## 3 Analysis of the Well-Resolved LES
### Analysis of the Turbulent Fluctuations  
The root-mean squares (rms) of the turbulent fluctuations denoted by \(u_{\text{rms}}\) and \(v_{\text{rms}}\) in the streamwise and spanwise directions, respectively, are studied next. Note that \(U_{\text{inf}}^{2}\) has been used to non-dimensionalize the turbulent fluctuations. Figure 5 exhibits the streamwise and the spanwise components of the turbulent fluctuations in a vertical plane at the urban array centerplane.  
Figure 4: Mean streamwise velocity \(U\) on the (**top**) \(z=0.85\) and (**bottom**) \(z=0.25\) planes, where colors range from (dark blue) \(-0.4\) to (dark red) \(1.1\).  
Figure 5: (**Top**) Streamwise normal Reynolds stress \(u_{\text{rms}}^{2}\), where colors range from (dark blue) \(0\) to (dark red) \(0.2\). (**Bottom**) Square of the rms spanwise velocity fluctuations \(v_{\text{rms}}^{2}\), where colors range from (dark blue) \(0\) to (dark red) \(0.25\). The \(y=0\) plane is shown.  
Figure 5 shows high levels of turbulence at the roof level in the first street and within the street at the upstream side of the downstream building. These high levels of turbulence suggest strong exchanges of fluid and scalar quantities between the streets and the mean flow above the urban array. Figure 5 also shows that the region of high turbulence at the upper-roof level is mainly due to the streamwise component of the velocity fluctuations, whereas, within the street, the turbulence is driven by the spanwise component. This notable energy exchange is related to the energy lost in overcoming the buildings, which is associated to the pressure drop between the windward and leeward sides of the obstacles. Note that this is in excellent agreement with the experimental results by [PERSON] et al. [9]. The wall-normal component (not shown) is not zero in those regions but is considerably weaker than the two other components. The strength of the separating shear layer near the upper-roof level decreases significantly from the first street to the following street as one moves downstream. Therefore, the exchanges of scalar quantities and fluid are considerably weaker between the urban canopy and the freestream above it. The presence of a canopy introduces new processes and, as described by [PERSON] et al. [15] in the case of forest canopies, turbulence is dissipated by a number of mechanisms. First, eddies of all scales work against the form drag of canopy elements. Turbulence is then transferred from larger eddies to the smallest scales and therefore quickly dissipated. Secondly, viscous dissipation is the second main process that dissipates turbulence. Figure 5 shows that, within the region where the flow adapts to the urban canopy, there are regions of high turbulence intensity, but as one moves downstream this turbulence is strongly damped through the canopy. In particular, the damping of \(u_{\text{rms}}^{2}\) is augmented by the return to isotropy and the turbulence hence evolves into an equilibrium form. The shear layer mentioned above develops at the canopy top where the coherent eddies also form and the exchanges of scalar quantities significantly dampen in the most downstream regions since the flow from above the canopy does not enter the streets. Note that the great wealth of data produced with high-fidelity simulations can help to develop robust data-driven tools to model certain aspects of the flow and to perform predictions of the complex flow behavior observed in urban areas [49; 50].