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Review of

„Investigating the physical mechanisms that modify wind plant blockage in stable boundary layers“

by Miguel Sanchez Gomez, Julie K. Lundquist , Jeffrey D. Mirocha, and Robert S. Arthur

The objective of the article is to investigate the mechanisms driving the development of the wind speed deceleration in front of wind farms responsible for the global blockage effect. To achieve this, the authors perform Large Eddy Simulations using WRF-LES. They compare simulations of two different atmospheric stability regimes (moderately stable and weakly stable) each with the actuator disk representation of a single turbine or a 10 x 4 turbines wind farm (NREL 5 MW).

The assessment of the physical effects driving global blockage is performed analyzing the different contributions to the steady state integral momentum equation for the u − velocity where the Coriolis force and turbulence contributions are neglected. A vertical momentum advection is identified as the main cause of global blockage.

The paper contributes to the currently increasing number of numerical investigations of the global blockage effect. Even though the findings that the vertical advection of momentum out of the farm inflow is correlated to global blockage (Strickland and Stevens, 2022), as well as the dependency of global blockage on atmospheric stability (Schneemann et al. 2021) is not new itself, the approach to separate the different contributions causing the flow deficit upstream a wind farm is novel and interesting. However, in the current draft the manuscript lacks a clear description of the interesting findings, compromising the achievement of the paper’s objective. The paper is generally well written but needs corrections and clarifications detailed below. Further, a revised manuscript should better follow a storyline. The Figures are mainly clear and support the results, some changes are suggested in the following. We recommend to publish the paper after our major concerns and questions are addressed.

Scientific comments

On the presentation of the physical mechanisms of global blockage

The paper’s objective is to clarify the fundamental physics of Global Blockage. However, the main findings are not highlighted well enough, and the argumentation towards the main results is hard to follow.

The different strengths in blockage comparing single turbine and wind farm resulting from different amounts of the flow being advected upwards (i.e. different vertical momentum transport), is one of the main findings of the paper, and it should be made clearer. The authors could e.g. display the different vertical wind speeds in front of the single turbine and the wind farm in a single plot.

Another important finding is that the horizontal pressure gradient upstream of a turbine in isolation and a turbine in the first row of the farm is substantially equal. However, these results are very counterintuitive. In internal tests, the horizontal pressure gradient has been observed to increase dramatically between a turbine in isolation and a turbine at the first row of a farm. Could the authors explain this discrepancy? Could the authors confirm that the pressure gradient force for the front-row turbine in Figure 15a is normalized with the horizontal momentum advected only through the surface S_x of Figure 10c, instead of 10b? Please distinguish the variables for both S_x used.

Furthermore, as the horizontal pressure gradient does not change across all the studied cases, the authors postulate that what drives the changes in the vertical momentum advection is a vertical pressure gradient developing upstream of the farm. This vertical pressure gradient seems then to be identified as the main mechanism causing global blockage. Unfortunately, most of the very little discussion on it is relegated to the Appendix. The authors should consider to introduce the plots for the integral momentum balance in the vertical direction in the body of the paper and expand the discussion on the vertical pressure gradient.

Further analysis should also be performed to make the point of the authors stronger. As done for the horizontal momentum, also the vertical momentum balance should be compared between the wind farm and the single wind turbine cases. The claim of the authors could be supported by demonstrating that the vertical pressure gradient increases in the wind farm case, in the same order as the blockage increases.

On gravity waves:

The authors write that gravity waves did not form in the weak free-atmosphere stratification simulation of Wu and Porté-Agel (2017) in Line 40-41. This statement might be misleading and it should be revised. In fact, Wu and Porté-Agel did not observe upstream propagating gravity waves in their simulation with a weak stratification in the free atmosphere. Wu and Porté-Agel (2017) differentiate between subcritical and supercritical flows. In subcritical flow gravity waves can move upstream, in supercritical flows they can’t. Wu and Porté-Agel (2017) do not state that there are no gravity waves in case of the supercritical flow. My suggestion is to apply the theory presented in Wu and Porté-Agel (2017) in order to determine whether the cases shown by the authors are cases of supercritical flows.

