# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 4 Results and Discussions
### Case 4: Bolund Island Field Experiment (239\({}^{\circ}\) Wind Direction)  
When the wind direction is 239\({}^{\circ}\), there are some similar conclusions to those when the wind direction is 270\({}^{\circ}\). At M0, the wind speed of the four RANS turbulence models is also in good agreement with the initial wind speed at the inlet (Figure 16), and the TKE values of the Std SST \(k\)-\(\omega\) model (\(e_{\rm TKE,M0}=44.3\%\); \(z=5\) m), Mod SST \(k\)-\(\omega\) model (\(e_{\rm TKE,M0}=25\%\); z = 5 m), and the Std RSM model (\(e_{\rm TKE,M0}=17.5\%\); z = 5 m) are significantly decayed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Turbulence** & \multicolumn{2}{c}{**Wind Speed**} & \multicolumn{2}{c}{**TKE**} \\ \cline{2-5}
**Model** & **MAE(m/s)** & **RRMSE** & **MAE(m/s)** & **RRMSE** \\ \hline Std SST \(k\)-\(\omega\) & 0.0716 & 0.1981 & 3.0342 & 0.9271 \\ Mod SST \(k\)-\(\omega\) & 0.5635 & 0.2455 & 2.5624 & 0.8906 \\ Std RSM & 0.5916 & 0.1613 & 1.9366 & 0.7148 \\ Mod RSM & 0.0960 & 0.1592 & 1.8774 & 0.7072 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical errors of the numerical results for all mass (M1-M8, 22 in total; Bolund island case, 270\({}^{\circ}\) wind direction). Figure 15: Vertical cross-section of the wind speed and TKE along line B (Bolund island case, 270\({}^{\circ}\) wind direction). The values of the wind speed (**a**) and TKE (**b**) for the white contour are 0 m/s and 3 m\({}^{2}\)/s\({}^{2}\), respectively. Along lines A and B, the numerical wind speed differs significantly at M4 and M8, and at M2 and M6 near the ground, and the other results are in good agreement with the experiment, except for the above measurement points (Figure 17). Regarding the TKE, the decay of the Std SST \(k\)-\(\omega\) model is obvious, and the Mod RSM model performs well, while the locations of the measurement points with the largest errors are the same as those for the wind speed. Through a comprehensive comparison, it is found that the Mod RSM model provides better predictions for both the wind speed and the TKE (Table 5). Figure 16: Vertical profiles of the wind speed and TKE at location M0 (Bolund island case, 239\({}^{\circ}\) 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. Figure 17: Vertical profiles of the wind speed and TKE (Bolund island case, 239\({}^{\circ}\) wind direction). ‘Cup’ and ‘Sonic’ stand for the different types of experimental data; \(z\) is the height above the ground. (**a**) Wind speed profile along line A; (**b**) Wind speed profile along line B; (**c**) Turbulent kinetic energy profile along line A; (**d**) Turbulent kinetic energy profile along line B. From Cases 3 and Case 4, it can be seen that, for the TKE, the RSM models, especially the modified RSM model, perform better than the two-equation models because the modified anisotropy models have better maintenance and can also produce a suitable TKE at the cliff. For the wind speed, it can also be seen that the anisotropic models are superior to the two-equation models and predict the speed in the separated region more accurately. In order to find out the similarities and differences in the effects of the four turbulence models on the simulation results for Cases 1-4, the MAE and RRMSE of the numerical result of the Std SST \(k\)-\(\omega\) model were used as the baseline for the analysis (as shown in Table 6).