# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 4 Results and Discussions
### Case 1: 3D Hill Wind Tunnel Experiment  
Figure 5 shows the numerical results upstream of the four RANS turbulence models. The mean velocity profiles with different turbulence models are almost the same and are consistent with the inlet conditions. Regarding the turbulence intensity (TI), the TI of the Std SST \(k\)-\(\omega\) model (\(e_{\text{TI,in}}=19.6\%\); \(z/H=0.5\)), the Mod SST \(k\)-\(\omega\) model (\(e_{\text{TI,in}}=11.8\%\); \(z/H=0.5\)) and Std RSM model (\(e_{\text{TI,in}}=10.7\%\); \(z/H=0.5\)) is significantly smaller than the initial given value, especially near the ground; the Mod RSM model (\(e_{\text{TI,in}}=3.2\%\), \(z/H=0.5\)) performs the best and has a good agreement with the inlet initial value. From the simulation results, it can be concluded that the inlet conditions based on anisotropic assumptions are more appropriate than those based on isotropic assumptions, and although the modified SST \(k\)-\(\omega\) model outperforms the standard model in terms of the consistency of the inlet profiles, the modified RSM model is more effective.  
Figure 5: Vertical profiles of the mean streamwise velocity and turbulence intensity in the upstream of Case 1, where the reference wind speed \(U_{\text{ref}}=5.8\) m/s, and the probe location is at \(x/L=-24\). (**a**) Dimensionless wind speed (\(U/U_{\text{ref}}\)); (**b**) Turbulence intensity in the streamwise direction (\(l_{u}\)).  
For the wind speed around the hill, it can be seen in Figure 6 that there is no difference between the four RANS models on the windward slope and the hilltop, and that, on the leeward slope and the wake zone of the hill, there is a significant difference between the models, especially at the lower layer (\(z/H<2\)); above this height, there is little difference between the models, and they agree with the experiment. On the leeward slope, the results of the four models are close to the measured data. In the hill wake zone, the wind speed of the Std RSM model and the Std SST \(k\)-\(\omega\) model are smaller than the experimental values (\(z/H<0.5\)). Considering all measurement points, the Mod RSM model and the Mod SST \(k\)-\(\omega\) model best predict the wind speed among the four RANS models. From Figure 7, the Std SST \(k\)-\(\omega\) model and the Mod SST \(k\)-\(\omega\) model perform slightly poorer in wind speed prediction compared to the standard RSM model and the Mod RSM model as the turbulence behind the hill shows anisotropy. The differences in the numerical wind speed of the different models are mainly due to the wind flow separation, which can also be seen in Figure 8, where the results of the Mod RSM model is closer to the experiment.  
Regarding the turbulence intensity (TI), it can be seen from Figure 6 that the RANS models generate less turbulence than the experiment behind the hill, especially in the height range of \(1<z/H<2\). In the region of \(z/H>2\), there is little difference between the RANS models, and in the region of \(0.5<z/H<1\), the TI of the Mod SST \(k\)-\(\omega\) model and the Mod RSM model are closer to the experiment, while the TI of the standard RSM model is significantly smaller than that of the experimental results in the \(z/H<0.5\) region. From  
Figure 6: Vertical profiles of the mean streamwise velocity and turbulence intensity on the central plane of the hill in Case 1, where the reference wind speed \(U_{\text{ref}}=5.8\) m/s, and \(x/L\) ranges from \(-1\) to \(2.5\). (**a**) Dimensionless wind speed (\(U/U_{\text{ref}}\)); (**b**) Turbulence intensity in the streamwise direction (\(\sigma_{u}/U_{\text{ref}}\)).