Line 43-45: “Note that Allaerts and Meyers (2017, 2018); Maas (2022) simulate the flow around an infinitely wide wind plant; therefore, the large vertical boundary layer displacement that excites gravity waves (and thus the velocity deceleration in the induction region) is likely overestimated compared to operational wind plants.” This statement is not obvious. Please add a better explanation based on existing literature here.

On the choice of grid spacing (Line 89-91):

Did the authors carry out any sensitivity tests in order to show that the grid spacing used by them is actually sufficiently fine? If not this should be mentioned in the manuscript.

On the choice of the model domain (Figure 1):

Did the authors check whether the 45 D long part of the model domain upstream of the wind farm is actually sufficiently long enough in order to avoid that the inflow boundary has an impact on the blockage that is found in the simulations?

Did the authors check whether the space in y-direction at the side of the the wind farm is sufficiently large in order to be able to exclude that the simulation results are disturbed by the lateral boundaries? Does the simulation approach the case of an isolated wind farm or that of an infinite wind farm in y-direction?

On the set-up of the large-eddy simulations (Section 2.1):

As the geostrophic wind is used as a boundary condition in the simulations, an information on the geographic coordinates where the simulations are carried out should be provided. The geographic coordinates will change the Coriolis parameter and therefore also the profiles of the wind components.

On Figure 2:

When is the averaging period that is used in this Figure? Has the simulation reached a stationary state yet?

On Figure 3:

A line illustrating a function of the type y=A+k^(-5/3) (Kolmogorov slope) should be added in order to show that the simulation actually resolves a part of the inertial subrange of turbulence.

On Figure 5:

The Figure shows clearly an inertial oscillation that is triggered when the cooling of the atmospheric boundary layer starts. Obviously, the inertial oscillation has not been completely damped after 8 h. What does this mean for the analysis of the global blockage effect?

On Figure 6:

It is difficult to show with Figure 6 that the Monin-Obukhov-length and the Richardson number have already reached stationary values within the simulation time used (even for the case with the stronger cooling rate).

Line 201:

When reading the manuscript I understood that independent of the simulation each differential control volume has an extension of 15 m along the x-direction. However, how does this work out when the grid spacing is 7 m in one of the two cases simulated?

Figure 11:

The authors should elaborate a bit more on the explanation of the observation that the decrease of pressure starts already slightly upstream of the actuator disk.

Figure B1:

This is one of the main findings and should be integrated in the results part of the manuscript.

