Observations of fohn in the Alps and other mountainous regions suggest that the underlying dynamics is often affected by gap-like features in elongated ridge-like topography. To assess the dynamics of these flows, idealized numerical experiments are conducted with a hydrostatic numerical model, using S-plane geometry and a free-slip lower boundary condition. The topography is taken to be a two-dimensional ridge oriented in the west/east direction with a valley transect of depth DeltaH across it. The upstream flow is westerly, with a constant wind speed U and constant Brunt-Vaisala frequency N. The control parameters defined by this setting are a dimensionless gap depth N DeltaH/U, the ratio between ridge height and gap depth H/DeltaH, a Rossby number describing the south-north width of the ridge, and additional parameters associated with the shape of the gap. with intermediate Rossby numbers (Ro approximate to 1) the setting resembles that of shallow Alpine south-fohn cases, which are characterized by a cross-Alpine flow essentially confined to valley transects. For small dimensionless gap depths and large Rossby numbers, the flow follows the predictions of linear theory and takes on an approximately symmetric pattern with respect to the ridge line. For N DeltaH/U greater than or similar to 1, flow separation and splitting takes place upstream and downstream of the gap, respectively. The how within the gap decouples from the flow aloft and is driven by the geostrophic south-north pressure gradient to yield a fohn-like flow. It is demonstrated that the limit f --> 0 is singular (i.e. the flow solution does not converge towards the symmetric f = 0 solution), and that there exist multiple stationary solutions for f = 0 (two with northerly and southerly flow across the gap, respectively, and one with north/south symmetry). The existence of these multiple steady states is related to a wake instability, yet vortex shedding is suppressed by the presence of the ridge downstream of the gap. Additional simulations are presented which demonstrate that a transient external forcing can induce transitions between the multiple flow solutions. The relationship of the idealized setting to Alpine shallow fohn is discussed, and additional experiments are conducted to assess the effects of surface friction and of an inversion present to the south of the ridge.
