Measurements of Roughness Length and Displacement Heights in Model Urban Canopies

We present the results of roughness length and displacement height based on PIV velocity measurements in a water tunnel experiment of flow over idealized models of urban canopies. Experiments were conducted with large roughness elements of regular arrays of buildings of uniform height with aspect ratios of 1 and 3. Mean velocity profile above the canopy is described by the log law and a simple optimization procedure to compute the roughness length and displacement height has been developed. Laterally averaged values of displacement height d/H increase from 0 to 1 with plan area density $\lambda_{\mathrm{p}}$ of the urban canopy. In contrast, laterally averaged roughness height z$_{\mathrm{0}}$/H increases to a maximum value (as $\lambda _{\mathrm{f}}$ approaches a value of 0.2) and then decreases to zero. We present data for effective roughness heights (z$_{\mathrm{0}}+$d)/H as a function of aspect ratio H/w$_{\mathrm{b}}$ of buildings. This also reveals three categories of values: street canyon, building wake, and laterally averaged values. Measurements taken at the centerline of canyons form a lower bound on the effective roughness height whereas measurements behind building wakes form an upper bound. Laterally averaged values of friction velocity u$_{\mathrm{\ast}}$/U$_{\mathrm{H}}$ varied inversely with the aspect ratio (U$_{\mathrm{H}}$ is the mean velocity at the building height).