Quasi-Steady Katabatic Winds on Slopes in Wide Valleys: Hydraulic Theory and Observations

Abstract

Theoretical and field observational studies on mean velocity and temperature fields of quasi-steady nocturnal downslope (katabatic) flows on sloping surfaces are reported for the case of very wide valleys in the presence of weak synoptic winds. Because of the lateral constraints on the flow, Coriolis effects are considered negligible. The layer-averaged equations of Manins and Sawford were used for the analysis. It is shown that (i) in the absence of significant turbulent entrainment into the current (i.e., at large Richardson numbers Ri = ?h cosα/U2) the downslope flow velocity U is related to the slope length (LH), slope angle (α), and the buoyancy jump between the current and the background atmosphere (?) as U = ?u(?LH sinα)1/2, where ?u is a constant and h is the flow depth; (ii) on very long slopes h is proportional to Lh(tanα)1/2; and (iii) under highly stable conditions (i.e., Ri > 1) the katabatic flow exhibits pulsations with period T0 = 2π/N sinα, where N is the buoyancy frequency of the background atmosphere. These predictions are verified principally using observations made during the Vertical Transport and Mixing Experiment (VTMX) conducted in Salt Lake City, Utah, in October 2000. By assuming the flow follows a straight line trajectory to the nearest ridgeline a good agreement was found between the predictions and observations over appropriate Richardson number ranges. For Ri > 1.5, ?u ≈ 0.2, although ?u was a decreasing function of Ri at lesser stabilities. Oscillations with period T0 are simply alongslope (critical) internal-wave oscillations with a slope-normal wavenumber, which are liable for degeneration into turbulence during their reflection. These critical internal waves may be responsible, at least partly, for weak sustained turbulence often observed in complex-terrain nocturnal boundary layer flows.