the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Oct 2025
Wind tunnel study of yawed porous discs subjected to veered inflow
Abstract. Atmospheric boundary layer flow during stably stratified conditions often exhibits wind veering—the change in wind direction with height—which significantly influences wind turbine wake dynamics and its downstream recovery. This study investigates the impact of veered inflow on turbine wakes through wind tunnel experiments using high-resolution stereo particle image velocimetry (SPIV). A porous disc of uniform porosity is employed as a surrogate for wind turbines to systematically examine wake characteristics under both non-yawed and yawed conditions. The results reveal that veered inflow induces an ellipsoidal-shaped wake for a non-yawed porous disc. Under yawed conditions, however, the interaction between yaw and veer leads to a complex wake shape, where the curled shape due to yaw is superimposed on the wake stretching due to veer. Furthermore, the strength of the two counter-rotating vortex pairs formed around yawed discs is reduced due to wind veering. A budget analysis of the streamwise momentum equation is performed to shed light on the mechanism of wake recovery. The results demonstrate that wind veering leads to faster wake recovery and more available power for downstream wind turbines. These findings imply that, under conditions of extreme wind veer, yawing the turbine may offer limited additional energy recovery, as wind veering alone facilitates significant wake re-energization.
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Status: open (until 06 Jan 2026)
- RC1: 'Comment on wes-2025-185', Anonymous Referee #1, 14 Nov 2025 reply
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RC2: 'Comment on wes-2025-185', Anonymous Referee #2, 08 Dec 2025
reply
This work deals with an interesting topic: how the wake of a wind turbine is affected by veer and yaw. As yawing is a key issue in wind farm optimisation, this topic is highly relevant. The authors take an experimental approach to this topic, using a porous disc in a wind tunnel for which they have constructed a veering grid. This is an innovative experimental approach. Their main finding is that veering leads to faster wake recovery. The paper is well structured.
Overall, this paper should definitely be published, but several points should first be clarified.
My main concern is the validity of their key conclusion that veering leads to faster wake recovery. The analysis of the wake data could be improved. I suggest they clearly demonstrate that veering causes more than advection of the wake in different directions. In other words, the recovery deviates from the simple additive effect of veer and yaw (as discussed in part in Mohammedi's citation). Due to the uncertainties arising from imperfect wind tunnel flow (see below), the wake quantities (mean velocity, TKE, wind power, etc.) should be analysed using an integral over the entire wake area, including symmetric, skewed and curled cases. Variation in thresholds to define the wake can indicate experimental precision. Such an analysis is very important for their power considerations. As detailed below, the power of a turbine in a wake should also be averaged over different y positions. Even a simple linear translation in a different direction by veer would automatically lead to faster power recovery in a fixed rotor plane. It is important to quantify the difference between such a simple advection model and the experimental data, only than one can conclude that a faster recovery is observed. I also miss a quantitative comparison of the experimental results with the models of Mohammadi et al. (2022) and Narasimhan et al. (2025).
Another serious issue is the inhomogeneity of the wind tunnel, which causes the V0Y0 case to drift to the left (see Fig. 5b). The periodic structures caused by the veering grid seen in Figures 6a and 7a should also be discussed more critically. I am not convinced that the results are not heavily influenced by this imperfect experimental setup. This is a clear drawback of the experimental design of this work. I expect an own subchapter on this point.
I miss a discussion of the choice of yaw angles which go only in the direction of veer. I think it is discussed in the literature which consequence a yawing in the other direction will have. This should be included in the paper at least as a discussion.
The paper is formally OK, but the presentation of results in figures should be revised. The same notation as that introduced for Fig. 16 should be used throughout the work. The presentation in the figures should also follow the same scheme wherever possible, e.g. yaw in the y-direction and veer in the x-direction, starting with yaw 0 veer 0 and the bar of colouring to the right.
The citation (Englberger, WES 5, 1359 (2020)) showing that the turbine's rotation plays a role should be mentioned, may be also as a further detail to be investigated in future. It could be added close to line 104, where the choice of a non-rotating porous disc is mentioned.
