AbstractObservations of föhn 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, usingf‐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 ΔHacross it. The upstream flow is westerly, with a constant wind speedUand constant Brunt‐Väisälä frequencyN. The control parameters defined by this setting are a dimensionless gap depthNΔH/U, the ratio between ridge height and gap depthH/ΔH, 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≈︁1) the setting resembles that of shallow Alpine south‐föhn 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. ForNΔH/U≳ 1, flow separation and splitting takes place upstream and downstream of the gap, respectively. The flow within the gap decouples from the flow aloft and is driven by the geostrophic south‐north pressure gradient to yield a föhn‐like flow. It is demonstrated that the limitf→ 0 is singular (i.e. the flow solution does not converge towards the symmetricf= 0 solution), and that there exist multiple stationary solutions forf= 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 föhn is discussed, and additional experiments are conducted to assess the effects of surface friction and of an inv