|Review of "The aerodynamics of the curled wake: A simplified model in view of flow control"|
I have joined the review process from this round, so my comments will be based on the latest version of the manuscript as well as previous reviewers’ comments. In this manuscript, a model based on linearized form of Navier-Stokes equations is developed that can capture and predict the curled wakes of yawed turbines. The paper is overall clear, well written, and it contains results that are indeed interesting and useful for the wind energy community, especially for those interested in yaw angle control. I especially appreciate the part where model advantages as well as its limitations are clearly presented. However, I have some major concerns over the way results are presented in this manuscript. I therefore believe the paper will merit publication in the wind energy science (WES), provided the authors can address my comments:
• It is useful that the model results are compared with those of the Gaussian model. However, the paper still suffers from the lack of quantitative comparison with the more conceptually similar model proposed by Shapiro et al. (2018). In my opinion, it is quite important to explicitly clarify the difference of the present work with the mentioned study in terms of model derivation, and then also add predictions of Shapiro et al. model to Figs. 8 and 9. I believe this comparison can be informative and useful for readers.
• Eq. 4: u’*du’/dx is neglected although it is later considered in Eq. 16.
• Figure 6: I understand that incoming turbulence is not directly used in the proposed model, but I think it is of interest to report the vertical profile of turbulence intensity, or at least please report the value of the streamwise turbulence intensity at hub height.
• Page 14, line 10: “It is interesting to note that both models under-predict the displacement in the far wake compared to the LES”. I found the previous sentence in contrast to what is reported in the Figure 8 for the Gaussian model predictions at x=8D.
• Figure 10: For the downwind turbine, which initial conditions are used for V and W? If, as mentioned in the introduction, each turbine is treated individually, and turbine wakes are added later using the sum of squares, I cannot understand how the curl of the first turbine can affect the wake of the second turbine.
• Figure 8: I found the near-wake deflection predicted by the Gaussian model much bigger than what I expect. For instance, the wake center deflection at x/D=3 seems to be less than 0.2D in model predictions reported by Bastankhah and Porte-Agel (2016) (See Fig. 21 in the original paper), whereas it is more than 0.5D in figure 8 of the current paper. Please report input parameters such as the wake growth rate, etc. and insure that the model is implemented properly.
• Introduction: I think “controls community” should be replaced by “control’s community”.
• Eq. 1: I suppose u, v and w are time-averaged velocity components as the effective viscosity is used. Please mention if that is the case.
• Page 3, Line 3: Please explain here what U, V, W and u,v,w mean physically so that it is easier for readers to understand the assumptions made in the following.
• Eq 9: If I understood well, z_i should be the location of i-th vortice with respect to the rotor coordinate system as opposed to z_i defined in Eq. 7 as the one with respect to each vortex position. Please clarify this.
• Figs. 4 and 5: Please change the color for LES results as they can be hardly seen in a printed version. Add “axial” before “velocity” in the figure captions.
• Page 11, line 1: Add “line” after “vertical”.
• Page 11, line 3: Replace “capture” with “captured”.