A Theoretical Study of Mountain Barrier Jets over Sloping Valleys

Abstract

A shallow-water model is developed to examine the dynamics of mountain-barrier jets over a mesoscale sloping valley between two mountain ridges. In this model, the cold air trapped in the valley is represented by a shallow-water layer that is coupled with the upper-layer flow through a free-slip interface. The pressure gradient exerted from the upper layer plus the pressure gradient generated by the sloping cold layer itself drive the cold air down the valley forming a jet against the surface friction. In the cross-valley direction, the jet-induced Coriolis force is balanced by the pressure gradient force. For a given cross-valley terrain profile, the solution is controlled by eight dimensional environmental parameters. In the nondimensional space, the solution is controlled only by three parameters: the Froude number modified by the ratio between the valley width and the Rossby radius of deformation, the surface drag coefficient normalized by the ratio between the valley depth and the inertial radius, and the upper-layer cross-valley pressure gradient scaled by the lower-layer along-valley pressure gradient. Analytical solutions are obtained for a given cross-valley terrain profile, and the results quantify the dependence of the jet intensity and cross-valley structure on the environmental parameters. The theoretical results are also compared with numerical model simulations.