Predicting mean velocity profiles inside urban canyons

Knowledge of mean wind profiles is important for applications in wind engineering and air quality modeling. Yet despite advances in our ability to simulate winds on street scales, existing theoretical predictions do not apply to the important limit of tall, closely packed buildings or generalize to realistic geometries. We present an alternative strategy based on the existence of intense layers of vorticity at solid boundaries and the roof level. Following the approach in vortex dynamics, wherein the velocity field is modelled by approximating the vorticity field, spatially and temporally averaged vertical profiles of the horizontal velocity components are derived from the numerical Green's functions for the three-dimensional Poisson equation and vortex sheets located at the top and bottom of an urban canyon; mean profiles of the spanwise velocity along the canyon axis are obtained similarly. The method is applied to skimming flow for idealised and realistic canyons and tested against building-resolving simulations. Good agreement is obtained for a wide range of external wind directions, including winds that are parallel to the canyon axis. For a unit-aspect-ratio street canyon, the relative error in the streamwise velocity is 30−50% over the entire canyon, but 10−20% when the top and bottom boundary layers are excluded; the errors in the spanwise velocity are smaller. It is shown that the model can be successfully calibrated from single-point measurements taken above the urban canopy.