## 3 Results and Discussion
### Air Turbulence Downwind the Building  
Spatial distributions of the turbulent kinetic energy (_TKE_) normalised by the square of the streamwise air velocity at the building height (\(U_{B}\)) at Plane 1 and Plane 2 for roof slopes of \(5^{\circ}\), \(15^{\circ}\), and \(25^{\circ}\) are compared in Figure 11. It was found that _TKE_ had different patterns from air velocities, where the region of low air velocities generally presented higher _TKE_ values. At Plane 1, the highest _TKE_ occurred at the centre of the building around the building height. This might be caused by the air collision of the reverse flow occurred in the wake and the bulk air flowed over the building, which increased the air turbulence in that region. At Plane 1, the high _TKE_ region was the smallest when the roof slope was \(5^{\circ}\). At Plane 2, higher _TKE_ was observed behind and above the building than in other areas. It indicated that the influence of the building on the downwind air turbulence reached Plane 2. Only minor _TKE_ pattern differences among different roof slopes were observed at Plane 2, which implied that the roof slope had almost no effects on _TKE_ at Plane 2. Figure 10: Variations of normalised streamwise air velocity \(U/U_{B}\) (**a**) and vertical air velocity \(W/U_{B}\) (**b**) with respect to the distance from the building (X) at heights (Z) of 0.02 m, 0.06 m, and 0.12 m for roof slopes of \(5^{\circ}\), \(15^{\circ}\), and \(25^{\circ}\). \(U_{B}\) is the streamwise air velocity at the building height. Figure 12 illustrates the normalised _TKE_ distributions at Plane 3 for three roof slopes. The highest _TKE_ was observed in the region in the vicinity of the building height. It decayed gradually as the distance to the building increased. The high _TKE_ region that is represented in red and yellow in Figure 12 extended up to approximately 0.5 m (i.e., \(3.8Z_{B}\)) downwind from the building. It was located right above the region in which the air velocity was low (as depicted in Figure 9). This could be attributed to the flow reattachment on the leeward roof that led to the production of _TKE_. [PERSON] et al. [45] also found a high turbulence production in the air recirculation region behind the scaled model. It is known that the transport of airborne pollutants is affected by both the mean air velocity and the air turbulence [46]. Therefore, in that low air velocity region, the aerial pollutants would be likely transported via the energetic turbulent eddies/turbulence diffusion. Figure 11: Spatial distributions of turbulence kinetic energy (_TKE_) normalised by the square of the air velocity at the building height (\(U_{B}^{2}\)) at Plane 1 (**a**) and Plane 2 (**b**) for roof slopes of \(5^{\circ}\), \(15^{\circ}\), and \(25^{\circ}\). Black dash lines indicate the profile of the scaled model. Figure 12: Dimensionless turbulence kinetic energy (_TKE_/\(U_{B}^{2}\)) distributions at Plane 3 for roof slopes of \(5^{\circ}\), \(15^{\circ}\), and \(25^{\circ}\). The influences of the roof slope on the air turbulence, denoted by the turbulence intensity (_TI_) and dimensionless turbulent kinetic energy (_TKE_/_U_\({}_{B}^{2}\)), with respect to the downwind distance from the building (_X_) at heights (_Z_) of 0.02 m, 0.06 m, and 0.12 m are described in Figure 13. A considerably higher _TI_ was found at \(X\) of 0.2 m-0.4 m for \(Z\) of 0.02 m and 0.06 m, where the air vortex was formed in the wake as depicted in Figure 9. The highest _TI_ was observed in the most downward roof structure (i.e., roof slope of 25\({}^{\circ}\)), which was attributed to an enhanced disturbance of the roof to the airflow. At \(Z\) of 0.12 m, the _TI_ had lower values compared with \(Z\) of 0.02 m and 0.06 m, and decreased slowly with distance from the building. The influence of the roof slope on the _TI_ was negligible when the distance from the building exceeded 0.5 m (i.e., 3.8\(Z_{B}\)) (Figure 13a). The highest _TKE_/_U_\({}_{B}^{2}\) occurred at \(Z\) of 0.12 m and decayed gradually away from the building.