Mountain Waves and Boundary Layers

Linear 3-D mountain wave theory is extended to include a thin frictional boundary layer (BL), parameterized using two characteristic relaxation times for wind adjustment. Both wave absorption and generation are considered. The slower boundary layer winds respond more strongly to imposed pressure gradients than do the faster free stream winds, but they also violate Bernoulli's Theorem because of friction. Wind maxima occur in regions of favorable pressure gradient; not in regions of minimum pressure. In hydrostatic flow, the boundary layer shifts the wind disturbance upstream and reduces mountain wave amplitude. The wave momentum flux is reduced more than the pressure drag reduction. The BL effect is very sensitive to the ratio of the friction coefficients at the bottom and top of the BL, giving a strong diurnal variation. In three dimensional hydrostatic flows, the boundary layer improves the linear theory description of windy peaks, gap flows and tip jets. The BL decreases the amount of upslope orographic precipitation. In irrotational (i.e. potential) flow, our BL formulation shifts the disturbance downstream causing a form drag but no wave momentum flux.