Mountain Waves Produced by a Stratified Boundary Layer Flow. Part I: Hydrostatic Case

A hydrostatic theory for mountain waves with a boundary layer of constant eddy viscosity is presented. It predicts that dissipation impacts the dynamics over an inner layer whose depth is controlled by the inner-layer scale d of viscous critical-level theory. The theory applies when the mountain height is smaller or near d and is validated with a fully nonlinear model. In this case the pressure drag and the wave Reynolds stress can be predicted by inviscid theory, if one takes for the incident wind its value around the inner-layer scale. In contrast with the inviscid theory and for small mountains the wave drag is compensated by an acceleration of the flow in the inner layer rather than of the solid earth. Still for small mountains and when stability increases, the emitted waves have smaller vertical scale and are more dissipated when traveling through the inner layer: a fraction of the wave drag is deposited around the top of the inner layer before reaching the outer regions. When the mountain height becomes comparable to the inner-layer scale, nonseparated upstream blocking and downslope winds develop. Theory and the model show that (i) the downslope winds penetrate well into the inner layer and (ii) upstream blocking and downslope winds are favored when the static stability is strong and (iii) are not associated with upper-level wave breaking.