A numerical study of the flow field and exchange processes within a canopy of urban-type roughness

Numerical modelling of the flow through a simplified domain representing regular cube arrays of three different packing densities was carried out, using seven-equation Reynolds stress turbulence modelling (RSM) with a high-resolution mesh. The cases considered were cube arrays of area density 0.0625, 0.16 and 0.44 in a simulated atmospheric boundary layer, as studied previously in experiments by Macdonald et al. (Measurements of mean velocity and turbulence in simple obstacle arrays at 1:200 scale, 2000) and LES by Hanna et al. (Atmos. Env. 36 (2002) 5067). Profiles of mean velocity and individual turbulence components were examined and found to be acceptable for the purposes of examining the flow field within the canopy and the processes of exchange at its top. The time-averaged flow field in sheltered regions was found to be dominated by large vortical flow patterns whose form varied with array packing density. It is suggested that the form of these vortices may influence the effectiveness of upward mixing within the canopy. The concept of exchange velocity, and the analytical model of Bentham and Britter (Atmos. Env. 37 (2003) 2037) were summarized, and values for the exchange velocities at the canopy top were estimated from the CFD solution. The exchange velocity, uE is an attempt to quantify the exchanges of mass, momentum or energy across the top of a canopy. This velocity was estimated to be around 1% of the wind velocity at 2.5 obstacle heights for the two lower-density arrays, and around 0.3% for the densest array. These values are thought to be lower bounds on the real magnitude of exchanges, as any in-canopy variations in pressure and momentum flux across a repeat unit of the canopy may lead to non-negligible advective fluxes through the canopy top. These fluxes are relevant to the removal of polluted air and heat from urban canopies, where spatial geometrical variations exist, and where the flow may not be fully adjusted to the roughness.