The Problem of Air Flow Over Mountains: A Summary of Theoretical Studies

Abstract

The theoretical researches on the problem of the disturbance of an atmospheric current flowing over a mountain range, carried on during the last ten years, prove that most of the characteristic observed features can be explained, to a very large extent, by the hydrodynamical theory of internal, small adiabatic perturbations in a stratified rotating atmosphere. In the case of a uniform current of velocity u, in which the coefficient of vertical stability is also uniform (θ is the potential temperature, g the gravity, z the elevation), the perturbation pattern corresponding to a smooth, low, gently-sloping mountain range varies widely according to the half-width a of this mountain range:i) If a is comparable to the critical value (Ls/2π) = (u/s) ≈ 1 km, there is a system of short stationary lee waves, or gravity waves, with the wave length Ls.ii) If a is comparable to (Lf/2π) = (u/f) ≈ 100 km, where f is the Coriolis parameter, there is a complex system of gravity-inertia lee waves, with the horizontal wave length Lf at ground level, and the vertical wave length Ls in the vertical plane of the crest.iii) In the case of a westerly wind, if a is comparable to the third critical value , where β is the latitudinal variation of f, there is a system of long geostrophic lee waves, of the type studied by Rossby, with the horizontal wave length Lβ at ground level.iv) In the other cases, there are no lee waves, and the wave system is either missing (cases a ≪ (u/s) and ≫ (u/f)) or restricted to the vicinity of the vertical plane of the crest, with the wave length Ls (case (u/s) ≪ a ≪ (u/f). One of the effects of the tropopause, and of atmospheric discontinuities in general, is to produce eventually an additional system of waves on the upwind side of the mountain range, but these waves must be generally much smaller than the lee waves. Similar results are obtained for a plateau with smooth sides, and in the case of a more complex mountain profile the perturbation can be computed by superimposing elementary solutions. If the current is not uniform, if the ground deformation is steep, or if the perturbation is not adiabatic, the preceding results are not valid, and the solution of the theoretical problem has been obtained in only very special cases.