Are Urban-Canopy Velocity Profiles Exponential?

Abstract

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer's logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.

Properties of Mixing Length and Dispersive Stress in Airflows over Urban-Like Roughness Obstacles with Variable Height

“…In CB04 it was considered that the mixing length is proportional to the distance from the surface within a sparse canopy but is constant within a dense canopy. By combining the characteristics of both canopies, CB04 represented the mixing length, denoted here as l m, CB , as follows: validating the present LES, the profile of l m, eff in V00 is compared with the DNS result of Branford et al (2011) and Castro (2017), and seems to correspond well with the DNS result. Above the canopy, the profiles of l m, CB in all the simulations agree with those of l m, eff at and around the canopy top, while l m, CB gradually deviates from l m, eff as the height increases.…”

“…In their studies, l m increases monotonically with height within the urban canopy as well as above the canopy top. In contrast, Castro (2017) showed that l m obtained from direct numerical simulation (DNS) and large-eddy simulation (LES) of flows over roughness obstacles with uniform height has a single local maximum within the canopy, and that l m has multiple local maxima within the canopy for flows over roughness with variable height. In this way, there are still unknowns on how and why the characteristics of l m appear depending on the urban geometrical feature.…”

“…We regard this effective mixing length as a baseline to evaluate the mixing-length properties. We further examine a mixing length calculated from the sum of Reynolds and dispersive stresses to estimate the impacts of dispersive stress (Castro 2017). This mixing length l m, sum is determined as:…”

“…Furthermore, dispersive stress was shown to have contributions equal to or greater than that of Reynolds stress to the total momentum flux within an urban canopy (Coceal et al 2006). Meanwhile, Castro (2017) indicated that the mixing length determined by the sum of Reynolds and dispersive stresses does not differ significantly from that determined only by Reynolds stress. However, the maximum value of the former was shown to be up to approximately 20% greater than that of the latter, depending on the density and arrangement of obstacles.…”

Introducing the urban wind island effect

“…The mixed-layer model only takes the mean boundary-layer wind into account, hence no vertical profiles of the wind can be modelled. In reality the boundary layer can experience vertical wind shear during neutral and weakly unstable conditions, especially in the complex terrain of cities [39][40][41], and knowledge of the vertical structure of wind speed is important for applications such as urban planning (e.g. through mechanical loads on buildings).…”