Coriolis effects in katabatic flow along a differentially cooled sloping surface in a stratified fluid

Inhomogeneous surface buoyancy fields are ubiquitous in nature. They arise from irregular snow/ice/soil cover, cloud cover, topographic shading (e.g., upper slopes are shaded while lower slopes are sunlit), soil moisture (e.g., from a surface rainfall gradient), variations in vegetation type or coverage, and changes in land use. In one of our previous studies, the classical one-dimensional katabatic wind model of Prandtl was extended to include one of the simplest possible surface inhomogeneities – surface buoyancy that varies linearly down the slope. Such inhomogeneity breaks the symmetry of the Prandtl model, and introduces such features as flow acceleration, convergence and associated vertical motions, and horizontal and vertical advection of both perturbation and base-state temperature fields. A scaling hypothesis appropriate for this problem reduces the steady-state Boussinesq equations of motion, mass conservation and thermodynamic energy to a set of nonlinear ordinary differential equations. Analytical solutions of these equations yield formulas for the boundary-layer thickness and slope-normal velocity component at the top of the boundary layer (entrainment velocity), and provide an upper bound to the along-slope surface-buoyancy gradient beyond which steady-state solutions do not exist (solution breakdown). Numerical solutions of the corresponding unsteady problem confirm the main results from the analytical theory, and show further that breakdown of the steady-state solution is associated with the self-generation of low-frequency gravity waves.

Our recent work to be reported at the conference shows how the Coriolis force can be incorporated into this idealized model framework. The extended model, which now applies to flows with arbitrary Rossby number, consists of eight coupled equations which are exact within the Boussinesq framework. Our focus will be on both the unsteady behavior of the solutions (including the self-generation of inertia-gravity waves for decelerating flows), and on the structure of the katabatic boundary layer, including jet strength and strength of the return flow above the jet.