Linear mountain drag and averaged pseudo-momentum flux profiles in the presence of trapped lee waves

Abstract

The linear mountain drag in the presence of trapped lee waves is calculated using a two-dimensional linear anelastic model. In many cases, it is shown that the drag is affected by the wave refraction index aloft, but remains well predicted by the drag due to hydrostatic freely propagating mountain waves. In contrary, the vertical profile of the waves' Reynolds stress is very sensitive to the mean flow variation, and often decays with altitude in the steady case and in the absence of dissipation. This apparent contradiction with the conventional Eliassen-Palm relation is simply related to the non-zonal, non-periodic geometry of the domain in which the momentum budget is calculated and to the presence of trapped lee-waves. In this context, the spatial average of the pseudo-momentum conservation equation shows that the wave drag at the ground is equal to the wave pseudo-momentum entering in the domain through its upper and leeward boundaries. In the presence of trapped lee-waves, the amount of pseudo-momentum entering through the leeward boundary represents a significant part of the drag, and explains the difference between the Reynolds stress and the surface drag. In this case, the large-scale flow does not need to be modified inside the physical domain, because the entering pseudo-momentum equals the entering momentum transported by the waves across the domain boundaries. It is suggested that conventional gravity wave drag schemes can easily represent the trapped waves by altering the large scale momentum at low level, when the waves are dissipated.