Modelling the mean velocity profile in the urban canopy layer

A simple model originally derived for mean wind speed profiles in vegetative canopy flows is modified for application to arrays of three-dimensional surface obstacles (cubes), which could be representative of a simple urban-type surface. It is shown that for cube arrays that are not too densely packed, the predicted exponential velocity profile provides an adequate fit to the spatially averaged velocity profile [u(z)] within the obstacle canopy. Application of the model to a set of wind-tunnel data allows for the evaluation of an empirical fitting parameter called the attenuation coefficient. This is related to the turbulence length scale, which can be found by manipulating the results of the gradient-diffusion model used to derive the velocity profile. The results show a reduction of the turbulence length scale with increasing obstacle packing density. By assuming a linear transition from this length scale at the top of the canopy to the classical Prandtl length scale in the overlying inertial sublayer, an acceptable model is obtained for the full velocity profile within simple obstacle arrays, from the ground up to the overlying semi-logarithmic region.