Katabatic flow induced by a top-hat profile of down-slope surface cooling

Katabatic flows driven by inhomogeneous surface forcings are ubiquitous in nature. They can arise from irregular snow, ice or ground cover, cloud cover, topographic shading (e.g., when upper slopes are shaded while lower slopes are sunlit), and variations in soil moisture, soil type or vegetation type. In this combined analytical/numerical study, we consider katabatic flow of a viscous stably-stratified fluid down a planar slope driven by surface cooling (negative buoyancy) that varies down the slope as a top-hat, but is uniform in the cross-slope direction. The two-dimensional linearized Boussinesq equations of motion and thermodynamic energy are solved by Fourier transformation, and the results compared with numerical solutions of the corresponding nonlinear equations. For the linear analysis, a judicious change of variables removes all parameters from the governing differential equations. The only parameters entering the problem are those stemming from the boundary conditions. It is found that for the isolated cold-strip, flow structures are controlled by a single non-dimensional parameter that depends on the strip width, slope angle, buoyancy frequency, and the viscosity and diffusivity coefficients. Key structures include the primary katabatic jet, rotors, gravity waves and two nearly horizontal environmental jets; one that feeds into the primary katabatic jet on the upslope end of the strip, and one that emanates from the boundary layer on the down-slope end of the strip. Results are interpreted from a vorticity-dynamics perspective.