Numerical simulations of stably stratified flow through a mountain pass

The effect of boundary-layer friction in stably stratified flow through a mountain pass is examined through a series of idealized numerical simulations. Both two-dimensional (2-D) simulations of flow through a valley which is infinitely long in the direction of the flow and three-dimensional (3-D) simulations of flow through a pass in a 2-D ridge are conducted. For the 2-D simulations the secondary flow induced by the flow turning in the boundary layer is investigated and the behaviour categorized depending on the location of any flow separation on the valley side. The separation (diagnosed using surface stresses) is found to depend primarily on a Froude number based on the valley depth. The generation of potential vorticity (PV) in the boundary layer adjacent to the valley sides is examined in the 2-D simulations, and numerical results are found to agree well with simple scaling analysis. In the 3-D case PV is still generated in the boundary layer adjacent to the sides of the pass, and this PV is advected out of the pass by the flow across the mountain. When the upstream flow is sufficiently strongly stratified (Froude number based on the mountain height less than unity) a hydraulic jump occurs on the lee side of the mountain ridge, enabling advection of the PV out of the boundary layer and into the interior of the flow. Examination of the PV structure on isentropic surfaces downwind of the mountain ridge reveals the presence of PV banners which originate from the sides of the pass. In these simulations frictional processes within the boundary layer appear to dominate the production of the PV banners, and gravity-wave breaking plays a relatively minor role.