Dear reviewer,

we would like to thanks you very much for taking your time to revise this extensive manuscript. We are aware that it contains a lot of information and text, which most likely made reviewing a quite time consuming task. Therefore, we appreciate that you were willing to invest this work and give us advice to improve it. We found your advice helpful and in a positive spirit in all cases and were hopefully able to implement the vast majority of your comments.

One major take-away for us was that our idea to distinguish unsteady and quasi-steady behaviour by using the word 'transient' did not lead to a more precise understanding but to confusion. The other major take-away is that we had to condense the information and leave more details to the appendix. We hope that reshaping the structure and putting more details into the appendix improved the readability of the manuscript.

We respond to some general comments in the following and have answered to the text-related comments in the attached PDF document.

- "Regarding the use of "transient" instead of "unsteady," it is recommended to revert to the original term "unsteady"..." 

We agree on this and followed your advice in the whole manuscript.

- "While surge motion primarily impacts axial properties such as axial induction and thrust force, the analysis predominantly focuses on the impact on angular momentum..."

Here, we want to point out two things: First, we agree that the surge motion strongly impacts the axial momentum balance of the rotor and the fluid. From our point of view, the axial momentum balance has a major influence on the angle of attack along the blade and consequently on the lift force at the blade sections. Our understanding is that the lift force is the main driver of both, torque/power and thrust force. Therefore, unsteady changes of the lift force will be visible in both, rotor thrust and torque, in a similar manner. Aside from this theoretical reasoning, the additional plots of the simulated torque and thrust in the investigated cases can be found in the appendix. If one compares the results for torque and thrust, no principal difference can be found between these. Therefore, we do not agree on the conclusion that our 'analysis predominantly focuses on the impact on angular momentum'. Second, we agree that the returning wake effect is the most interesting unsteady effect for the reader and needs to be explained and evaluated in detail due to the low public awareness of this effect. However, our analysis potentially includes all possible unsteady effects, while the influence of two (unsteady airfoil effect and returning wake effect) could be pointed out directly. The third known effect (dynamic wake/inflow effect) is most likely present, but could not be observed in an isolated manner. However, it could be pointed out that it seems to have very limited influence on the rotor torque and thrust in the investigated cases. Therefore, all three relevant unsteady aerodynamic effects are addressed in this work.

- "The manuscript appears lengthy, suggesting the need for restructuring to condense its content and its focus. Many ...."

We agree on this and reshaped the paper. We put more of the numerical and experimental details in the appendix to make the reading more fluent, but still hold the necessary facts to reproduce the simulations and judge on the quality of the measurements available. We added some sentences (see PDF) to explain why both FVW methods have different advantages and a comparison between these is of interest for us. Regarding the three different rotors investigated, we have simple reasons why we believe that the extension to the analysis to the UNAFLOW and the IEA15MW is important for us: From a physical point of view, the occurrence of the returning wake effect is more or less the same for all three rotors. However, when considering the current discussion on unsteady aerodynamic effects of FOWT in literature, the OC6 project is a milestone because more the 20 different simulation codes were utilised to identify unsteady aerodynamic effects. However, in the publication on the load analysis (Bergua et al., 2023), a more or less purely quasi-steady behaviour was found for the UNAFLOW rotor at constant rotational speed. Therefore, we assume that at least the over 60 experts authoring of this paper have a strong interest in checking if the returning wake effect can also be proven for the UNAFLOW rotor. A side effect is that all these people have the simulation model of this rotor including this kind of load cases ready and are able to obtain the same results within a few days. (This has already happened after the work was presented at WESC, see https://doi.org/10.5194/wes-2023-109). From the perspective of a code user (e.g. designers, certification companies, researchers), the boiling point is whether they can continue using BEMT methods for FOWT simulations or not. Therefore, we believe that it is critical to show in which conditions (i.e. wind speed and wave frequency) one has to account for this effect when considering modern wind turbines. 

- "There are many typos and grammar errors in the manuscript."

We corrected all marked errors and performed a new spell checking with different readers.

Best regards and many thanks for your extensive review,

Christian W. Schulz on behalf of the authors

Dear reviewer,

we would like to express our deep thank to you for your careful review of our work. We tried to incorporate all your comments, which we found generally very helpful and formulated in a positive way. We believe that the manuscript could be improved greatly in this way.

One major take-away for us was that our idea to distinguish unsteady and quasi-steady behaviour by using the word 'transient' did not lead to a more precise understanding but to confusion. The other major take-away is that we had to condense the information and leave more details to the appendix. We hope that reshaping the structure and putting more details into the appendix improved the readability of the manuscript.

Please find our detailed answers to your comments in the attached PDF.

Best regards and many thanks for your extensive review,

Christian W. Schulz on behalf of the authors