Unsteady Thermally Driven Flows on Gentle Slopes

Abstract

The theoretical and laboratory studies on mean velocity and temperature fields of an unsteady atmospheric boundary layer on sloping surfaces reported here were motivated by recent field observations on thermally driven circulation in very wide valleys in the presence of negligible synoptic winds. The upslope (anabatic) flow on a long, shallow, heated (with a buoyancy flux F_bs) slope of inclination α located adjoining a level plane and the effects of cooling of the slope on this flow during the evening transition are studied for the case of a gentle slope for which the length of the sloping plane far exceeds the thickness h of the convective boundary layer. First, a theoretical analysis is presented for the mean upslope flow velocity U_M, noting that the turbulence but not the mean flow structure therein is similar to that on a level terrain. The analysis, which is based on mean momentum and heat equations as well as closure involving level-terrain turbulence parameterizations, shows that U_M is proportional to α^1/3w∗, where w∗ = (F_bsh)^1/3. Second, new physical effects associated with evening transition are elicited by considering the idealized case of (specified) cooling the upslope flow on a simple slope. Theory and available field data show that, because of their inertia and although the heating ceases, upslope winds decay only slowly over a period of about 10(h/U_M), which is tantamount to several hours on gentle slopes, whereupon flow reversal occurs from upslope to downslope. During this stage, because the air is cooling as it rises up the slope, its potential energy increases, resulting in momentary stagnation of the airflow at a location within a few meters above the surface (in the form of a transition front) followed by local overturning due to convective instabilities; this scenario is consistent with some field observations but has not been observed in mesoscale model simulations because of insufficient resolution to capture the front. A laboratory experiment conducted by subjecting an upslope flow to a rapidly changing surface flux confirmed the theoretical result that flow reversal occurs at a finite distance along the slope with the appearance of a front, which quickly migrates down the slope as the first front of the ensuing katabatic current.