# Parametrization of Drag and Turbulence for Urban Neighbourhoods with Trees

## Abstract

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 root-mean-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 the canopy on average for the highest leaf area density scenarios tested: \(0.50\hbox { m}^{2}~\hbox {m}^{-3}\). *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.

## Keywords

Column model Computational fluid dynamics model Momentum transfer Turbulent kinetic energy Urban forest Vegetation## Notes

### Acknowledgments

This research was funded by Discovery Grants (TRO & AC) and a Canada Graduate Scholarship (ESK) from the Natural Sciences and Engineering Research Council of Canada, and by the Spanish Ministry for Economy and Competitiveness Project CGL2011-26173 (AM & JLS). This last project funded a visit by ESK to CIEMAT, where part of the work was completed.

## Supplementary material

## References

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