## 4 Numerical Simulations and Results
### Results and Discussion
#### 4.2.1 Motion Responses  
The selected time histories of the main motions for case 5 when wave and current in the X direction and Y direction are shown in Figures 6 and 7, respectively. As shown in Figure 6, the surge motion is evidently affected  
interaction still has limited influence on heave and pitch motion when wave and current move in the Y direction. In order to assess the effect of wave and current interaction on the motion responses of the CSS FOWT in different cases, the mean values of the standard deviation of the main motions in the X and Y directions are displayed in Figures 8 and 9, respectively. As shown in Figure 8, when waves and currents propagate in the X direction, the mean values of the main motions when considering the wave-current interaction are almost all larger than those when not considering the coupling interaction. The mean values of surge motion are more fluctuating than those of the heave and pitch motion. The values of standard deviation of the main motions fluctuate more in case 5 through case 8. In case 6 and 8, the biggest difference between considering the coupling interaction or not of surge  
Figure 6: Time histories of the main motions for case 5 in the X direction. and heave motion is up to 17% and 20%, respectively, when waves are traveling on an opposite current. In Figure 9, when waves and currents propagate in the Y direction, the mean values and standard deviation values of the sway motion exhibit significant variation in the presence of large waves. In case 5 and case 7, the mean values of sway motion when considering the coupling effect are two times those when not considering the coupling interaction. The impact of wave-current interaction is evident based on the standard deviation values of sway motion in case 8 when waves and currents propagate in the Y direction. The standard deviation values of sway motion differ by 24.3%, clearly demonstrating the significant difference when considering the effect of wave-current interaction compared to when these effects are not considered. There is nearly no change for pitch motion based on the mean values. By comparing the results in Figures 8 and 9, it is observed that the interaction effect of the waves and currents on the heave and pitch motion is nearly the same irrespective of whether the waves and currents act along either the X or the Y direction. The mean values and standard deviation values in the figures demonstrate that the coupled interactions generally amplify the dynamic motion responses of the CSS FOWT when the waves and currents propagate in opposite directions. This observation aligns with the adjustment of the wave spectrum of irregular waves due to the presence of currents, as depicted in Figure 5. The alteration in the wave spectrum primarily stems from the modification in wave height induced by the presence of currents. Moreover, the impact of the coupling interaction on the dynamic motion responses of the CSS FOWT intensifies as the wave height and the velocity of the current increase. Figure 7: Time histories of the main motions for case 5 in the Y direction. According to the comparison of three situations defined in the simulation setting, it can be found that in some cases, the effect of wave-current interaction is much more significant than the other two situations, and this is important for the safety of structures in the design process. The detailed comparative analysis is as follows. For the chosen case 7 and case 8 in Table 3, the dynamic motion responses of the CSS FOWT in the X and Y direction are illustrated in Figures 10 and 11, respectively. Figure 10 shows the time history and the power spectral density (PSD) value of the surge motion of the CSS FOWT for case 7 in the X direction. It can be seen that, considering the interaction between waves and currents, the surge displacement is greater in comparison to the outcomes obtained in the remaining two scenarios, and the current tends to enhance the dynamic response of the surge motion in the frequency range of 0.057 to 0.084 Hz.