Comment on wes-2021-7

The study presents numerical simulation runs by the WRF model to investigate recovery processes from an hypothetical 50x50 km2 offshore wind farm. The WRF is driven by real weather data. The experiments quantify the recovery processes under different wind speeds and wind turbine spacing. The study is well structured and written, although the language can be improved at some parts. The results are presented clearly, but some figures need be improved to be more accessible to the reader. The discussion picks up on the novel results but also remains very superficial at some points. My main criticism of the study is the neglection of the stability, which is a main control parameter for wake recovery. This is further explained in the comment sections. With the consideration of this aspect and further improvement, the study can be a very valuable contribution to the offshore wind energy community.


General comments
The abstract gives a detailed description of the study, but remains very vague on the results. The results need to be presented more precisely and concretely, (e.g how is high inter turbine spacing defined, densely packed etc…). For more details please see the specific comments.
My main criticism is that the study does not take into account the stability and boundarylayer height regarding wake recovery. For the description of offshore wind farm impacts on the atmosphere (such as far wake effects/blockage effect or the influence of the farm on vertical turbulent moment flux, as mentioned on p.13 l.24), a consideration of the stability and ABL top (as mentioned in p.10 l.25) as major parameter, along with the park layout and wind speed, have been identified in several recent studies (e.g. Djath et al . 2018, Siedesleben et al . 2018, Cañadillas et al. 2019, Platis et al. 2020. However, this study only takes turbine spacing and the wind speed into account. In addition, the results from these mentioned studies and further recent studies about the ongoing investigation of the far field effects of offshore wind farms are not addressed in the study. Also on p.13 l.24: Turbulent vertical mixing depends on the thermal and dynamic stability. Also for strong horizontal wind speed during strong convective conditions vertical recovery may remain the main contributor. Therefore, I highly suggest at least to take the stability (e.g. lapse rate or Richardson bulk number) for the investigated cases into account and include them in the discussion.
Figures have to be re-worked including units to the scales. For some figures I also recommend to enlarge them to make them more readable. Also the range of the scale hat to be rearranged as e.g in figure 6 a) the variation is seen hardly.
To make things easier for the reader, I suggest to define the mean wind direction as positive x. This will help the reader to compare easier cases A with B and C. This will also help to better distinguished between flow effect parallel and perpendicular to the flow e.g., the interpretation of Figures 3 b) , 4, 5 and 6.
Why is the recovery only presented for the wind farm domain (Fig. 6). I expect also far field effects similar to the wake effects to be seen in the vicinity of the wind farm. Also this will give a broader picture of the upwind and downwind effects.

Specific comments
p.1 l.14. How is high defined? Narrow spacing? Please be more precise.
p.1 l.16: What is meant by can be quantified using low-order empirical equations? Please be more more concrete. Eq. 15: The denominator on the right-hand side of Eq. 9 should contain the unit. I also suggest to write 140m -28m p.7 l.25 Why small v ? Fig. 3. The figure is hard to read, especially 3c). Please enlarge the plots and the labels. Please add a unit to the scales. For case A the resolution is way to small to be able to follow the analysis on page. 9. l. 15-16. p.10. l.5: Not true several other studies such as Platis et al. 2018, 2020, Siedersleben et al. 2018 reported a deceleration of up to 40 % in the wake of offshore wind farms. Fig. 4. I recommend to mark the area where the wind farm is located. Fig. 4: Case A III. Why is there a deceleration and then an acceleration of the flow between 0-1000 m and at x= 780-850 km? Fig. 4 The upwind deceleration seem very impressive. I am wondering whether a too small simulation domain is causing an intensification by boundary reflections? Is there a way to assess this influence ? Fig. 4 b. Why is a streak pattern visible? Can this be also attributed to artifacts caused by the simulation? p.11.9 ff. I do not understand how this argument contributes to case C-I. Please describe more clearly.  p.11. l.17. It would be helpful for the reader just to mention again very briefly the difference between synoptic and micro scale.
p.11 l.8-10. "It is possible that this meso-scale momentum transport aids in the wind farm recovery by making more momentum available for downward mixing by turbulence." This is very speculative. Is there a way to justify it ? Can the variations at different heights be explained?