Orogenic blocking and deflection of stratified air flow on an f-plane

The stationary, finite-amplitude, orogenic disturbance of a straight barotropic air current on the rotating earth is studied numerically on the basis of quasi-static equations. Three quantifiable characteristics are defined in order to provide evaluation of the upstream flow structure: (i) the point of incipient splitting; (ii) the strength of blocking; (iii) the extent of streamline displacement. The numerical results have been used to investigate the dependence of these characteristics on the Rossby number, Ro, the non-dimensional mountain height, H, and the non-dimensional mountain shape factor, A (across-stream length/along-stream length), with the non-dimensional stability fixed. The experiments provide an indication of how the critical non-dimensional mountain height for stagnation and for splitting, respectively, depends on the Ro and A. The experiments show that the proportion of flow that goes around the mountain increases as A becomes smaller. For the cases when Ro·H ≥ A, the surface-level flows upstream of the mountains are mostly or even fully diverted around it and partly blocked by the mountain. In agreement with the inferences drawn by Pierrehumbert and Wyman (1985), it is shown that for an across-stream length of mountains greater or equal to the radius of deformation, i.e. Ro·H ≤ A, the maximum extent of the upstream influence is of the order of the radius of deformation, Ro·H. For Ro·H ≥ A, this extent is limited by horizontal dispersion to a distance proportional to A.