Upslope Flows in Atmosphere and Water Tank, Part II: Fluid-Dynamical Smoothness as a Possible Cause for Velocity Similarity Violation

Abstract

Water-tank models of meso-scale atmospheric processes often show good qualitative agreement of bulk quantities and flow characteristics and good quantitative agreement of turbulence quantities with field observations. However, it was demonstrated in the first part of this two-part communication that the similarity of velocities of thermally driven upslope flows in atmosphere and water tank is violated. It is shown in this part that the velocities of thermally driven upslope flows in the atmosphere and in a water-tank model have statistically different dependences on proposed governing parameters. Of four substantially different hypotheses of upslope velocities, three agree with field observations because of large uncertainties and sparse data, but all hypotheses disagree with tank observations. One hypothesis that includes the influence of the total slope height agrees with field and tank observations when assuming fluid-dynamically rough atmospheric flows and fluid-dynamically smooth tank flows. The non-dimensional upslope flow velocities corresponding to rough and smooth flows depend differently on the governing parameters. Therefore, non-dimensional upslope flow velocities are different for atmosphere and water tank. Furthermore, as this hypothesis includes a dependence of the upslope flow velocity on the total height of the slope it implies that upslope flow systems are non-local phenomena. Because fluid-dynamical roughness is technically difficult to achieve in water-tank models, velocity similarity violations can also be expected in water-tank models of other thermally driven meso-scale flows and our technique of explicitly including roughness length dependence may have wider applications.