Coriolis effects in heterogeneous katabatic flows

Katabatic flows along a planar slope in a viscous stably-stratified fluid on a rotating earth are investigated analytically and numerically. Of special interest are differences in the action of the Coriolis force in one-dimensional (classical Prandtl framework) and two-dimensional (a class of heterogeneous) frameworks, and the different flow structures found in the respective steady states. The considered two-dimensional flows are induced by a cold surface strip of finite width running down the slope. In the case of the one-dimensional flows, the down-slope velocity field has a boundary layer structure but the buoyancy and cross-slope velocity component spread inexorably upward. In contrast, in the two-dimensional strip flow, a steady state is reached in which the cross-slope wind and buoyancy fields vanish far above the slope, but the down-slope and slope-normal velocity fields do not vanish. These latter two components comprise two purely horizontal along-isentrope currents: an up-slope current entering the top of the boundary layer obliquely on one side of the strip, and a down-slope current leaving the boundary layer obliquely into the environment on the other side of the strip. The slope-normal vorticity associated with these currents originates in the stretching of planetary vorticity in a broad zone of convergent flow over the cold strip. The generation of this shear flow is analogous to the katabatic-flow-induced spin-up effect in polar vortex over the Antarctic continent.