Pierrehumbert, R. T., and B. Wyman, 1985: Upstream effects of mesoscale mountains. Journal of the Atmospheric Sciences, 42 (10), 977-1003.

Abstract: The Alpine Experiment (ALPEX) has revealed that low-level air is typically diverted around the Alps without reaching the mountaintop. In pursuit of an understanding of the physical basis of this phenomenon and of its generality, we have explored the characteristics of orographic blocking of a rotating continuously stratified fluid, as revealed in a simple model problem retaining full nonlinear and transient effects. Hydrostatic dynamics is assumed, and the obstacleis taken to be an infinitely long ridge with height h(x). The key questions treated are the strength of the upstream deceleration of cross-mountain flow and the length scale over which the decelerated region extends. By means of scale analysis, the controlling parameters are found to be the Rossby number Ro = U/fL and the Froude number Fr = Nh_m/U, where U is the speed of the oncoming flow, f is the Coriolis parameter, L the mountain half-width, N the Brunt Väisälä frequency, and h_m is the maximum mountain height. The scale analysis also determines the qualitative dependence of the strength of the blocking on Ro and Fr; these predictions were confirmed and made quantitative via extensive numerical simulation.
In the nonrotating limit, Fr is the sole parameter. In this case, it is found that for sufficiently large Fr a decelerated layer of fluid forms near the obstacle and propagates arbitrarily far upstream with time, in a manner similar to that familiar in one-layer hydraulic theory. The upstream influence requires neither downstream lee wave trains nor vertical confinement by a rigid lid; rather, the upstream modes appear to be generated by wave breaking above the lee slope of the mountain. For a Gaussian mountain profile, wave breaking and upstream influence set in near Fr = 0.75; low-level flow upstream of the mountain is decelerated to rest for Fr > 1.5. In the rotating case, the decelerated zone does not propagate infinitely far. Instead, it attains a maximum extent on the order of the radius of deformation Nh_m/f before retreating toward the mountain. The upstream scales remaining after a long time has passed are also discussed.
The theory accounts for a number of aspects of the ALPEX data, as well as for features seen in earlier observations of barrier winds elsewhere. It appears though that the sharp transition between flow over and flow around found in certain ALPEX vertical soundings obtained from aircraft cannot be explained in terms of inviscid theory. It is conjectured that the sharp division is due to low-level convective mixing.