## 4 Numerical Simulations and Results  
### Simulation Setting  
For the purpose of comparing the effect of wave-current coupling interaction on the dynamic response of a CSS FOWT, three distinct situations were conducted in the subsequent simulations: (1) irregular waves only; (2) irregular waves and currents without coupling interaction; (3) irregular waves and currents with coupling interaction.  
All the PM spectra of waves were developed and calculated in MATLAB (2020b) based on the theory in Section 3, and then transferred as subsequent input to AQWA as user defined wave spectra. Based on realistic environmental conditions in the South China Sea, two kinds of irregular waves corresponding to the 1- and 50-year return period of waves are employed here, and the related current velocities are 0.5, 0.609, 1.0, and 1.31 m/s. Table 3 lists the eight study cases to be emulated for the combination of waves and currents, taking into account both waves on positive currents and on opposite currents. Concurrently, waves and currents traveling together in the X and Y directions are assessed. The wind spectrum used in all simulations is the Kaimal spectrum with reference wind speed equaling to 12 m/s at hub height. The turbulent wind field based on the Kaimal spectrum is presented in Figure 4. Lateral and vertical position are the coordinate positions of the rotor plane. Due to different cases in Table 3 and the directions of the waves and currents, there are a total of 36 numerical simulations, and each simulation was executed for 3000 s.  
Figure 4: Turbulent wind field with a reference wind speed of 12 m/s at the hub height.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Wave**} & \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**Waves**} & \multicolumn{2}{c}{**Currents**} \\ \cline{3-6}  & & **Significant** & **Peak Period** & \multirow{2}{*}{**Velocity/m/s**} & \multirow{2}{*}{**Directions**} \\  & & **Height H\({}_{s}\)/m** & **T\({}_{p}\)/s** & & \\ \hline  & 1 & 4.6 & 7.7 & 0.5 & Positive \\ Wave in the & 2 & 4.6 & 7.7 & 0.5 & Opposite \\ positive X & 3 & 4.6 & 7.7 & 0.609 & Positive \\ direction/ & 4 & 4.6 & 7.7 & 0.609 & Opposite \\ Wave in the & 5 & 8.2 & 13.8 & 1.0 & Positive \\ positive Y & 6 & 8.2 & 13.8 & 1.0 & Opposite \\ direction & 7 & 8.2 & 13.8 & 1.31 & Positive \\  & 8 & 8.2 & 13.8 & 1.31 & Opposite \\ \hline \hline \end{tabular}
\end{table}
Table 3: Definition of study cases.  
Figure 5 illustrates the impact of varying currents on the PM wave spectrum of a 50-year return period. As a result of the presence and influence of the current, the PM wave spectrum experiences alterations in its peak amplitude, while the corresponding peak frequency undergoes minor changes. As shown in Figure 3, when waves propagate on positive currents, the peak amplitude is smaller than that without taking into account the effect of ocean current, and the peak amplitude will show a smaller trend as velocity increases. When waves propagate on opposite currents, the peak amplitude is larger when accounting for the influence of ocean currents, and the peak amplitude will rise with the increase in velocity. These findings are also relevant to other waves of different return periods propagating along currents with differing velocities. Additionally, Figure 3 illustrates the maximum value and the corresponding percentage interpolation of the peak value of the wave spectrum for a return period of 50 years, under conditions of current velocities of 0, 1.31, and \(-\)1.31 m/s, respectively. The difference between the spectra is evident, as both variations surpass 20%.  
In cases where the current is in the opposite direction to that of the wave, Equation (12) is used to rectify the high frequency segment of the spectra with \(a^{*}=0.015\). Consequently, the spectra are limited above the cutoff frequency, which is defined as four times the peak frequency, according to [PERSON] [46].