Turbulent flow over groups of cubical urban-like obstacles

We present high resolution simulations of turbulent boundary layer flow over regular arrays of cubical urban-like obstacles, which for the first time are obtained by 'direct numerical simulation'. Hence the turbulence in the simulations is computed explicitly from the Navier-Stokes equations, without any turbulence modelling or tuning of parameters (unlike previous simulations based on LES or RANS). The Reynolds number of the flow is high enough, namely 5000, for Reynolds number independence. Numerical tests are performed to demonstrate the credibility of the simulations and detailed comparisons with wind tunnel data show excellent agreement. Flow visualisation demonstrates the existence of vortex structures in the flow, both above and within the arrays. The unsteady flow dynamics depart significantly from the time mean flow. The spatially averaged momentum balance over the buildings is computed and is compared with that over plant canopies. It is found that the magnitude of the dispersive stress is negligible above the urban canopy but is significant within. A strong shear layer develops at the top of the arrays and blocks eddies both above and below. This supports the view that, at the obstacle density investigated here (0.25), the flow within the canopy is decoupled from that above. Comparisons also show that the flow depends very much on the layout of the obstacles. The results provide a benchmark against which to compare other more approximate simulations, such as LES, and a complete set of data to evaluate simplified modelling approaches such as urban canopy models.