Urban canopy parameterizations (UCPs) are necessary in mesoscale modelling to take into account the effects of buildings on wind and turbulent structures. This study is focused on the dynamical part of UCPs. The main objective is twofold: first, computing important UCP input parameters (turbulent length scales and the sectional drag coefficient) by means of Reynolds-averaged Navier-Stokes (RANS) simulations of turbulent flow; and second, comparing UCP variables with spatially-averaged properties obtained from RANS simulations for the same configurations. The results show the importance of using a suitable parameterization of the drag force for different packing densities. An urban canopy parameterization that is a compromise between simplicity and accuracy is proposed. This scheme accounts for the variation of drag coefficients with packing densities, and has a parameterization of turbulent length scales. The technique adopted ensures that, at least for the simple configurations studied, the urban canopy parameterization gives values of spatially-averaged variables similar to those computed from a more complex simulation, such as RANS that resolves explicitly the flow around buildings.
Air flow inside an array of cubes is simulated. Cubes (edge length 0.15 m) are arranged in a regular array, separated by 0.15 m in the streamwise and spanwise directions. Numerical simulations are performed based on Reynolds-averaged Navier-Stokes equations (RANS), solved in a computational fluid dynamics model (CFD), with standard k-ε turbulent closure (two prognostic equations are solved for the turbulent kinetic energy k and its dissipation ε, respectively). Simulations are validated against wind-tunnel data using a technique based on hit-rate calculations, and calculated statistical parameters. The results show that the horizontal velocity is very well modelled, and despite some discrepancies, the model that fulfils the hit-rate test criteria gives useful results that are used to investigate three-dimensional (3-D) flow structures. The 3-D analysis of the flow shows interesting patterns: the centre of the canyon vortex is at 3/4 of the canyon height, and stronger downward than upward motions are present within the canyon. Such behaviour is explained by the presence of a compensation flow through the side of the canyon, which enters the canyon from the upper part and exits from the lower part. This complex 3-D structure affects the tracer dispersion, and is responsible for pollutant transport and diffusion.
Reynolds-averaged Navier-Stokes (RANS) simulations of turbulent flow over groups of buildings with different packing densities are reported. The results for a selected packing density are compared with direct numerical simulations (DNS) previously validated against wind-tunnel data. The present study is focused on average properties of the flow, especially on the drag coefficients, and is a first attempt to provide information on these parameters (their values are not generally known) for a range of packing densities, for a given staggered arrangement of cubes using RANS methods. However, some of the limitations of RANS have come to light. Hence, it is recommended that such simulations are 'calibrated' against experimental or DNS data, as is done here.
Urban canopy parametrizations designed to be coupled with mesoscale models must predict the integrated effect of urban obstacles on the flow at each height in the canopy. To assess these neighbourhood-scale effects, results of microscale simulations may be horizontally-averaged. Obstacle-resolving computational fluid dynamics (CFD) simulations of neutrally-stratified flow through canopies of blocks (buildings) with varying distributions and densities of porous media (tree foliage) are conducted, and the spatially-averaged impacts on the flow of these building-tree combinations are assessed. The accuracy with which a one-dimensional (column) model with a one-equation (k-l) turbulence scheme represents spatially-averaged CFD results is evaluated. Individual physical mechanisms by which trees and buildings affect flow in the column model are evaluated in terms of relative importance. For the treed urban configurations considered, effects of buildings and trees may be considered independently. Building drag coefficients and length scale effects need not be altered due to the presence of tree foliage; therefore, parametrization of spatially-averaged flow through urban neighbourhoods with trees is greatly simplified. The new parametrization includes only source and sink terms significant for the prediction of spatially-averaged flow profiles: momentum drag due to buildings and trees (and the associated wake production of turbulent kinetic energy), modification of length scales by buildings, and enhanced dissipation of turbulent kinetic energy due to the small scale of tree foliage elements. Coefficients for the Santiago and Martilli (Boundary-Layer Meteorol 137: 417-439, 2010) parametrization of building drag coefficients and length scales are revised. Inclusion of foliage terms from the new parametrization in addition to the Santiago and Martilli building terms reduces rootmean-square difference (RMSD) of the column model streamwise velocity component and turbulent kinetic energy relative to the CFD model by 89 % in the canopy and 71 % above Electronic supplementary material The online version of this article (123 158 E. S. Krayenhoff et al.the canopy on average for the highest leaf area density scenarios tested: 0.50 m 2 m −3 . RMSD values with the new parametrization are less than 20 % of mean layer magnitude for the streamwise velocity component within and above the canopy, and for above-canopy turbulent kinetic energy; RMSD values for within-canopy turbulent kinetic energy are negligible for most scenarios. The foliage-related portion of the new parametrization is required for scenarios with tree foliage of equal or greater height than the buildings, and for scenarios with foliage below roof height for building plan area densities less than approximately 0.25.
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