## 1 Introduction to Urban Flows
### Structure of the Flow above the Urban Canopy  
Urban obstacles such as buildings create a relatively large drag force on the atmospheric boundary layer (ABL). [PERSON] and [PERSON] [2], as well as [PERSON] and [PERSON] [12], described the structure of the ABL above urban areas with three major sublayers: the _urban canopy sublayer_, the _roughness sublayer_ and the _inertial sublayer_. In the so-called inertial sublayer, the turbulent fluxes are almost constant because the boundary layer has adapted to the effect of the urban obstacles. Therefore, it is treated by standard atmospheric boundary layer formulas and, thus, the mean velocity profile can be approximated fairly well by the following logarithmic law:  
\[U(z)=\frac{u_{*}}{\kappa}\ln\left(\frac{z-d_{0}}{z_{0}}\right), \tag{1}\]  
where \(d_{0}\) is the displacement height, \(z_{0}\) is the roughness length, \(u_{*}\) is the friction velocity and \(\kappa=0.4\) is the Von Karman constant. Note that \(U\) is the mean velocity in the streamwisedirection and \(z\) is the wall-normal coordinate; similarly, \(V\) and \(W\) are the mean velocity components in the spanwise and the vertical directions, respectively.  
[PERSON] and [PERSON] [13] used particle-image-velocimetry (PIV) measurements to investigate the flow through an urban environment. They observed that in the outer region the roughness does not significantly affect the mean velocity profiles and the Reynolds-stress profiles. The logarithmic law can adequately model the mean velocity profile in the inertial sublayer. The inflection point identified by [PERSON] [14] and later by [PERSON] et al. [15] using LES in the context of forest canopies was also observed by [PERSON] and [PERSON] [13] in the case of urban canopies. This inflection point is at the top of the roughness layer and marks the transition between the roughness layer (where the mean profiles are still disturbed by the roughness elements) and the inertial sublayer (where the mean profiles follow the logarithmic law).  
On the other hand, within the urban canopy layer, the flow is directly affected by the urban obstacles and, in the roughness sublayer, the flow is still adjusting to the effects of many obstacles ([PERSON] and [PERSON] [12], [PERSON] and [PERSON] [2] and [PERSON] [16]). Therefore, within both sublayers, the flow has a rather complex structure. In the vertical direction, the roughness sublayer extends from the ground to a level at which the flow can be taken horizontally homogeneous, as it has been investigated by [PERSON] [14], [PERSON] et al. [15] and [PERSON] and [PERSON] [17] using LES in the case of the flow above a forest canopy and by [PERSON] and [PERSON] [2] and [PERSON] and [PERSON] [13] in the urban context. This can occur from 2 times to 5 times the average height of the urban obstacles. Therefore, in areas with high buildings such as most of large American cities, the roughness sublayer represents a significant part of the urban boundary layer. As most of pollution problems occur in this sublayer, predictive models for the spread of pollution require information of the flow structure within the roughness sublayer [4].