Trapped lee waves and horizontal momentum transport

The boundary layer theory for non-hydrostatic mountain waves presented in Part II is extended to include upward propagating gravity waves and trapped lee waves. To do so, the background wind with constant shear used in Part II is smoothly curved and becomes constant above a "boundary-layer" height d which is much larger than the inner layer scale δ. As in Part II, the pressure drag stays well predicted by a gravity wave drag when the surface Richardson number J > 1 and by a form drag due to non separated sheltering when J < 1. As in Part II also, the sign of the Reynolds stress is predominantly positive in the near neutral case (J < 1) and negative in the stable case (J > 1) but situations characterized by positive and negative Reynolds stress now combine when J ∼ 1. In the latter case, and even when dissipation produces positive stress in the lower part of the inner layer, a property we associated with non separated sheltering in Part II, negative stresses are quite systematically found aloft. These negative stresses are due to upward propagating waves and trapped lee waves, the first being associated with negative vertical flux of pseudo-momentum aloft the inner layer, the second to negative horizontal flux of pseudo-momentum downstream the obstacle. These results suggest that the significance of mountain waves for the large-scale flow is more substantial than expected and when compared to the form drag due to non separated sheltering.