Planetary scale flow over steep mountains

Abstract

The problem of the excitation of stationary planetary scale waves by steep mountains is here examined. The equations of a Boussinesq fluid in a β-plane infinite domain in the presence of a North-South ridge of width much smaller than the Rossby deformation radius,Rd, are considered. By using scaling arguments, the problem of matching a global quasi-geostrophic stationary Rossby wave, of scale much larger thanRd, to a local semigeostrophic solution of the kind discussed by Merkine [17] is analyzed and solved. The difference between the above solution and the totally quasi-geostrophic one, discussed, for example, by Janowitz [15] is analyzed and found to be crucial to the problem of resonant excitation of planetary topographic waves.