# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 4 Results and Discussions
### Case 3: Bolund Island Field Experiment (270\({}^{\circ}\) Wind Direction)  
Figure 13 shows the numerical results of the vertical profile (M0) of the wind speed and TKE with different turbulence models. The numerical wind speed of the four RANS turbulence models is also in good agreement with the experiments, while the result of the LES [47] is slightly smaller than the experimental value at the height of 2 m. Regarding the TKE, it is seen from Figure 13 that, at M0, the TKE profile of the ESDU fits well with the experimental data. Similar to Cases 1 and 2, the TKE of the Std SST \(k\)-\(\omega\) model (\(e_{\text{TKE,M0}}=38\%\); \(z=5\) m) and the Std RSM model (\(e_{\text{TKE,M0}}=18\%\); \(z=5\) m) have a significant decay near the ground, and the Mod SST \(k\)-\(\omega\) and Mod RSM models agree well with the experimental values, while the TKE of the LES model is smaller than the experimental value above the 5 m height. Figure 14 shows the four RANS turbulence models for the wind speed over the island. Along lines B and A, the numerical results are better above the 2 m height. Below 2 m, some  
Figure 12: Statistical error of the wind speed (\(U\)) and turbulent kinetic energy (TKE) in Figure 11, considering all of the sites of Askervein hill (wind speed measurement sites: 40 in total; TKE measurement sites: 12 in total) in Case 2. (**a**) Mean absolute error of \(U\) and \(TKE\); (**b**) Relative root mean square error of \(U\) and \(TKE\). Figure 13: Vertical profiles of wind speed and TKE at location M0 (Bolund island case, 270\({}^{\circ}\) wind direction); \(z\) is the height above the ground, which, for M0, is above sea level. (**a**) Wind speed profile; (**b**) Turbulent kinetic energy profile. measurement points deviate from the experimental values, and similar conclusions can be found in reference [10]. The differences in the wind speed predictions between various RANS turbulence models are also evident near the ground due to the separation and reattachment of the wind flow. The size of the separation zone with different turbulence models can be seen in Figure 15, especially near M6 and M8, where the differences in the separation zone is obvious. Similar to Case 1, the standard models have larger separation zones in the leeward slope. Although, for M3, the LES model is more accurate at a 2 m height, for M6 (M2), it is larger than the experiment at a 2 m height, so the LES model also has some errors on the whole. Figure 14: Vertical profiles of the wind speed and TKE (Bolund island case, 270\({}^{\circ}\) wind direction). ‘Cup’ and ‘Sonic’ stand for different types of experiment data; \(z\) is the height above the ground and ‘\(H/H_{\text{top}}\)’ stands for the dimensionless island height. (**a**) Wind speed profile along line B; (**b**) Wind speed profile along line A; (**c**) Turbulent kinetic energy profile along line B; (**d**) Turbulent kinetic energy profile along Line A; (**e**) Measurement locations along line B; (**f**) Measurement locations along line A. The wind speed prediction accuracy of the four RANS turbulence models was evaluated by combining the numerical statistical errors of all anemometers from M1 to M8. As can be seen from Table 4, the RRMSE values of all four RANS models are within 0.25, indicating that the wind speed is simulated with a good accuracy. Combined with the other wind speed error statistical indices, the best performance is the Mod RSM model. Along lines B and A, it can be seen in Figure 14 that the TKE of the Std SST \(k\)-\(\omega\) model is smaller than the experimental value at all measurement points, and the Mod RSM model has better predictions of the TKE than the Std RSM model and the Mod SST \(k\)-\(\omega\) model, which can also be seen in Table 4. It can be seen from Figures 14 and 15 that the Std SST \(k\)-\(\omega\) model generates less turbulent kinetic energy around M6 and M8 than the other models due to the TKE decay and the limitations of the turbulence model itself.