## 4 Numerical Simulations and Results
### Results and Discussion
#### 4.2.2 Mooring Tension  
Similarly, in order to assess the effect of wave-current interaction on the mooring tension of the CSS FOWT, the mean values and standard deviation values of the main motions in the X and Y directions are displayed in Figures 12 and 13, respectively. As the catenary mooring system of the CSS FOWT is characterized by symmetry along the X direction, the associated response of cables 2 and 3 is similar when the waves and currents come from the X direction. Hence, the mooring tensions of cables 1 and 2 are drawn in Figure 12 when the waves and currents propagate in the X direction. Figure 13 shows the mooring tension of cables 1, 2, and 3, when the waves and currents propagate in the Y direction.  
Figure 9: The mean and standard deviation values of the main motions in the Y direction.  
Figure 11: _Cont._  
Figure 10: Dynamic response of surge motion for case 7 in the X direction.  
Figure 11: Dynamic response of sway motion for case 8 in the Y direction.  
Figure 12: The mean and standard deviation values of the mooring tension in the X direction.  
By comparing the results in Figures 12 and 13, the results presented in the figures reveal that the wave-current interaction has a greater impact on the mooring tension under specific conditions, especially when the waves and currents propagate in opposite directions. For instance, in case 8 of Table 3, the SDs of the mooring tension for cable 2 differ by 22.7%, indicating the importance of accounting for this coupled interaction when estimating the fatigue loads and fatigue life of the cables. This observation is the same as the motion responses and is still consistent with the change of the wave spectrum of irregular waves due to the presence of currents.  
Figure 14 displays the maximum values of mooring tension for various mooring cables when waves and currents propagate in the Y direction. The figure clearly demonstrates  
Figure 13: The mean and standard deviation values of the mooring tension in the Y direction.  
the significant difference in the response of the CSS FOWT when considering the effects of wave-current interaction compared to when these effects are not considered. Furthermore, Figure 14 presents the results of comparing the maximum dynamic mooring tension of the cables after subtracting the mean mooring tension. It is evident that the maximum mooring tension can increase by more than 15% when the waves propagate on the opposite current in the Y direction, as illustrated in case 8 of Table 3. This observation indicates that waves and currents propagating in the Y direction exert a more pronounced influence on the tension experienced by the cables.  
Figure 15 shows the results of the time history and the PSD values of the mooring tension of cable 2 in case 8, where both the waves and the currents propagate in the Y direction. It can be seen that the wave-current interaction tends to enhance the cable tension in the frequency range of 0.01 to 0.08 Hz and 0.1 to 0.15 Hz. For the examples considered, the wave-current interaction seems to further increase the mooring cables' tension.  
Figure 14: Maximum mooring tensions of various cables when the waves and currents are in the Y direction.