*5.2. Wavelength Factor*

For sea state 3, the wavelength is 54.38 [m]. The water particle path reaches 27.19 [m] from the water surface, then it starts to decay dramatically. The turbine hub is at a height of approximately 21 [m] from the seabed and the turbine diameter is 20 [m], the upper part of the rotor is in the range of wave circular orbits, the lower part of the rotor is at the location where the wave decays rapidly as shown in Figure 12. This indicates that the wave affected approximately half of the rotor swept area during operation, but excited the buoy significantly. Furthermore, the load reduction for the mooring supported turbine does no better than that of the rigid supported turbine because the wave just reaches the hub of the turbine and affects half of the turbine; moreover, the superposition of the buoy and turbine oscillations in this sea state makes the performance unexpected. Further investigation of this kind of sea state will be part of future work.

**Figure 12.** Water particle paths under waves in deep water and the turbine position.

#### *5.3. Morison Effects*

According to the results above, the variation of torque values on tension mooring supported turbines is larger than that of rigid supported ones in similar sea states. The reason for this is the added mass effects on blade sections and the inertia force added into the in-plane force to calculate the torque. The relative velocity term for a rigid supported turbine is only the wave particle velocity in the vertical direction transferred to the local rotating blade coordinate system. However, the inertia velocity of the turbine itself is coupled with the wave particle velocity in calculating the inertia force for the mooring supported turbine as in Equation (23); this results in an increase of inertia forces on blade sections in the mooring supported turbine. Then the total torque increases as the in-plane forces rise. Moreover, the method calculating the inertia force on the blade section for a rigid supported turbine may not be applicable for a turbine that can move in the water as a tension mooring supported turbine does.

Figure 13 presents the torque on the mooring supported turbine without Morison effects in sea state 1, and the torque reduces as expected. This indicates that the Morison effect, the added mass on the blade, plays a significant role in torque on a turbine that can move vertically. Moreover, the Morison effect module in BEMT could be improved in the future and the added mass effects on the mooring supported turbine blade should be further investigated.

**Figure 13.** Morison effect in torque
