Rotational aspects of stratified gap flows and shallow föhn

Abstract

Observations 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, using f‐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 ΔH across it. The upstream flow is westerly, with a constant wind speed U and constant Brunt‐Väisälä frequency N. The control parameters defined by this setting are a dimensionless gap depth NΔH/U, the ratio between ridge height and gap depth H/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. For NΔH/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 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 föhn 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.

Idealized numerical simulations of shallow föhn

“…The impact of surface friction is studied extensively. The results are compared with those obtained by Sprenger and Schär (2001) for an in nite mountain ridge with a gap. Sensitivity experiments are performed with an arc-shaped mountain giving a better representation of the real Alps than a straight mountain ridge.…”

“…The in uence of the geostrophic pressure gradient on gap ows, particularly on shallow föhn, has recently been investigated by Sprenger and Schär (2001) (henceforth referred to as SS01). They considered an in nitely long mountain ridge with a gap exposed to a uniform, ridge-parallel ow in geostrophic balance.…”

A review of recent advances in understanding the meso- and microscale properties of the severe Bora wind

“…Some of rotational effects related to gap flows in the Alps are assessed by Sprenger and Schär (2001). They find that the flow within the gap decouples from the flow aloft, which is driven by the geostrophic south‐north pressure gradient to yield a föhn‐like flow.…”

Gap Flows through Idealized Topography. Part II: Effects of Rotation and Surface Friction

“…They found that southerly gap winds could occur in free-slip simulations provided the col was low enough to create a deep cross-mountain pathway. Zängl (2002a) extended the work of Sprenger and Schär (2001) to the case of geostrophically balanced westerly flow parallel to an east-west ridge of finite length cut by a north-south gap. He found that mesoscale circulations created by the interaction of the large-scale flow and the isolated ridge exerted a dramatic influence on the gap winds.…”

“…The underlying dynamics, in which topographically constrained ageostrophic winds blow along the gap from high to low pressure, was named "pressure driven channeling" by Whiteman and Doran (1993), who found it to be the dominant mechanism for generating light or moderate winds within the relatively broad Tennessee Valley. Idealized gap winds driven by the large-scale pressure gradient have also been simulated by Sprenger and Schär (2001), who examined a stratified geostrophically balanced westerly flow parallel to the axis of an infinitely long east-west ridge transected by a north-south gap with a col. They found that southerly gap winds could occur in free-slip simulations provided the col was low enough to create a deep cross-mountain pathway.…”