Review of the manuscript “On the characteristics of the wake of a wind turbine undergoing large motions caused by a floating structure: an insight based on experiments and multi-fidelity simulations from the OC6 Phase III Project”.

In this manuscript, the characteristics of the wake and tip vortices of a floating wind turbine calculated by numerical simulations are compared to experiments in a wind tunnel. It is a continuation of previous studies that investigated the experimental results and compared to simulations with different levels of fidelity. The results are also compared to a linear model. The simulations show different levels of agreement, which is discussed in the paper. Discussion of the results in an appropriate level is presented.

A well-performed experiment and comparison with numerical simulations is of high relevance to the study of floating offshore wind turbines (FOWTs). The effort put into generating the data and compiling it in a comprehensive paper is remarkable. This manuscript is a valuable contribution to the topic and suitable for publication in WES.

Nevertheless, there is room for improvement. It is worth noting that the authors are comparing quantities that are difficult to measure accurately, for this reason the order of magnitude of the uncertainties might relevant. For this manuscript to become a work that can be used as a reference study, it is important to make clear the uncertainties of the experimental data. Additionally, there are minor issues that should be improved. Therefore, I believe the authors should revise the paper taking into consideration the following comments:

1. In the last paragraph of the introduction: Kleine et al. (2022) did not performed FVW simulations. They used 2 methods: CFD simulations using an actuator line model; and an analytical model based on the Biot-Savart law.
2. The call to equation 8 reads “The amplitude of the oscillation can be calculated as Eq. (8)”. Equation 8 does not show the amplitude of the oscillation.
3. The phase is disregarded in equations (8) and (12). However, no justification is included for this. From what I understood, equation (8) is the ratio of maximum change of circulation and maximum tip displacement (analogous for eq. (12)). Please make this explicit. If this is not the case, please clarify.
4. In section 2.1, it is worth mentioning that other linearized quasi-steady models might predict a phase shift different from 90°, if different assumptions are used. For example see: Wei, N. J., & Dabiri, J. O. (2022). Phase-averaged dynamics of a periodically surging wind turbine. Journal of Renewable and Sustainable Energy, 14(1), 013305.
5. Include references for the methods in table 2.
6. Please include the Reynolds number of the experiment (using density and viscosity obtained from local ambient conditions).
7. To allow a better characterization of the inflow conditions, please include more information on the turbulence levels of the wind tunnel. Include at least the integral length scale. If more information is available, please include.
8. Please include the frequency of rotation in Hz. The fact that the frequency of rotation, 4 Hz, is an integer multiple of the platform frequency is a relevant information (this simple calculation should not be left for the reader).
9. The phrase “by reducing the amplitude of motion by a factor of 75” in section 5 is not clear. From what I understood, the amplitude of motion, in meters, is reduced for surge but the amplitude of motion, in degrees, is not reduced for pitch. Is that correct? A better way to say is that the non-dimensional amplitude of motion is maintained, where the non-dimensional amplitude of motion is defined as Ax/D for surge and the amplitude angle for pitch.
10. My calculations did not agree with the reduced frequency shown in Table 4. For example, for case 2.5, using equation (15): fr=1.0*2.381/4=0.595, which is different from 0.568. Can you explain?
11. The circulation, calculated using eq. (16) possibly would have significant errors. Please estimate the uncertainties and include error bars in the plots. If this is not possible for all numerical results, please include at least for the experimental results. Please include the “accuracy analysis of the vorticity distributions of both simulations and experiments” as an appendix. If not present in the accuracy analysis, a suggestion is to perform the calculation of the circulation using the line integral of the velocity and compare to area integral of the vorticity (the line integral avoids the derivative).
12. Please estimate the uncertainties of the vortex core radius and include error bars in the plots. If this is not possible for all numerical results, please include at least for the experimental results.
13. Please estimate the uncertainties of the position of the vortex core and include error bars in the plots. If this is not possible for all numerical results, please include at least for the experimental results.
14. The phrase “The vorticity plots are shown using a threshold of \omega = 5 m^2/s” is not clear in the legend of figure 4. The threshold  does not seem to be 5.
15. In equation (18): is * a symbol for multiplication?
16. Regarding phase shift for the experimental results: Do I understand correctly: only 4 points are used to calculate the phase shift experimentally? It seems to me that 4 points is too low for experimental data. My perception is that a small uncertainty or noise in the value of the function at the points would lead to very different results of phase shift. Also, I have the impression that the error related to aliasing would be very significant. Please investigate this question in detail. Before comparing the numerical results to the experimental phase shift, the authors should show that the errors are low. If the experimental phase shift results are not reliable, the discussion should be revised.
17. It would be very useful if the data used to calculate the quantities in section 7.2.2 could be provided as supplementary material (or in an appendix) in the format of the plots of section 7.2.1. The plots of section 7.2.1 give important information to interpret the results of section 7.2.2. For example, it is possible to observe in figure 9 that the method used to calculate the vortex strength does not seem very reliable for some methods (example: SJTU and NREL).
18. Results in general: please show the distance in the streamwise direction and the amplitudes in non-dimensional format (x/D and A/D).
19. Suggestion: show the velocities in the streamwise direction (u/Uinf) and other quantities in non-dimensional format.

Some typos and other presentation comments:

1. Missing “et al.” in some references (examples: Arabgolarcheh (2022) and Ramos-Garcia (2022a)).
2. Equation (14): \Omega does not follow nomenclature of this paper.
3. In section 7.2.2: reference to figure 10, instead of figure 11.
4. References: many references included as pre-prints have already been published.

Dear authors, many thanks for your interesting manuscript. Please find my remarks attached