## 4 Results
### Aerodynamic and Hydrodynamic Load
The standard deviation of the oscillations of the tower top does not change either, but for the TLP a significant reduction of the standard deviation can be seen at the wave frequency of 1.7 Hz compared to a wave frequency of 0.6 Hz. To compare how the power of the displacement time series is distributed over frequency, the PSD is calculated. The PSD of the time series data of the displacement of the TLP from the experiments and simulations can be seen in Figure 12.  
The frequency at which the first peak is located on all of the six PSDs is at the first natural frequency of the TLP in surge. There is a good agreement in which frequency which the first natural frequency occurs in the simulations and experiments. The amplitude of the peak though differs from both the theoretical model and FAST. The amplitude of the peak in FAST is significantly higher than the experimentally found. This is properly likewise due to the damping of the TLP and higher aerodynamic load, which should be looked further into, as mentioned previously in Section 4.3. The second peak occurs due to the hydrodynamic loading from the waves on the TLP. This peak is only visible at the first column of PSDs, where the waves applied are monochromatic waves with a frequency of 0.6 Hz. There is a very good agreement between the simulation and experiment in which frequency it occurs and the amplitude of the peak. Likewise, the PSD of the time series data of the displacement of the tower top from the experiments and simulations can be seen in Figure 13. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**4 m/s**} & \multicolumn{2}{c}{**7 m/s**} & \multicolumn{2}{c}{**8.6 m/s**} \\ \cline{3-8}  & & \(\mu\) **(mm)** & \(\sigma\) **(mm)** & \(\mu\) **(mm)** & \(\sigma\) **(mm)** & \(\mu\) **(mm)** & \(\sigma\) **(mm)** \\ \hline \multirow{3}{*}{TLP} & Experiment & 7.3 & 0.5 & 21.5 & 1.2 & 21.2 & 1.2 \\  & FAST & 10.7 & 2.6 & 31.6 & 5.6 & 42.0 & 5.1 \\  & Theoretical & 9.9 & 1.2 & 34.7 & 3.0 & 33.0 & 4.0 \\ \hline \multirow{3}{*}{Tower Top} & Experiment & 2.5 & 1.4 & 8.9 & 1.9 & 7.5 & 2.1 \\  & FAST & 2.3 & 0.8 & 7.6 & 0.9 & 11.2 & 1.0 \\ \cline{1-1}  & Theoretical & 3.1 & 1.2 & 11.1 & 1.6 & 9.9 & 1.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The mean (\(\mu\)) and standard deviation (\(\sigma\)) of the displacement in surge of the TLP and tower top at simultaneous wind and wave loading. The wind speeds which is tested at 4 m/s, 7 m/s and 8.6 m/s and monocromatic waves with a wave height of 0.01 m and wave frequency of 1.7 Hz. There are four distinct peaks which can be seen, these are the wave loading frequency, the 1P and 3P effect and the first natural frequency of the tower. The frequencies at which the peaks occur in the simulations PSD is in good agreement with the experimental PSD. The amplitude of the peaks obtained from FAST tends to underestimate the energy, especially at the first natural frequency of the tower. The theoretical model tends to estimate the energy located at the different peaks well, except at the 1P frequency which is underestimated. Figure 12: The PSD of the displacement time series of the TLP in surge from experiments and simulation by FAST and the theoretical model under different aerodynamic and hydrodynamic loading conditions. The waves are monochromatic with an amplitude which is set to 0.01 m. **(a)** Wave frequency set to 0.6 Hz and wind speed set to 4 m/s. **(b)** Wave frequency set to 1.7 Hz and wind speed set to 4 m/s. **(c)** Wave frequency set to 0.6 Hz and wind speed set to 7 m/s. **(d)** Wave frequency set to 1.7 Hz and wind speed set to 7 m/s. **(e)** Wave frequency set to 0.6 Hz and wind speed set to 8.6 m/s. **(f)** Wave frequency set to 1.7 Hz and wind speed set to 8.6 m/s. At last the FOWT was tested in a scaled offshore envirom at a mean wind speed of 7 m/s and irregular waves which was generated from the same JONSWAP spectrum as given in Figure 6b. The experiment was conducted for 50 min, while the simulation time was set to 30 min.