## 4 Numerical Results
### Irregular Wave  
When irregular waves impact the floating wind turbine, their movement time series becomes nonlinear and irregular. Thus, fast Fourier transform should be utilized to convert time-domain dynamic response results into frequency-domain. The frequency\(-\)amplitude curves and first peak values on the curves are presented and analyzed. Figures 13-15 present frequency\(-\)amplitude curves and first peak values on the frequency\(-\)amplitude curves of wind turbine surge, pitch, and yaw movement under C4-6. From the frequency\(-\)amplitude curves for surge movement, it can be observed that surge amplitudes for T0 were obviously larger than those with T1-4 within 0-0.02 Hz; the curves for T1-3 exhibited a small difference (approximately 0.05 m difference) from each other; and the curve for T4 was larger than that of T1. These indicate that the developed mooring  
Figure 10: Surge movement maximum, minimum, and average values in (**a**) C1, (**b**) C2, and (**c**) C3. system could effectively control the wind turbine surge movement when under irregular waves, and the maximum surge movement reduction occurred when using T3, with a reduction of 0.7 m. Compared with the six-fairlead mooring system, the mooring system with three fairleads and 40\({}^{\circ}\) included angle between two mooring lines in the same group performed better, which was similar to the observations in the regular wave results. As the included angle increased, the developed mooring system performed better and better. The first peak value for T3 reduced by 0.05 m compared with that for T1. In C4, the first peak values for T0, T3, and T4 were 1.43 m, 0.63 m, and 0.75 m, respectively. Hence, it can be said that the optimal mooring system configuration T3 could significantly reduce wind turbine surge movement by 56.08% when under irregular waves. The six-fairlead mooring system T4 could also reduce wind turbine surge movement by 47.55%, but it performed worse than T3 with 8.53% surge movement reduction difference between them. Figure 11: Pitch movement maximum, minimum, and average values in **(a)** C1, **(b)** C2, and **(c)** C3. Figure 12: Yaw movement maximum, minimum, and average values in (**a**) C1, (**b**) C2, and (**c**) C3. Figure 13: Frequency\(-\)amplitude curve and first peak amplitude in C4: (**a**) and (**b**) surge; (**c**) and (**d**) pitch; (**e**) and (**f**) yaw. From Figures 13-15, the pitch movement frequency-amplitude curves for T0 exceeded those for T1-4 within 0-0.02 Hz, while the curves for T1-4 exhibited little difference between them. From the first peak values for T1-4, it can be directly observed that the first peak values for T1-3 were almost the same, while the first peak value for T4 was slightly greater than that of T3 with a difference of 0.004\({}^{\circ}\). These imply that the developed mooring systems could reduce wind turbine pitch movement when under irregular waves, and the mooring system with three fairleads and a 40\({}^{\circ}\) included angle between the two mooring lines in the same group performs better than that with six fairleads. For the mooring system with three fairleads, the included angle between the two mooring lines in the same group had a negligible effect on its performance. In C4, the first peak values for T0, T3, and T4 were 0.04\({}^{\circ}\), 0.03\({}^{\circ}\), and 0.034\({}^{\circ}\), respectively, quantitatively supporting the conclusion that the developed mooring system could reduce pitch movement by 25% when under irregular waves. From Figures 13-15, it can be seen that the wind turbine yaw movement amplitudes under irregular waves were smaller than those under regular waves. The frequency\(-\)amplitude curves for T0 exceeded those for T1-4 within 0-0.02 Hz. Frequency\(-\)amplitude curves for T1-4 almost coincided with each other. These indicate that the developed mooring system with six mooring lines can effectively reduce wind turbine yaw movement when under irregular waves.