A wind tunnel study of flows over idealised urban surfaces with roughness sublayer corrections

Dynamics in the roughness (RSLs) and inertial (ISLs) sublayers in the turbulent boundary layers (TBLs) over idealised urban surfaces are investigated analytically and experimentally. In this paper, we derive an analytical solution to the mean velocity profile, which is a continuous function applicable to both RSL and ISL, over rough surfaces in isothermal conditions. Afterwards, a modified mixing-length model for RSL/ISL transport is developed that elucidates how surface roughness affects the turbulence motions. A series of wind tunnel experiments are conducted to measure the vertical profiles of mean and fluctuating velocities, together with momentum flux over various configurations of surface-mounted ribs in cross flows using hot-wire anemometry (HWA). The analytical solution agrees well with the wind tunnel result that improves the estimate to mean velocity profile over urban surfaces and TBL dynamics as well. The thicknesses of RSL and ISL are calculated by monitoring the convergence/divergence between the temporally averaged and spatio-temporally averaged profiles of momentum flux. It is found that the height of RSL/ISL interface is a function of surface roughness. Examining the direct, physical influence of roughness elements on near-surface RSL flows reveals that the TBL flows over rough surfaces exhibit turbulence motions of two different length scales which are functions of the RSL and ISL structure. Conclusively, given a TBL, the rougher the surface, the higher is the RSL intruding upward that would thinner the ISL up to 50 %. Therefore, the conventional ISL log-law approximation to TBL flows over urban surfaces should be applied with caution.