## 3 Results and Discussion
### Mean Air Velocities Downwind the Building
Airflow streamlines and contours of the air velocity magnitude (\(V_{2D}\)) normalised by \(U_{B}\) at Plane 3 for the three roof slopes are compared in Figure 9. The axes \(X\) and \(Z\) indicate the downwind distance to the building and the height from the wind tunnel floor, respectively. There was an elliptic-shaped low air velocity region with \(V_{2D}\)/\(U_{B}\) of smaller than 0.4 behind the building with a height of 0.13 m (i.e., \(1Z_{B}\)) and a downstream distance of 0.5 m (i.e., \(3.8Z_{B}\) and corresponding to 25 m in full-scale) for all three roof slopes. This region is expected to have a high concentration of air pollutants. This is because airborne pollutants are mainly transported by mean airflow, which results in the concentration of pollutants being inversely related to the air velocity downwind the building if no recirculation regions are presented [44]. If applying additional air pollutant treatment technologies, for example using pollutant traps or sprinklers to collect or wash high-concentrated air pollutants in this low air velocity region might effectively mitigate air contaminants and release their burden to the surrounding environment and residents. Additionally, within this low air velocity region, a wake zone with reversed airflow was observed at Plane 3, implying an anti-clockwise air recirculation in which air pollutants would accumulate. The size and shape of the wake was affected by the roof slope. For the roof slope of 5\({}^{\circ}\), 15\({}^{\circ}\), and 25\({}^{\circ}\), the wake height (in \(Z\) direction) was 0.103 m, 0.099 m, and 0.084 m, respectively. Accordingly, the wake length (in \(X\) direction) was 0.254 m, 0.261 m, and 0.290 m, respectively. It showed that the larger the roof slope was, the lower and longer the wake became, and vice versa. As a result, the accumulated air pollutants would disperse farther for a steeper roof slope. The wake length  
Figure 8: Spatial distributions of (**a**) streamwise (\(U\)) and (**b**) vertical (\(W\)) air velocities normalised by the air velocity at building height (\(U_{B}\)) at Plane 2 for roof slopes of 5\({}^{\circ}\), 15\({}^{\circ}\), and 25\({}^{\circ}\). Black dash lines indicate the profile of the scaled model. observed by [PERSON] et al. [23] was \(2.5Z_{B}\) and \(2.8Z_{B}\) for a gable-roof building (without openings) with the roof slope of \(16.7^{\circ}\) and \(26.6^{\circ}\), respectively, which is slightly greater than \(2.0Z_{B}\) and \(2.2Z_{B}\) for the roof slope of \(15^{\circ}\) and \(25^{\circ}\) respectively obtained in our study. This is because the sealed building structure could result in a much lower pressure field behind the building and thus a larger air recirculation region. In contrast to the results in this paper where the wakes were found from the floor level until above the roof, in a wind tunnel study of Ikeguchi and Okushima [18] using naturally ventilated dairy building models without outdoor exercise yards, the wakes were only observed above the leeward roof. One possible reason could be the large sidewall openings used in their study, which resulted in a cross ventilation through the building. In contrast, in our study, a small slot inlet opening with a high sidewall led to an up-jet airflow pattern inside the housing area. Additionally, the exercise yard with an upwind sidewall further complicated the airflow and resulted in the reversed flow behind the building. Therefore, our results are expected to be applicable to naturally ventilated livestock buildings with small inlet openings and downwind outdoor yards in a perpendicular wind direction. Figure 10 shows the variations of the dimensionless air velocities with distance to the building at heights (\(Z\)) of 0.02 m, 0.06 m, and 0.12 m, which corresponded to 1 m, 3 m, and 6 m in full-scale. At \(Z\) of 0.02 m, the roof slope of \(25^{\circ}\) resulted in lower \(U\)/\(U_{B}\) and \(W\)/\(U_{B}\) velocities than roof slopes of \(5^{\circ}\) and \(15^{\circ}\) until a distance of around 0.7 m from the building.