A bulk theory for air mass motion along a high mountain ridge

A steady-state, spatial, large-scale, non-linear problem of the air mass motion along an undulating mountain ridge is considered in the framework of bulk theory. The ridge is assumed to be so high that the air mass cannot top it, and, instead of the actual ridge itself, a high vertical wall with sinuousities identical to those of the ridge is considered. It is assumed that the air mass is bounded above by an inversion interface (idealized inversion layer) overlain by a geostrophic, polytropic, atmosphere that is thermally homogeneous along the horizontal and stably stratified with a constant geostrophic wind blowing along the mean direction of the ridge. The inversion strength (potential temperature deficit) is not constant and considered as an additional dependent variable. Because of the Earth's rotation effects, the air mass flow to the left of the ridge and that to the right of the ridge differ considerably in their features. The fact that the characteristic transverse linear scale of the problem (the generalized Rossby radius of deformation) is small compared with the longitudinal scale permits making simplifications that result in a semi-geostrophic model of the boundary-layer type. Then the problem can be reduced to an ordinary differential equation, which admits a closed-form solution. Analysis of the solution enables one to deduce some general features of the process under investigation such as, for example, orographic front formation, a transition from sub-critical to super-critical wind and others.