General and technical comments

• Whole document: Use non-italic units, introduce a Space between number and unit, avoid line breaks between number and unit, add clickable links in the pdf for references on figures etc.
• Line 17: Please add a reference for wind turbine and cluster wakes each.
• Line 18-19: Why are so many references given here? One reference with a more general view on blockage like Bleeg et al., 2018 is sufficient, the others will be addressed in the state of the art.
• Line 21: “know” needs to be replaced by “known”
• Line 29-30: Please sort relevant references to the named factors influencing global blockage (“ size and layout of the wind plant, atmospheric conditions, wind turbine characteristics, and wind speed”)
• Line 33-35: The named references show different velocity deficits in different distances upstream. Please specify the general statement here.
• Line 62: “neutral LES” This is uncommon terminology. Please change to e.g. “The authors simulated a neutrally stratified boundary layer flow using LES...” 
• Line 89: The terminology introduced here for the state of the atmosphere should be kept throughout the document. The authors simulate a weakly stable boundary layer and a moderately stable boundary layer. Changing this to “moderately and weakly stratified flow” without referring to “stable” is misleading.
• Figure 1: Please add the turbine spacing in x and y direction in the Figure or the caption.
• Table 1: Please add information about the stability, i.e. the cooling rate applied.
• Line 113: Adding the word “temporal” makes the method more clear here: ... we prescribe a temporal cooling rate rather than...
• Line 113: flow -> flows are...
• Figure 2: Please label the height axis as z. Please add information about the period the data is averaged on. How long was the cooling applied before the averaging period? Further, Figure 2 shows the resulting profiles while Figure 3 and 4 jump back to the pre run simulations. This is a bit confusing while reading and should be restructured.
• Figure 3: The legend just holds two entries while the Figure includes many different curves / colors. The colours seem not to be consistent through the subplots.The evolution is hard to follow and the description from Line 126 ff could not be reproduced. Please change the legend or introduce a colour scale. In my opinion the amount of curves shown can and should be reduced. Further, please add the Kolmogorov slope into the plots. Please state in the caption that this is a plot of a pre-run of the LES.
• Figure 4: z for height axis, readable legend covering all cases as for Figure 3. Maybe Figure 3 and 4 can be even combined.
• Caption Figure 4: “Horizontal velocity profile” is misleading, e.g. “vertical profile of the horizontal wind” is more clear.
• Line 131: Delete “On average”, the information is double.
• Line 149: “Nose” is a not common expression for the wind speed maximum of a LLJ. Please use a more common expression.
• Figure 6: Where is the benefit in showing both L and Ri_bulk? Further, both cases seem not to have converged. Please elaborate on this.
• Line 155: Better use ° instead of deg in the whole document.
• Figure 7: A second x-axis in units of D could support readability. Within the stippled areas the wind field can not be well seen. We suggest to remove the stipples and just keep the bordering lines and lables. Why is the wake region marked as well?
• Figure 9: Caption could refer to Figure 8 saving copy/pasted information. Even better could be to combine both plots as subplots in a single Figure. Same could be applied for some of the following results plots.
• Line 192, Equation 1: Labelling of the different terms can help the reader to follow more easily.
• Line 224ff: The small differences described could not be seen in the Figure. At which position does the difference occur?
• Line 254: “atmoshperic” needs to be changed to atmospheric
• Line 259: Please elaborate a bit more on the mentioned secondary circulation as it is not obvious to the reader.
• Line 260: “ The increase in vertical velocity is driven by a vertical pressure gradient...” What is the driver for this pressure gradient? This seems to be one of the most relevant findings, please better explain and highlight.
• Line 287: please change “x1.9” to 1.9 times
• Line 291-292: Bleeg et al. (2018) suggest (plural)
• Line 332-343: Please elaborate more on the difference between momentum advection and a deflection of momentum upwards. This is not obvious.

Literature

Allaerts, D. and Meyers, J.: Boundary-layer development and gravity waves in conventionally neutral wind farms, Journal of Fluid Mechanics, 814, 95–130, https://doi.org/10.1017/jfm.2017.11, 2017.

Allaerts, D. and Meyers, J.: Gravity Waves and Wind-Farm Efficiency in Neutral and Stable Conditions, Boundary-Layer Meteorology, 166, 269–299, https://doi.org/10.1007/s10546-017-0307-5, 2018.

Bleeg, J., Purcell, M., Ruisi, R., and Traiger, E.: Wind Farm Blockage and the Consequences of Neglecting Its Impact on Energy Production, Energies, 11, 1609, https://doi.org/10.3390/en11061609, 2018.

Maas, O.: From gigawatt to multi-gigawatt wind farms: wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations, https://doi.org/10.5194/wes-2022-63, 2022.

Schneemann, J., Theuer, F., Rott, A., Dörenkämper, M., and Kühn, M.: Offshore wind farm global blockage measured with scanning lidar, Wind Energy Science, 6, 521–538, https://doi.org/10.5194/wes-6-521-2021, 2021.

Strickland, J. M. and Stevens, R. J.: Investigating wind farm blockage in a neutral boundary layer using large-eddy simulations, European Journal of Mechanics - B/Fluids, 95, 303–314, https://doi.org/10.1016/j.euromechflu.2022.05.004, 2022.

Wu, K. and Porté-Agel, F.: Flow Adjustment Inside and Around Large Finite-Size Wind Farms, Energies, 10, 2164, https://doi.org/10.3390/en10122164, 2017.

Publisher’s note: a supplement was added to this comment on 27 March 2023.

Please see the attache review