Review report for the manuscript entitled “Modeling the effects of active wake mixing on wake behavior through large scale coherent structures” by Cheung et al. submitted to Wind Energy Science

In this work, the authors proposed an engineering wake model to consider the effects of active wake mixing strategies. The proposed model is based on the triple decomposition of instantaneous velocity into time-averaged components, wave components, and turbulent fluctuations. The time-averaged component is computed by solving the parabolic RANS equations with the turbulent fluctuations modelled using the k-epsilon model. The wave component is modelled using a simplified spatial linear stability formulation. The model predictions are compared with the large-eddy simulation results. An overall good agreement was demonstrated. It is a nice work, allowing fast estimations of different AWM strategies on accelerating the wake flow recovery. Specific comments are as follows:

1. Double check eq. (2), and equations on lines 97 and 99.
2. It is suggested to plot in figure 1: instantaneous, time-average, wave component and turbulent fluctuations.
3. Line 261: “he wave”.
4. The proposed model assumes axisymmetry. In LES the ground is included, making the comparison between the two unfair. It is suggested to run ideal LES cases under uniform inflow and with symmetry BCs on the four sides to verify the model first.
5. Discrepancies shown in figure 9 are large. Discussions are necessary.
6. There are models in the literature developed to predict coherent flow structures in wind turbine wakes (e.g., J. Fluid Mech. (2024), vol. 980, A48, doi:10.1017/jfm.2023.1097). It is suggested to review them in the introduction section.

The paper aims to develop a framework for modeling active wake farm mixing, with particular attention to the impacts of large scale coherent structures and turbulence on the mean flow. The model is interesting and provide a new way to analyze a promising approach for reducing wake effects. However, the literature review is incomplete and focuses on models not designed to capture the features of interest and other attempts to investigate coherent structures in the wakes, which actually makes the paper claims less compelling. Detailed comments regarding this point as well as other minor comments/questions follow.

The introduction and comparisons focus on the improvement of the model with respect to static wake models, which are not designed to capture dynamic behavior. There are a number of dynamic models that would serve as a better focus of both the literature review and comparisons.

Resolvant analysis has been recently applied to study wind farm wakes and it would be useful to compare this approach (or at least include it the literature review), i.e. on the top of page 3 where the authors mention that large-scale coherent structures have not been studied in this context. There have also been POD and DMD based studies of wind farm wakes that precisely aim to characterize coherent structures in wind farm wakes. DMD is in fact a dynamic approach.

The paper mentions the focus being on offshore and stable atmospheric conditions (line 70) but none of the results and model development are applicable to stable conditions. This point should be clarified, in fact I suggest removing this statement since it does not accurately reflect the paper content (which clearly states the linear stability analysis does not include key effects of a stable boundary layer line 170)

Why is RANS the best approach for this work? Many RANS closure models are known to have some limitations simultaneously capturing both the mean flow and wave behavior and it would be useful to understand how/why the configuration selected overcomes these issues and why this approach is better than the alternatives.

There are a number of grammatical issues (another careful proof reading is likely to catch these)

The coordinate frame should be specified. The authors use y and r, clearly different coordinate frames are used, so clarification would be useful.

In many shear flows, singular values (e.g. resolvant modes or POD modes) provide more accurate characterization of the behavior of coherent structures, why are eigenvalues the best approach here?