## 1 Introduction to Urban Flows
### Description of the Flow Inside the Urban Roughness Sublayer  
According to [PERSON] [16], the urban roughness sublayer can be decomposed into two distinct regions. The region just above the top of the buildings is denoted as the _wake layer_ and the region beneath it is named the _urban canopy_. Within the urban canopy, the flow is slightly disturbed by the urban obstacles. [PERSON] et al. [9] highlighted that the flow between blocks can be separated into two different regions. The low-speed region, which is close to the leeward side of the upstream obstacle, shows low TKE whereas a higher speed area, close to the windward side of the downstream block exhibits higher turbulence. The experimental results from [PERSON] et al. [9] are consistent with DNS from [PERSON] et al. [27]. By analyzing the mean velocity vectors between two cubes in a similar array of obstacles, they highlighted the recirculation bubble shown by [PERSON] et al. [27]. The regions of low velocity fluctuations and low TKE downstream of the first obstacle and of high velocity fluctuations and high TKE upstream of the second obstacle (observed by [PERSON] et al. [9]) have also been identified by [PERSON] et al. [27]. Particle-image-velocimetry data from [PERSON] and [PERSON] [13] and DNS from [PERSON] et al. [27] also established that the mean velocity profiles strongly depend on the spatial location within the urban canopy (which is not the case in the inertial sublayer where the mean flow follows a logarithmic law). Near the wall and within the urban canopy, the variations in shear-stress follow those in mean velocity, whereas near the canopy top, the shear-stress exhibits prominent peaks. [PERSON] et al. [9] also investigated the TKE distribution and highlighted the decrease in turbulence within the urban canopy due to the drag force produced by the obstacles. In this region, the velocity and vorticity profiles are determined by a balance between the vertical divergence of the turbulent flux and the sources and sinks of momentum and scalar diffusion. In the wake layer, which is a transition region between the urban-canopy and the inertial sublayers (where the velocity profile is logarithmic), the roughness effects due to the canopy edge are not negligible. In this region, the turbulence is dominated by large and coherent eddies which enhance mixing. The flow within the street canyons has been widely studied, both experimentally ([PERSON] and [PERSON] [30] and [PERSON] et al. [22]) and computationally ([PERSON] and [PERSON] [31] and [PERSON] et al. [32]). [PERSON] and [PERSON] [30] conducted an experimental study of the flow within a real street in Oklahoma City in order to understand the relationship between the upper-level wind conditions and the presence of horizontal vortices they noticed at the end of the street canyons. These vortices were also observed by [PERSON] and [PERSON] [31] and they established that these end vortices result in air exchange between the air above the edge of the urban canopy and the flow within the street canyons. On the other hand, [PERSON] et al. [32] found, using the standard \(k-\epsilon\) Reynolds-averaged Navier-Stokes (RANS) model [33], that the strength of these vortices decreased with the height of the buildings. The presence of such horizontal vortical structures (usually less studied than the vertical structures) is of greater interest for pollutant dispersion within the streets. Indeed, it has been established by several studies, including those by [PERSON] and [PERSON] [34] and [PERSON] et al. [35], that the presence of the street-canyon end vortices can significantly affect the air ventilation and thus the local pollutant dispersion. Similarly, [PERSON] et al. [36] worked on understanding the ventilation patterns towards the streets and the impact of the shape of the urban obstacles roofs on pollutant dispersion. [PERSON] [26] described in 2D the structure of the flow between two urban obstacles. Two regimes of the flow were found and later described in three dimensions (3D) by [PERSON] and [PERSON] [25].