Adjustment of Turbulent Boundary-Layer Flow to Idealized Urban Surfaces: A Large-Eddy Simulation Study

Abstract

Large-eddy simulations (LES) are performed to simulate the atmospheric boundary-layer (ABL) flow through idealized urban canopies represented by uniform arrays of cubes in order to better understand atmospheric flow over rural-to-urban surface transitions. The LES framework is first validated with wind-tunnel experimental data. Good agreement between the simulation results and the experimental data are found for the vertical and spanwise profiles of the mean velocities and velocity standard deviations at different streamwise locations. Next, the model is used to simulate ABL flows over surface transitions from a flat homogeneous terrain to aligned and staggered arrays of cubes with height $h$. For both configurations, five different frontal area densities $(\uplambda _\mathrm{f})$, equal to 0.028, 0.063, 0.111, 0.174 and 0.250, are considered. Within the arrays, the flow is found to adjust quickly and shows similar structure to the wake of the cubes after the second row of cubes. An internal boundary layer is identified above the cube arrays and found to have a similar depth in all different cases. At a downstream location where the flow immediately above the cube array is already adjusted to the surface, the spatially-averaged velocity is found to have a logarithmic profile in the vertical. The values of the displacement height are found to be quite insensitive to the canopy layout (aligned vs. staggered) and increase roughly from $0.65h$ to $0.9h$ as $\uplambda _\mathrm{f}$ increases from 0.028 to 0.25. Relatively larger values of the aerodynamic roughness length $(z_0)$ are obtained for the staggered arrays, compared with the aligned cases, and a maximum value of $z_0$ is found at $\uplambda _\mathrm{f} = 0.111$ for both configurations. By explicitly calculating the drag exerted by the cubes on the flow and the drag coefficients of the cubes using our LES results, and comparing the results with existing theoretical expressions, we show that the larger values of $z_0$ for the staggered arrays are related to the relatively larger drag coefficients of the cubes for that configuration compared with the aligned one. The effective mixing length $(l_\mathrm{m})$ within and above different cube arrays is also calculated and a local maximum of $l_\mathrm{m}$ within the canopy is found in all the cases, with values ranging from $0.2h$ to $0.4h$. These patterns of $l_\mathrm{m}$ are different from those used in existing urban canopy models.