## 6 Dynamic Responses of Floating OWTs
### OC3-Hywind Spar  
Since the RAOs appear considerable excitation in the surge, heave and pitch modes among all 6-DOF motions [30], only these three RAOs computed by using hydrodynamic simulator and WAMIT [31], which is based on the linear and second-order potential theory, with a series of regular waves (\(H_{0}=5\) m, \(T_{0}=2.5\sim 20\) s) are compared for the OC3-Hywind spar, as shown in Figure 15a-c, respectively. Although a small frequency shift is occurred for the pitch response at the natural frequency, the computed RAOs with mooring loads from hydrodynamic simulator agree well with the results predicted by WAMIT.  
Figure 15: The performance of (**a**) surge, (**b**) heave, and (**c**) pitch RAOs as a function of wave frequency for the OC3-Hywind spar by comparing hydrodynamic simulator with WAMIT.  
In Figure 15a, the surge RAO predicted by using hydrodynamic simulator with the mooring load is smaller than the one predicted by WAMIT in the high-frequency region because the mooring load is overestimated in absence of the damping matrix of the mooring system. For the case with the mooring effect, there is a resonance peak at the natural frequency (\(f_{p}\) = 0.008 Hz) in the surge mode. Although it is not shown here, the numerical simulation indicates that the mooring load has the effect on the RAO as well as the natural frequency. It is exhibited in Figure 15b that the discrepancy of the heave RAO between WAMIT and our numerical simulation is small. Meanwhile, the OC3-Hywind spar basically follows the wave in heave for an extremely low-frequency wave. In case of the mooring effect, the frequency shift of the resonance peak in pitch RAO between hydrodynamic simulator and WAMIT as shown in Figure 15c could be due to a slight stiffening of the catenary mooring lines in the WAMIT simulation. In our mooring load equation, the mooring force was calculated by using linear quasi-static mooring stiffness. For simplifying the numerical computation, the elements in the damping matrix of the mooring system are all set to zero. Therefore, the mooring effect on the pitch motion could be overestimated.  
Figure 16a-c exhibit time variations of wave exciting force (\(F_{ext}\))/moment (\(M_{ext}\)), radiation damping force (\(F_{Rd}\))/moment (\(M_{Rd}\)), radiation added-mass force (\(F_{Ra}\))/moment (\(M_{Rd}\)), buoyancy force (\(F_{B}\))/moment (\(M_{B}\)) and mooring force (\(F_{M}\))/moment (\(M_{M}\)) at the natural frequencies of the surge, heave and pitch, respectively. The input wave condition for calculating the force at the natural frequency of each mode is a regular wave \(H_{0}\) = 5m and \(T_{0}\) = \(T_{n}\) (\(T_{n}\): Natural period). The phase lags in time histories of wave-load components indicate the relationships between the wave exciting force and other wave-load components. It is obvious in Figure 16a that \(F_{M}\) is the most superior force at the surge natural frequency among all wave-load components, which is able to explain the contribution of the mooring load to the surge RAO in Figure 15a. However, it is noted that the quasi-static mooring force could be overestimated when ignoring the damping effect of the mooring system. This adequately explains why the mooring force is greater than the wave exciting force in the surge mode. It is found in Figure 16(b) that \(F_{M}\) has less influence on the dynamic response of the OC3-Hywind spar at the heave natural frequency. However, \(F_{B}\) is the dominant force at the heave natural frequency due to deeply draft of the slender body. Figure 16c indicates that \(M_{ext}\) plays the most significant part at the pitch natural frequency, which is mainly attributed to the large pitch inertia about CM.  
Figure 16: _Cont._