In this paper PIV measurements are used to study the dynamic behavior of the wake of an oscillating porous disk. In this way the study aims to gain more insights in wake dynamics of offshore floating wind turbines. The authors discuss the used approximations of their method and its limitations in the text (i.e. the porous disk approximation). However, it would also be good to mention the Reynolds number, and the fact that this study does not include the interaction with the dynamic ocean surface, which is also important for floating turbines and the spatio-temporal wake development. Instead of time-averaged wake analysis, the authors use conditional averaging of the wake velocity to capture its periodic behavior.  Wake analysis is performed using a classical fixed frame of reference, and a moving frame of reference in which the meandering of the wake center in the measurement plane is followed.

The results and discussion in the paper are a valuable contribution to the study of wakes of floating wind turbines. The paper is generally very well written, with clear figures, and analyses. Below several minor comment for the authors:

line 4’: Previous studies showed that harmonic motions with realistic amplitude and frequency and under a modelled atmospheric boundary layer have no significant impact on time-averaged values, but that frequency signatures are still visible in spectra of wake parameters. ‘ 

—> The reviewer finds this a confusing statement, and an incorrect generalization:

1. By definition the spectral content has an impact on the time averaged statistics. It is however indeed possible that in a turbulent boundary layer or flow with high background turbulence levels the impact on the time averaged statistics becomes masked or is relatively small, but there should be some connection to the statistics.
2. This conclusion depends strongly on the measured conditions ( background turbulence, motion frequency and amplitude of the turbine), and the measured location (near wake vs far wake). There are studies that show a meaningful difference in the time averaged mean wake properties, showing that wake recovery and spreading can be affected, and others where it is indeed small. But be careful in generalizing this statement.

line 98: similar comment: Be careful with this conclusion, this is true if there is a significant amount of background turbulence, for the tested conditions, and for the tested motion amplitude and frequencies, as stated in the sentence above. However, there are also studies that have seen an impact on time averaged statistics. Possibly because of the different conditions, motions, or the use of a rotor model? As an extreme example: a very slow motion / at a very small Strouhal frequency, will visibly spread the wake out, and thus affect time-averaged as well as spectral properties.

line 120: It can be interesting to add the length over which the boundary layer is developed in the wind tunnel.

line 134: It is best to note that this is a ‘hypothetical’, ‘fictive’ or ‘representative’ power coefficient, given that it is a porous disk.

line 150: Can the authors provide more information about the laser sheet thickness needed for the measurements, and the estimated measurement uncertainty of the PIV velocities?

line 195: The PIV measurements are performed pretty far downstream (x/D=8.125), where the wake is likely overwhelmed by ambient turbulence from the turbulent boundary layer. This must make it challenging to pinpoint the wake center in instantaneous snapshots given the broken up wake shape.  Given that the instantaneous wake shapes are likely very irregular / dispersed at this distance, can the larger uncertainty of the wake center affect the analysis in this paper in any way? For example: can errors of wake center add artificial ‘meandering’ to the analysis of the MFoR?

line 217: Do the authors find similar conclusions if a different value is used?  How sensitive are the conclusions to this value?

line 235: One has to be very careful with this sentence. For a turbine at a fixed downstream location the FFoR is still what matters in determining the available downstream power. In that case it is generally not relevant for the downstream turbine if the wake power is lower or higher in a MFoR, unless when temporal interaction like dynamic loading are investigated. The reviewer agrees however that it can be interesting from a wake modeling point of view to separate the impact of wake meandering in the MFoR approach.

On the other hand, for a floating turbine with variable position, both the MFoR and the FFoR are not a complete description because the spatio-temporal characteristics of the wake need to be considered in combination with the dynamic motion of the downstream turbine. 

line 306: Figure 11 is however also an interesting graph because it shows that pitch is not just surge + heave, due to the angular misalignment of the rotor. Due to the pitch angle the porous disk deflects the wake up or down, generating a lift force, accompanied by a counter rotating vortex pair. An interaction of this CVP with the shear in the boundary layer, and possibly the presence of a tower could explain why pitch affects the y-location slightly, and periodically.

line 389 : It would be helpful to add to this sentence that there is also a geometric misalignment angle for pitch, deflecting the wake up or down, on top of the heave and surge motion.

line 417: Using the word ‘turbine model’ would insinuate that the tests were done with an actual rotor. ‘porous disk model’ is the most correct wording.

line 423: From the sentence it is not clear what is meant: the second-order motions should be relatively smaller than the simulated amplitudes/frequencies? Or what is meant with ’second-order’ ? larger/smaller / a background motion on which the pitch/heave/etc are superimposed?

line 428: This is a main conclusion for the paper, and it is also in agreement with results in the literature. Can the authors discuss or comment on the agreement with results in the literature?

line 432: As discussed in a previous comment: In my opinion this is only a misrepresentation if one wants to understand the characteristics of instantaneous wake properties without the impact of meandering. For the purpose of characterizing the available power for a fixed downstream turbine, there is no misrepresentation with the FFoR method.

line 438-439: this conclusion seems to be in agreement with findings in the literature. In that case, it would be helpful to discuss the agreement.

line 439: ‘The results show that.. ‘ This sentence is not clear. If there is momentum conservation the wake would have the same power independent of the area? Or is the variation in power in the wake a result of the porous disk creating a stronger wake when it moves forward (higher velocity difference), and a smaller wake when it moves backwards, as also modeled by the authors using the wake model?  Can the authors elaborate more clearly?

line 444: ‘when the wake goes to its highest point, it has a large surface and a low available power’ Are any of these observations in agreement with what is available in the literature? For example, studies of static tilt misaligned turbine models also find higher wake deficit when the wake is deflected upwards.

line 454: There are in fact experiments in the literature with rotating turbine models subject to floating motions, some also with conditionally averaged wake analyses. Do the authors find agreements between their findings which can also be used to strengthen their results and porous disk approach?