## 6 Fully Coupled Wind-Wave Simulation
Due to the unavailability of MARIN test data for the wind and wave conditions simulated herein, the comparison was only performed with the result from a previous study. All the 3-DOFs, i.e., heave, surge, and pitch showed small amplitudes compared to the results of the regular wave test without wind conditions. The incoming wind from the x-direction obviously has a significant effect on the restoring force of the mooring line; hence, the FOWT system cannot be restored to the equilibrium position as in the regular wave test. The incoming wind increased the aerodynamic thrust towards the floating system and pushed the platform further away in the backward direction, also leading to an increase in the mean surge. Nevertheless, the close agreement between the results for the 3-DOFs demonstrates the capability of this method. Figure 14: Instantaneous iso-velocity contours within one period: (**a**) upwind direction movement; (**b**) downwind direction movement. Figure 13: Velocity scene and water elevation. Thrust and power are two critical aerodynamic performance factors for evaluating a wind turbine. Thrust is defined as the integrated force component normal to the rotor plane. The power output and thrust force time-histories for the coupled simulation are presented in Figure 15 along with the dynamic responses of the pitch motion rate of the platform. The response curves of power and thrust act at the same frequency as the incident wave. Due to the tower shade effect, the curves of power and thrust force exhibit periodical fluctuations with a period of 120\({}^{\circ}\) for the blade rotation. However, the effect of tower dam effects on the power output of the wind turbine is less than 5%. The variation of pitch motion also acts at the same frequency as the inlet wave. When the platform moves in the upwind direction, the power output and thrust force both increase, while the aerodynamic load decreases as the sign of the pitch motion changes. This is because the upwind pitch motion of the FOWT increases the relative velocity between the wind turbine and the inlet wind, and the angle of attack for each blade section increases correspondingly. The dynamic responses of the wind turbine performance and typical platform motions after 300 s of the simulation are presented in Table 8. The power output varies from 3446 kW to 4698 kW at a rated wind speed. The variation in power is larger than that in the thrust force, that is, the power output is more sensitive than the thrust force to platform motion. Then, aerodynamic performances of the onshore fixed wind turbine and offshore floating wind turbine were compared and the average thrust value was calculated over the last four periods. In the case of thrust, a 7.8% increase was observed in a floating offshore turbine, the floating offshore wind turbine had an average thrust around 796 kN and the onshore wind turbine had an average thrust of 738 kN, which indicated a relatively small load on the hub and blades. This is because of the thrust force acting on the top of the tower, meaning \begin{table}
\begin{tabular}{c c c} \hline \hline
**Motion** & **Wave Only** & **Wind-Wave Coupled** \\ \hline Surge (m/m) & 0.70 & 0.12 \\ Heave (m/m) & 0.36 & 0.13 \\ Pitch (deg/m) & 0.33 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Motion response amplitude operators (RAOs) in different environment conditions. Figure 15: Fully coupled FOWT aerodynamic performance. the platform always moves in the upwind direction to offset the capsizing moment induced by the thrust force. In the case of the power curve, the average power value was calculated over the last four periods. A 10% decrease was observed in the floating offshore wind turbine, which is likely due to the smaller project area and relative income wind speed when the platform pitches, as shown in Figure 16. Accordingly, the platform surges from 7.9 to 9.8 m, which is also due to the thrust force that must be offset by the mooring line tension.