Upslope Flows in Atmosphere and Water Tank, Part I: Scaling

Abstract

Upslope flows are a crucial mechanism in the transport of air pollutants in complex terrain, both as separate flow systems and as part of other thermally driven flows. Resolving steep complex terrain in numerical models requires horizontal resolutions that are difficult to achieve. Water-tank models of upslope flows provide additional insights but require idealizations that have typically limited comparisons with atmospheric observations to order-of-magnitude estimations. This paper applies scaling to a water tank that was specifically designed to achieve quantitative similarity with field measurements at a particular site. Non-dimensional boundary-layer depths near the base of slope in atmosphere and water tank agree within the measurement uncertainties of the field observations (20%). We show that boundary-layer depth and upslope flow velocity at any point in time are completely determined by instantaneous and integrated surface heat fluxes (from the beginning of positive heat flux to the point in time), regardless of the surface heat flux's particular path in time. While velocities in two independent tank experiments with steady and sinusoidal surface heat flux, respectively, agree reasonably well at the expected time of similarity, they disagree statistically significantly with velocities in the atmosphere. This disagreement implies a dependence on molecular quantities (viscosity, thermal diffusivity). Since different definitions of Reynolds numbers provide inconclusive values and both the appropriate velocity scale and length scale for a Reynolds number are functions of the flow itself, we derive an alternative set of governing parameters. This set provides the basis for a detailed hypothesis for the similarity violation of upslope flow velocities in atmosphere and water tank in a companion paper.