The authors present a study on the coupling between the dynamic induction pulse wake mixing control and the dynamics of floating offshore wind turbines. The model set up is detailed for enhanced reproducibility and set up choices are motivated based on an appropriate convergence study. Simulations in the frequency domain are supplemented with specific time-domain simulations at identified frequencies of interest. The paper is interesting and I enjoyed reading it. It is clearly and concisely written and credibly supports its research findings with clear figures. Below, I list a few comments which I believe would further improve the quality of the paper.

Main comments

• In the abstract, the authors highlight that the expected gain in average wind speed is more sensitive to excitation frequency for floating than bottom-fixed turbines (this is supported by Figure 9). However, I think an equally of not more important conclusion is that the "gain in average wind speed" (i.e. the enhanced wake recovery) by applying Pulse control is lower for floating than for bottom-fixed turbines due to turbine motions. If the authors agree, this should be added in the abstract.
• In line 111, the authors claim that, "without loss of generality, the NREL 5MW mounted on an OC3 spar-buoy is used". However, in line 179, they also state that "the motion of the nacelle is mainly dependent on the floater design". These statements appear to contradict. Can the authors comment on to which extent their results can be extrapolated to (1) larger turbines representative of current and near-future offshore wind turbines (2) Different floater concepts.
  
  I expect it is difficult to generalize this, and would invite the authors to comment on this in the manuscript.
• The authors refer to the work of Munters and Meyers (2018) (I will refer to this as MM18), where the Pulse concept was first identified. However, some important differences that complicate a direct comparison (e.g. on optimal excitation frequencies and impact on wake recovery) should be kept in mind which are not addressed in the paper. It would be useful for authors to comment on these in the paper.
• The work of MM18 considers a turbulent boundary layer inflow, whereas the current work based on Qblade-Ocean appears to consider a uniform and steady inflow (although it is not explicitly mentioned). This significantly impacts natural wake recovery. Please comment on this and potentially mention it as an important area for future work.
• L285: The authors mention that their finding of "at a 5D distance, the wind speed has converged to nearly identical values." aligns with those in Munters and Meyers (2018). However, Fig. 17a in MM18 clearly shows that overall power gains remain quite different for the different St values of 0.125, 0.25, and 0.5 presented here. Therefore, I do not follow this statement, please explain. 
  
   

Minor / typographical comments

• In table 1, the maximum wake length is shown as "100 Rotor Diameters". In the accompanying text, the authors indicate that the wake is cut off either when this length is exceed, or the maximum number of wake elements is reached. Does this setup length of 100 diameters effectively mean that the latter condition is always the most stringent? If not, 100 Rotor diameters appear excessive for the purposes of this paper. Can the authors shortly comment on this?
• Page 7, L 157: Can the authors add a short comment that, as described in MM18, the Pulse only works for freestream turbines, and that, for waked turbines further research is needed?
• Page 11, L216. "the Pulse becomes less effective as the blades are pitching at a too high frequency" add why the high frequency causes an ineffective Pulse, e.g. since the wake roll-up dynamics are not receptive to these high frequencies.
• Figure 4, bottom panel: I assume the ylabel should be "Phase" and not "Gain"
• Page 14, L268: "This section analyzes the wind speed in the wake, another measure for wake mixing", I would suggest a different phrasing, as the wind speed in the wake is the direct product of enhanced wake recovery / wake mixing, not just another measure. Related, I suggest the authors amend the statement at the end of section 4.1 as "This is likely reducing the overall effectiveness of the wake mixing strategy, as investigated in the next section".
• Figure 7 makes mention of a velocity profile for visualization, yet the figure does not show profiles, but a wake visualization and a planar color plot. Can the authors describe what is exactly shown in the figure? (e.g. the locus of wake elements on the left and contours of axial velocity on the right?)

• Some of the captions can be a little more descriptive to aid the reader to distinguish between plots. For example, in Figure 8, can authors please add in the caption that the top panel is at St = 0.125, etc. It is included in the labels, but mentioning this in the caption makes it easier to distinguish.
• The authors comment on computational cost / time a few times throughout their paper, especially when referring to choices in the simulation setup. Can they illustrate this by mentioning an order of magnitude for the QBlade-Ocean frequency and time-domain simulation times?