A Note on Friction Velocity and Viscous Effect for Idealized Urban Canopy Flows

Friction velocity is one of the important scaling parameters in atmospheric boundary layer studies. However, several definitions of friction velocity exist in the literature: e.g. estimated from the total drag force or used only pressure drag, etc. In this study, a series of large-eddy simulation (LES) calculations were carried out to evaluate the impact of various definitions on the friction velocity for idealized urban geometries, i.e. staggered array of cubes with different packing densities and wind directions. We first compared the normalized velocity fields with the literature data for the case with a packing density of 25%. The results show that the LES data normalized by the friction velocity derived from the Reynolds stress using the extrinsic spatial average is more consistent with the direct numerical simulation (DNS) data. Furthermore, when varying the wind direction, the distribution of Reynolds stress and pressure drag show significant change in streamwise and spanwise directions. We further found that for packing density of 44.44%, the frictional drag accounts for more than a quarter of the total drag, and even higher than the pressure drag in parallel wind direction. This leads to the deviation of friction velocity estimated from the pressure drag and that calculated from the total drag force up to 33%. Such characteristic of viscous effect challenges the assumption widely used in wind tunnel experiments and urban canopy parameterizations that the contribution of viscous force is negligible, especially for ultra-dense arrays.