Some Measurements of Surface Drag in Urban-Type Boundary Layers at Various Wind Angles

Using experimental data obtained in naturally grown boundary layers over a generic urban-type roughness (height h) it is shown that the surface drag is strongly dependent on the flow direction with respect to the roughness orientation. The variations with wind direction are accompanied by corresponding changes in the parameters contained in the usual logarithmic description of the flow in the near-wall inertial layer, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${U/u_\tau=\frac{1}{\kappa}\ln[(z-d)/z_{\rm o}]}$$\end{document}, principally the roughness length zo, which can vary by a factor of around three. The maximum surface drag (and roughness length) occur when the flow direction is at an angle around 45° to the faces of the cubical roughness elements, consistent with the known fact that the drag of an isolated cube in a thick boundary layer is much larger at that orientation than for flow directions normal to the faces. An accurate electronic balance was used to determine the surface drag (and hence friction velocity uτ) and pressure-tapped roughness elements allowed estimation of the zero plane displacement d. It is shown that the best logarithmic-law fits then generally require values of the von Kármán ‘constant’ κ significantly lower than its classical value of around 0.41. For a factor of six increase in the Reynolds number (from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${U_{\rm ref}h/\nu\approx 3,500}$$\end{document}), Reynolds number effects are shown to be very weak and, coupled with the form drag and total drag data, the results thus suggest that frictional contributions to the total surface drag are relatively small.