Coriolis effects in inhomogeneous katabatic flows

The classical Prandtl katabatic flow model provides a simple but qualitatively realistic description of the steady boundary layer flow of a viscous negatively buoyant fluid down an inclined planar slope in a stably-stratified environment. It has long been recognized that when this model is extended to include the Coriolis force, the cross-slope wind and buoyancy fields inexorably diffuse upward from the surface, resulting in solutions that do not have the boundary layer character. This behavior of the cross-slope wind and buoyancy contrasts markedly with the down-slope velocity component that retains a boundary-layer type structure.

In this presentation we consider the effect of the Coriolis force on the structure of katabatic flow of finite cross-slope extent (a strip of negative surface buoyancy along the slope). Key results are obtained analytically, through linear analysis of the two-dimensional viscous Boussinesq equations of motion and mass conservation, and numerically, through direct numerical simulation. The two-dimensional flow associated with the finite cross-slope surface buoyancy differs profoundly from that in the one-dimensional Prandtl model with Coriolis forcing. In particular, both cross-slope wind and buoyancy fields within the new two-dimensional model framework are of the boundary layer type, albeit of a complex nature. Moreover, the down-slope velocity component now has a residual component far above the surface. This remote down-slope component is part of a horizontal streaming motion (horse-shoe-like circulation) in which air parcels approach the boundary layer along environmental isotherms on one side of the strip, move cross slope, and then stream outward into the outer flow region along environmental isotherms on the other side of the strip. In contrast, the flow within the boundary layer exhibits a corkscrew-like behavior.