## 3 Analysis of the Well-Resolved LES
### Analysis of the Mean Flow  
The mean velocity components have been scaled by \(U_{\infty}\). Figure 3 shows both the streamwise and the wall-normal mean velocity component of the flow in an \(xz\)-plane at the centerplane for the four streets. The non-dimensional streamwise component of the mean flow highlights three regions. Above the building height, at \(z/H\simeq 1.4\), one can identify a high-speed region (\(U/U_{\infty}\approx 1.1\)). In this region, the influence of the urban obstacle is not visible at a local scale which is contrary to the region of the flow beneath the upper-roof level. Two regions can be identified for \(z/H<1.3\): first, a thin shear layer (\(0.8<z/H<1.2\)) interacts with a strong wall-normal velocity gradient \(\partial U/\partial z\). The canopy drag significantly slows down the flow as it enters the streets and it leads to regions of close-to-zero mean streamwise velocity, with a region of reversed flow close to the downstream side of each building. Close to the wall and the windward side of each building, there is a  
Figure 2: Slices of the spectral-element mesh: (**top**) slice at \(z=0\) and (**bottom**) slice at \(y=0.1\) (where the lengths are scaled with the building height). Note that the GLL points within elements are not shown. very small region of reversed flow which confirms the patterns described by [PERSON] and [PERSON] [23]: A separation point in front of each cubical obstacle results in a small recirculation bubble. This pattern observed for a single obstacle is present in front of each building of the urban array. Despite the strong canopy drag force, the structure of the flow around each cubical obstacle of the array is very similar to that found around a single block, such as the reversed flow region that one can identify downstream of each building. On the other hand, some features of the flow around a cubical obstacle can only be identified in the first building. For example, one can observe a small area of reversed flow above the roof of the first obstacle, which confirms the presence of the roof vortex identified by [PERSON] [19]. This roof vortex is a direct consequence of the detachment of the boundary layer on the roof of the first obstacle and it leads to a wake-layer region in which the flow is separated and where turbulence is dominated by large and coherent eddies. These results provide an interesting parallelism with the behavior in wind farms, where beyond the third row of wind turbines the wake profiles become independent of the row and the lost energy is provided to the flow through vertical exchange. The wall-normal mean velocity component, shown in Figure 3 (bottom), exhibits two regions for the four streets: an area of downward flow close to the downstream building and an area of upward flow near the upstream building. However, by analyzing the magnitude of the wall-normal velocity component, it can inferred that only a small fraction of the flow is going back down towards the street. There is also a small region of upward flow at the upstream corner of each obstacle (even if its intensity decreases considerably as one moves downstream). This region, along with the region of downward flow above each street (\(1.2>z/H>0.8\)), explains how the flow bypasses each urban obstacle. The fact that the region of downward flow mentioned above does not reach the near-wall region within the street is a direct consequence of the (approximate) skimming-flow regime presented here: The bulk of the flow from above the urban canopy does not enter the street canys and therefore the flow from above the urban canopy does not interact with the flow from within the urban canopy. Globally, the urban-canopy drag decelerates the wind so that there is a mass flux upwards and away from the top of the canopy. Downwind the urban environment, there is an exit region similar to the one observed by [PERSON] et al. [15] in the case of forest canopies.