Abstract
Flow incident on a mountain ridge with a linear vertical windshear is studied for a Boussinesq, adiabatic, inviscid fluid on the f-plane. A scale analysis indicates that the semigeostrophic approximation of a geostrophic mountain-parallel wind holds for sufficiently shallow mountain slopes if the Rossby number squared is small. In such a limit, the equation for the vertical displacement of a fluid parcel is elliptic if there is forward shear (wind increasing with height) or weak backward shear (wind decreasing with height) but hyperbolic if there is strong backward shear such that the incident wind vanishes at some level in the flow.
Steady-state results indicate that forward shear weakens the cold-core geostrophic mountain anticyclone predicted by barotropic theory while weak backshear strengthens it. This behavior arises from the warm- (cold-) air advection in the forward (backward) shear case. While the total ageostrophic flux of mass across the mountain peak is greater for the forward shear case, the maximum ageostrophic cross-mountain wind is less.
Results for the semigeostrophic initial-value problem with a critical level depict the development of a stronger and narrower baroclinic lee trough than for quasi-geostrophic theory.