Minor points and some more details :
Fig 1(an and b): The sketches how the laser is positioned is in my opinion wrong. The laser beam is aligned with the plane of the light sheet. I see a discrepancy to Fig 2 - isn’t here the laser below the flowing is directed in z direction.
Your definition of x=0D is the location of the disc (line 167)- which does not fit to Fig 1 a
Table 1 - please write what w/o disc means. Does it mean with and without disc?
and Line 164: 'Baseline uniform inflow' is unclear. it is unclear what this means - I suggest to have one clear way of terminology
Line 226 - `all inflow conditions` , better all three inflow conditions
Fig 4. - There are clear deviation of the veer at z between 0 and -0.2 D wich seem to be caused by the imperfect veer generation. This has to be discussed as it is just in the region where the wakes are measured.
Line 244 - why is the veer reported for x=5D and not like before for 7D
Line 265 . Sentence wrong: `As the tower is relatively thicker than the diameter of the porous disc
Periodic structures in Figs. 6 and 7 a show that the veer is not constant in y-direction, a plot of veer in y- direction in addition to Fig. 4 c and d is necessary. Here I have problems that these periodic veer structures do not affect the whole results as indicated above this has to be discussed more in this paper. The reader must get convinced that the results remains sensual.
It is important to quantify this veer structure, how much is the veer change in your-direction? In the discretization of color calibration does not allow to the the veer imperfection.
Fig 8 the wake center calculation for the kidney shaped cases makes not much sense. In Figs 6 and 7 the wakes are characterized more by two wake centers. Tower and veer generator will have an impact on this.
Fig 8a (no- veer case) shows that the wakes are pushed to the left, is there any reason, I guess this must be an effect of the wind tunnel itself. This strong displacement to the left is not see in the cited publications. The argument : `This is likely because the laser sheet is not perfectly parallel to the wind tunnel exit plane and is slightly misaligned.` - if this is the reason this is a bad set, which should be redone or calibrated correctly. Such a bias from the set-up must be avoided or taken out. This has to be corrected! I am not convinced that this is only due to the laser sheet setting. As all wakes have this tendency. It is very important to show that this is not due to a flow pattern in the wind tunnel. If it is just a misalignment of a laser, I can not understand that the position changes downstream and becomes maximal at 7D? This looks much more like an advection in this direction! Please clarify this properly.
Furthermore, the estimation method for the wake center after equation 5 appears to be affected by the tower deficit, resulting in an asymmetrical wake (see Fig. 5b, right). This gives rise to a negative bias in the z-direction of the wake centre, as shown in Fig. 8a.Line 287: „Also, it is quite obvious that yawing the disc moves the wake center in the opposite direction of yaw as seen in Fig. 8a, ....„ - in Figure 8a in comparison with Fig 8 b and c
Line 310 ff: The wake deficit is not well quantifies by maximum of the deficit. It is better to integrate over the wake area, choosing a threshold. This allow a much better quantification.
The conclusion that `within each veer case, increasing yaw from 0◦ to 30◦ does not alter the peak deficits ´for me not convincing. I propose to take aa advection model where veer is just advecting the wake in different direction, and ompared with the measurements with such a simple advection model.
Line 343 `…tion in the CVP (Fig. 10c, `. the end of the brackets is missing
Fig 12 . For veer 20° the background structure are clearly seen in term I - see comments above.
For equation (7) it should be noted that the 1/overbar{u} is a nontrivial local term, which changes the pattern of Fig 12. This leads to the conclusion of line 412: „more entrainment of fluid occurs into the wake from the vertical direction than the spanwise direction.“ What is not obvious in Fig 12
Notation of case Fig 13 WV10Y30. This notation is introduced and explained later in Fig 16 WVϕYθ . This is a bad style - see comments above to use throughout the whole paper clear well defined notions.
Fig 14 the calibration bar for TKE on top is unusually.
Fig 15 I do not see why the veer specification are given two time for each figure part.
