A criterion for the generation of turbulent anabatic flows

Turbulent convection over a heated infinite horizontal plane is ideally characterized by updrafts and downdrafts with no net mean motion, but a mean upslope (or anabatic) flow can be generated if the plane is even slightly inclined. A study on the mechanism responsible for the generation of upslope flow is described in this paper. When the heat flux is sufficiently large, the upslope flow becomes turbulent and is signified by thermals rising from the surface and deflected upslope to feed into the anabatic flow. It is argued theoretically and demonstrated experimentally that for a certain Prandtl number (Pr) range the tendency for heated thermals to deflect and follow the slope is inversely proportional to Pr and directly proportional to the inclination angle (β), and thus the critical angle above which the upslope flow can be sustained is given by βc=cPr, where c is a constant. This finding can explain the existence of well-developed atmospheric (Pr∼1) upslope flows above very gentle slopes in areas of complex topography.