## 3 Results and Discussions
### Coupled Flow and Noise Simulations for a Wind Turbine Array
#### 3.4.4 Wind Turbine ANPropagation across Multi-Wake  
As shown in Figure 13, the RSPL or \(\Delta L\) is simulated along 1500 m propagation distance, at \(f\) = 300 Hz and with the noise spectrum in Figure 11. The first wind turbine locates at \(x\) = 0 m, the second at 560 m and the third at 1120 m. The distance between each wind turbine are relative large. The wind turbine ANSource are placed at a height of 70 m. The ANSources from the second and third wind turbines, depicted as white lines, are not considered so as to focus on the propagation phenomenon through the wakes. In Figure 13, RSPL results are shown under several conditions: (1) Case 1, ANPropagation under homogeneous atmospheric condition, no wake effect; (2) Case 2, ANPropagation under homogeneous atmospheric condition, considering multi-wakes; (3) Case 3, ANPropagation under atmospheric condition of down-ward refraction, considering multi-wakes; (4) Case 4, ANPropagation under atmospheric condition of upward refraction, considering multi-wakes. It is shown that the wind turbine ANPropagation is clearly affected by the complicated flow environment. For the case without any wake effect shown in Figure 13a, the ANPropagation is mainly influenced by the reflection and absorption of ground. As is shown in Figure 13b, the contours of RSPL is more complicated than that of Figure 13a which distinctly shows the influences of wake. For atmospheric condition of downward refracting depicted in Figure 13c, the 'noise pollution' band also shows a downward  
Figure 12: Initial sound speed profiles at upstream and effective sound speed contours in the wake flow. (**a**) Uniform initial sound profile transmitted into wake; (**b**) upward refraction sound profile transmitted into wake; (**c**) downward refraction sound profile transmitted into wake. reflecting behavior. Additionally, a low-noise zone, shown in blue, can be found near \(x=1000\) m. In Figure 13d, a much quieter situation is observed under an upward refraction condition. In such a case, the quiet zone is located between wind turbine #2 and #3. It should be emphasized that uniform inflow boundary condition is applied in the flowfield simulations of Figure 13c,d. However, the un-uniform or down/up-ward atmospheric conditions, which means atmospheric altitude-dependent variation of the sound speed, are used in the ANPropagation computations. Figure 13: ANPropagation from the first ANSource: (**a**) Case 1, homogeneous atmospheric condition, no wake effect; (**b**) Case 2, homogeneous atmospheric condition with multi-wakes; (**c**) Case 3, downward refraction and multi-wakes; (**d**) Case 4, upward refraction and multi-wakes. Manifesting the noise received by humans, the RSPL or \(\Delta L\) at \(h\) = 2 m is extracted from Figure 13 and shown in Figure 14.The sound attenuation \(\Delta\)L of Case 1 starts to vary linearly with the propagation distance at around \(x\) = 400 m, because the reflection effect becomes weaker after that. In contrast, the \(\Delta L\) of Case 2, 3, and 4 vary obviously even after a long distance. In Cases 2 and 3, \(\Delta L\) fluctuates over distance due to the wake effect and the strong downward refraction respectively. Whereas in Case 4, a more significant RSPL loss is shown which is caused by the upward refraction. It should be mentioned that the \(\Delta L\) values might be quite different when the observer height changes. From this comparison, it can be concluded that ANPropagation can be greatly influenced by the environmental conditions. What is more, the change of SPL in the near downstream is much smaller than that at far downstream (\(x\) > 400 m), which shows the significance of long distance wind turbine noise predictions under complex atmospheric conditions. The near field (\(x\) < 400 m) simulations and measurements only belong to ANSource study which is not identical to the long-path ANPropagation. Result shown in Figure 14 represents the \(\Delta L\) solely due to propagation which is computed at a fixed frequency of \(f\) = 300 Hz.