the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Nov 2025
Analytical yaw models: a two-dimensional comparison
Abstract. Analytical wake models are essential for wind farm design and control. However, they often lack validation beyond scale data. This study compares six, two-dimensional yawed wake models which include single-Gaussian, super-Gaussian, lifting line, and vortex sheet methods. An additional double-Gaussian model is also proposed. All models are calibrated and tested against three datasets: near-wake and far-wake PIV measurements, as well as full-scale turbine data. The proposed double-Gaussian model achieves the lowest mean absolute error (2.6 %) across all datasets. However, all models struggle to predict the full-scale dataset under yawed conditions, emphasising the necessity for validating models against a wide range of turbine operating conditions.
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Status: final response (author comments only)
- RC1: 'Comment on wes-2025-218', Anonymous Referee #1, 30 Nov 2025
- RC2: 'Comment on wes-2025-218', Anonymous Referee #2, 05 Dec 2025
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General comments:
The paper compares six analytical wake models with three different experimental datasets
The model comparisons are first tuned and then compared for a non-yawed turbine wake and thereafter compared for several yawed wake configurations.
The work includes a novel experimental dataset (near wake model scale) and two existing datasets from other publications. Furthermore, the work proposes a new wake model with yaw-capabilities. From the model description it seems that the new model mainly combines the wake deflection sub-model by Bastankhah and Porte-Agel (2016) and the double Gaussian deficit model by Keane (2021). The model description should be clearer about which equations were adapted from these models, and which are new additions.
The paper is well-organized, features concise language, and is very interesting to read. It features a detailed analysis of the modeled mean velocity deficits and a quantification of the mean absolute error for the different wake configurations.
The paper addresses the scientifically relevant topic of improved analytical wake modelling for non-yawed and yawed cases, while specifically the near-wake modelling and the full-scale applicability are highlighted as novel contributions. Full-scale wake flow validations are indeed considered essential, and the authors emphasize the need for validating yawed wake models for further full-scale cases. The need for accurate modelling of the near-wake could be justified more, as it is not completely clear how wind farm models would benefit from improved near- wake modeling. The importance of accurate near-wake models for wind farm simulations should be motivated in more detail.
Major comments:
(1) Reproducibility of the wake data comparison / Missing information on input data
A quantitative model comparison of models with tunable input parameters is always somehow “tricky”. Dependent on the model tuning the difference to the measured reference data can be actively influenced. Here, the authors present a consistent way of model tuning by minimizing the absolute mean error of every model to the measured reference data. However, it is not transparent to which values the tunable parameters of each model have been set. For reproducibility of the presented results, the values of these parameters is required. I would suggest including an additional table:
Futhermore, an overview of the main parameters of the three reference datasets is missing. Most of this information can be found in the cited original papers, while information about the turbine thrust coefficient CT is missing completely. Especially turbine’s CT and the turbulence intensity in the inflow are regarded as crucial input parameters to the models. It would be interesting to see how similar/different they are for the three reference datasets.
Futhermore, an overview of the main parameters of the three reference datasets is missing. Most of this information can be found in the cited original papers, while information about the turbine thrust coefficient CT is missing completely. Especially turbine’s CT and the turbulence intensity in the inflow are regarded as crucial input parameters to the models. It would be interesting to see how similar/different they are for the three reference datasets.
(2) Experimental details/limitations
There are some important details about the wind turbine experiment missing in the paper:
(a) First of all, what was the measured thrust coefficient CT at the design tip speed ratio? This crucial input parameter for the wake models is not mentioned anywhere.
(b) Secondly, were power and thrust of the turbine measured for different tip speed ratios, i.e. CP-λ and CT-λ curves? Did the power peak for the tip speed ratio it was designed for? (λ = 5.7)?
(c) What was the chord-based Reynolds number for your turbine at the inflow wind speed of U∞ = 7.8 m/s? From the information given in Table A1, the chord-based Reynolds number should be around Rec,root = 26000 at the innermost blade element and Rec,tip = 74000 at the blade tip. According to Giguere and Selig (1998), the airfoil was designed for Rec = 250 000, while the lowest Reynolds number the polars were measured for was Rec = 100 000. A Reynolds-number independent performance of the turbine should be shown for these low Re-numbers (i.e. by Reynolds-number independent CP-λ curves measured at different inflow speeds) or the mismatch at least discussed.
(d) What was the wind tunnel blockage ratio in your experiment? It seems to be low enough, but could the wake deflection be influenced by the side walls of the wind tunnel? At least a basic discussion of this should be included in the description of the experimental setup.
(e) The measured near-wake distances at x/D=2.7 +- 0.6 are very similar. If near-wake measurements are deemed important for this model comparison, why were not measurements closer to the turbine, i.e. x/D < 2, performed? Please justify that in the paper.
(3) Discussion/conclusions on “model flexibility” vs “model complexity” of additional tuning parameters in the proposed wake model.
Also, a critical discussion about the interplay of model tuning and error reduction should be included in the paper. Section 5 closes with “the model’s flexibility resulting from having tunable parameters”. Isn’t it somehow expectable that the MAE is reduced when additional tuning parameters are introduced? How does that make the model more complex to handle on the other hand? Include some lines of discussing that.
In the abstract/conclusions it is mentioned: “The proposed double-Gaussian model achieves the lowest absolute mean error across all datasets.” This is correct but not surprising as the model has the highest number of tunable parameters. Also, the main contributor to the lowest absolute mean error across all datasets mainly stems from the near-wake results, that some of the other models are not designed for. I propose another, more realistic conclusion along the lines of “The proposed double-Gaussian model shows improved modelling of the near-wake”.
Minor comments:
(1) ΔU/U∞ axis in wake profile plots: Although the figure text describes that the distance between two vertical lines corresponds to ΔU/U∞ = 0.25 or 0.50, additional ΔU/U∞ axes on top of the profile plots would be helpful to quantify the differences in the predictions.
(2) Figures 5 and 10: Is it necessary to show all distances between x/D=4 and x/D=11 in these plots? A reduction to x/D = 4,7,9,11 (or similar) would show the same main trends and be more manageable for the reader.
(3) Analysis of both the Mean Absolute Error (MAE) and Root Mean Square Error (RMSE): It is very important to quantify the deviations of the model predictions from the measured velocity data. However, the MAE and the RMSE show the absolute same trends for all comparisons made in this article. Wouldn’t it be enough to focus on one error quantification method?
Side note: Figure 9 includes 8x2 error comparisons, which is a lot of information for little variation in the conclusions to be drawn from the error comparison. In my opinion error comparisons of three yaw angles, e.g. for gamma = 10, 20, 30 degrees, would be sufficient here.
Technical comments: