Rotational aspects of stratified gap flows and shallow fohn

Observations of fohn in the Alps and other mountainous regions suggest that the underlying dynamics is often affected by gap-like features in elongate d ridge-like topography. To assess the dynamics of these flows, idealized n umerical experiments are conducted with a hydrostatic numerical model, usin g 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 wes terly, with a constant wind speed U and constant Brunt-Vaisala frequency N. The control parameters defined by this setting are a dimensionless gap dep th N DeltaH/U, the ratio between ridge height and gap depth H/DeltaH, a Ros sby number describing the south-north width of the ridge, and additional pa rameters associated with the shape of the gap. with intermediate Rossby num bers (Ro approximate to 1) the setting resembles that of shallow Alpine sou th-fohn cases, which are characterized by a cross-Alpine flow essentially c onfined to valley transects. For small dimensionless gap depths and large R ossby 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-n orth pressure gradient to yield a fohn-like flow. It is demonstrated that t he limit f --> 0 is singular (i.e. the flow solution does not converge towa rds 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 m ultiple steady states is related to a wake instability, yet vortex shedding is suppressed by the presence of the ridge downstream of the gap. Addition al simulations are presented which demonstrate that a transient external fo rcing can induce transitions between the multiple flow solutions. The relat ionship of the idealized setting to Alpine shallow fohn is discussed, and a dditional experiments are conducted to assess the effects of surface fricti on and of an inversion present to the south of the ridge.