A Simple Mixing-Length Model for Urban Canopy Flows

Urban canopy models (UCMs) developed based on Prandtl mixing-length theory provide a simple method for predicting urban flows. In the existing models, the Prandtl mixing length and the sectional drag coefficient of buildings are usually assumed to be uniform with height within urban canopies. This leads to exponential vertical profiles of the time-averaged and horizontally space-averaged streamwise velocity component within urban canopies, which was recently found to be inaccurate. In this study, in order to improve the current UCM predictions, a new mixing-length parametrization is proposed for urban canopy flows by considering the strong shear layer at the canopy roof level. It assumes that, within the shear layer, the mixing length increases linearly with the distance from the canopy roof level with a proportionality constant approximately equal to 0.8. Using the new parametrization, good predictions of the space-averaged mean wind profiles are obtained against building-resolved large-eddy simulation and direct numerical simulation results.