## 4 Numerical Results
### Regular Wave
Hence, it can be said that when under regular waves, the wind turbine pitch movement could be reduced by both of the developed mooring systems with three and six fairleads, and the included angle has negligible effects on wind turbine pitch movement. Figure 9 presents wind turbine yaw movements with T0-4 under C1-3. It can be observed that yaw movement of T0 had the maximum peak and minimum valley compared with those of T1-4; that is, yaw movement of T0 had the maximum amplitude compared with those of T1-4. The maximum difference between the amplitudes was approximately 10%. Interestingly, the yaw movement of T1-4 all almost coincided with each other, implying that the developed mooring systems had negligible effects on the yaw movement control. Increasing both the included angle and the number of fairleads could hardly improve the mooring system performance on yaw movement control. To quantitatively examine the developed mooring system performances, the maximum, minimum, and average values of the movement time series were calculated and analyzed. Figure 10 presents the wind turbine surge movement maximum, minimum, and average values with T0-4 under C1-3. It can be directly seen that the surge movement maximum, minimum, and average values of T0 were the greatest compared with those of T1-4. As the included angle increased, the surge movement's statistical values (maximum, minimum, and average) decreased gradually. T4 performed better than T0, while it performed worse than T1-3. In C1, the surge movement maximum, minimum, and average values of T0 were 13.9 m, 10.7 m, and 12.3 m, respectively. They were 9.23 m, 5.66 m, and 7.44 m, respectively, for T3, and 10.1 m, 6.51 m, and 8.29 m, respectively, for T4. That is, the developed mooring system with three fairleads and 40\({}^{\circ}\) included angle (T3) could effectively reduce wind turbine surge movement by 39.51%, and the developed mooring system with six fairleads (T4) could reduce wind turbine surge movement by  
Figure 8: Wind turbine pitch movement time series in (**a**) C1, (**b**) C2, and (**c**) C3. 32.6%. Compared with the six-fairlead mooring system, three fairleads with a 40\({}^{\circ}\) included angle could further reduce the wind turbine surge movement by 6.91%. Figure 11 shows the wind turbine pitch movement maximum, minimum, and average values for T0-4 under C1-3. It can be seen that these statistic values of T0 were approximately 0.2\({}^{\circ}\) larger than those of T1-4, while they were almost at the same level for T1-4. In C1, the pitch movement maximum, minimum, and average values were respectively 3.34\({}^{\circ}\), 1.67\({}^{\circ}\), and 2.5\({}^{\circ}\). They were 3.17\({}^{\circ}\), 1.49\({}^{\circ}\), and 2.33\({}^{\circ}\), respectively, for T3. Meanwhile, they were 3.19\({}^{\circ}\), 1.51\({}^{\circ}\), and 2.35\({}^{\circ}\), respectively, for T4. This quantitatively indicates that the developed mooring systems could only reduce wind turbine pitch movement by 6.8% when under regular waves. Although increasing the included angle could improve its performance, the pitch movement difference resulting from the included angle change was only 0.02\({}^{\circ}\) per 10\({}^{\circ}\), which can be ignored because it is significantly smaller than the pitch movement average values. Figure 9: Wind turbine yaw movement time series in (**a**) C1, (**b**) C2, and (**c**) C3. Figure 12 presents wind turbine yaw movement maximum, minimum, and average values for T0-4 under C1-3. The yaw movement maximum value of T0 was slightly larger than those of T1-4, while the yaw movement maximum values of T1-4 were almost the same. In C1, the yaw movement maximum value of T0 was 0.308\({}^{\circ}\), and it was 0.27\({}^{\circ}\) for T3. This indicates that the optimal configuration for the developed mooring system (T3) could reduce wind turbine yaw movement by approximately 12.34%. Generally, the developed mooring system with three fairleads and 40\({}^{\circ}\) included angle performed better than that with six fairleads.