On the Momentum and Scalar Roughness Lengths of Urban Surfaces

Large-eddy simulations (LES) of flow and scalar transport over regular arrays of cuboid roughness elements are conducted to study the surface exchanges of momentum and scalars over very rough walls. By independently varying the frontal area density $\lambda_f$ and plan area density $\lambda_p$, we examine the effects of surface geometry on the momentum and scalar roughness lengths ($z_{0m}$ and $z_{0s}$). The opposing effects of $\lambda_f$ and $\lambda_p$ give rise to the characteristic non-monotonic behavior in $z_{0m}$. The results indicate that It is in general possible to derive morphologically-based parameterizations for $z_{0m}$ that give satisfactory performance. However, this is not the case for the scalar roughness length: spatially-variable surface scalar transfer coefficients cannot be easily determined a priori from geometric parameters alone. However, invoking the surface renewal theory, we here show that a general scaling relation between the logarithmic ratio $\log(z_{0m}/z_{0s})$ and the roughness Reynolds number $Re_*$ can be obtained for very rough surfaces such as urban terrain.