Bridging the Urban Canopy Sublayer to Aerodynamic Parameters of the Atmospheric Surface Layer

Abstract

Within the roughness sublayer (RSL) of dense urban canopies composed of uniformly distributed cuboids, the time and planar-averaged mean velocity profile exhibits an approximate exponential shape characterized by a depth-independent attenuation coefficient a. A formulation that links a to the zero-plane displacement d and aerodynamic roughness length $z_{\mathrm{om}}$ is proposed using a one-dimensional momentum balance between the background mean horizontal pressure gradient, vertical gradients of total stresses, and the drag force. Dispersive effects on a within the urban RSL are then explored using large-eddy simulations (LESs) that vary independently the planar ($\lambda _{\mathrm{p}}$) and frontal ($\lambda _{\mathrm{f}}$) densities of the cuboids. The LES results are used to compute d and $z_{\mathrm{om}}$ by fitting a log-profile to the mean velocity above the canopy. Within the canopy, the LES results are also used to estimate (i) a by fitting an exponential profile to the computed time and planar-averaged velocity, (ii) profiles of drag coefficients, and (iii) turbulent as well as dispersive stresses. The LES results demonstrate that dispersive stresses can be commensurate with turbulent stresses in magnitude and act in the same direction. Moreover, dispersive transport, determined from vertical gradients of dispersive stresses, is some 25–75% of turbulent stress gradients. These dispersive effects impact a (and thus d and $z_{\mathrm{om}}$) via two mechanisms: (i) reducing the effective adjustment length scale that leads to an increase in a and (ii) increasing the effective mixing length that leads to a reduction in a across a wide range of $\lambda _{\mathrm{f}}$ and $\lambda _{\mathrm{p}}$. These two effects are shown to be partly compensatory giving rise to an apparent constant a with respect to height inside the canopy. The effects of mean recirculation and the usage of the drag force centroid method to estimate d are discussed. The analysis also evaluates the consequences of a finite roughness sublayer thickness extending above the canopy on the derived expressions.