Line 430 the statement `The increase in TKE for the veered cases can be explained by looking at the profiles of shear production of turbulence` is not well documented. It is hard to compare Fig. 14 with Figure 15 due to different presentations. Taking the case, no veer no yaw and x/D=3 - on sees that the production is maximal at the sides of the rotor plane, the TKE is maximal at the lower part of the wake, contradicting the statement. For the veered cases the double structure of the production is not seen for TKE. This comparison should be worked out better, from the presentation as well as from the discussion. Overall this discussion of turb. production and TKE is not good, it is very superficial.
Line 452 - please specify more precisely the location of hub height zT and lateral position yT. Are the turbines aligned with the wind speed direction at hub height?
Line 450 ff the power comparison is not acceptable. Wind turbines are operating in general not aligned with the direction of the incident flow. An integration over different lateral positions would be much more adequate for the investigated cases. In this analysis also the experimental inaccuracy becomes important, like for the WV0Y0 case the center is displaced as shown in Fig 5b. This inhomogeneity of the wind tunnel has to be taken into account. The presented results indicate that the WV0Y0 cases of Fig 16 are affected by the drift of the wake to the left even for this symmetric case. Averaging over different y-positions could scope with this insufficiency of the wind tunnel.
The whole discussion of AP has to be revised, this is not acceptable. I also fear that the veer structure of the gird will have an effect of AP as the locations of the wakes seem to be impacted by these - see for example Fig 7c.
Fig 17 rearrange the plots. Up to here, it was always started with no veer - quite often vertical direction are the veer cases and horizontal the yaw cases - work out one scheme used in the whole paper consistently. As stated above an integration over the cases of Fig 17 are interesting and should be worked out.
Citation: https://doi.org/10.5194/wes-2025-185-RC2 -
RC3: 'Comment on wes-2025-185', Anonymous Referee #3, 11 Dec 2025
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The article subject is significant to wind energy and wake dynamics. The results are interesting and worthy of publication. Comments primarily call for extended clarity and accuracy, especially in terms of experimental methods and flow characterization.
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The authors present an experimental wind-tunnel study on the wake behaviour of a statically yawed porous disc subjected to veered inflow. Stereoscopic particle image velocimetry is used to investigate the spatial evolution of the wake across different planes and streamwise distances, including the available power, momentum budgets, and vorticity fields.
I find the manuscript very well written, with a sound analysis of wind-energy flows based on a state-of-the-art facility and experimental technique. I therefore consider the manuscript suitable for publication, provided that the authors address the following minor remarks:
-I did not find the distance between the porous disc and the grids, although it is mentioned that the disc is placed quite close to them. As the flow near the grid is not fully developed, what may generate spurious anisotropy and turbulence production effects, could the authors comment further on the flow properties at the disc position? This is partially discussed in Section 2.6, but such near-field effects may affect the reproducibility and applicability of the results.
-The authors discuss the PIV spatial resolution (line 190), but it is not clear to me what the final resolution of the fields is, including the overlap for the smallest interrogation windows. In addition, did the authors verify that 100 vector fields are sufficient for convergence? Some terms in the budgets from equations 6 and 7 may require larger datasets to converge properly.
-In Figure 5a and others, local velocities appear to exceed the inflow velocity. Is this correct, or an artefact of the colormap? If such higher velocities are indeed observed, this may imply blockage effects caused by the proximity of the plates to the tunnel exit.
-In Bastankhah et al., JFM 2020 (already discussed by the authors), a model is presented to describe the displacement of the centroid of a wake behind a yawed wind turbine. Even though only three streamwise distances are available for the yaw-only case, did the authors consider verifying whether their results are consistent with this model?
-While the introduction is clear and well written, there appear to be issues with the use of textual and parenthetical citations. Moreover, the literature review is extensive and precise. Still—this is only a suggestion—the authors may wish to mention that another avenue currently under development concerns the use of active grids to generate veered inflows.
-Despite the authors’ efforts, Figure 2 remains difficult to read. Is it possible to edit the background of the room to remove spurious objects?