Publisher’s note: this comment was edited on 2 July 2025. The following text is not identical to the original comment, but the adjustments were minor without effect on the scientific meaning.

Review of the manuscript “Coriolis Recovery of Wind Farm Wakes” by Ronald B. Smith and Brian J. Gribben

In the manuscript “Coriolis Recovery of Wind Farm Wakes” the authors present a linearized two-layer model of the effects of the Coriolis force on wind farm wake recovery.

General remarks

Wind turbine and wind farm wakes have been studied extensively using numerical models, both engineering models (e.g., Calaf et al. 2010, Porte-Agen et al. 2020) and numerical weather prediction models (Aitken et al 2014, Rosencrans et al. 2024). The authors developed a linearized two-layer for wind farm wake recovery. The model accounts for the wake recovery by the Coriolis force. While recent work by Heck and Howland 2025 showed that the Coriolis force can play some role in the wind turbine wake recovery that effect is relatively small. Considering the length scale of (in particular) offshore wind farms it can be expect that the Coriolis effect on wind farm wake recovery is larger. However, the study presented in the manuscript does not provide a convincing argument for this hypothesis.

While the authors presented an elegant mathematical model that, for the most part, can be treated analytically, there are several assumptions that are not well articulated. First, the linearization used in the derivation does not properly account for the effects of atmospheric boundary layer (ABL) stability. Not accounting properly for the ABL stability effects likely exaggerates the impact of Coriolis force on the wake recover.  Furthermore, specific application, wind farm wakes, imposes certain constraints on the problem that are not addressed in the manuscript. For example, wind turbine and wind farm wake recovery under convective atmospheric conditions is significantly faster due to energetic convective eddies, i.e. requires shorter distance from a wind turbine or a wind farm than under stably stratified conditions. The effect of Coriolis force and associated wind veering in a convective atmospheric boundary layer (ABL) are negligible and therefore the approach presented in the manuscript is likely not applicable to such cases, however, this was not considered since ABL turbulence was neglected. Furthermore, wind turbine and wind farm wakes depend also on wind speed. Under weak winds wind turbines either do not operate or generate relatively weak wakes. This means that the impact of wind farm wakes is most significant under near neutral to weakly stably stratified conditions. This is also ignored in the manuscript. The authors treat stratification through reduced gravity, giving values between 0.1 and 10, while never providing a definition of the reduced gravity. If we assume that the reduced gravity is commonly defined as: g’ = g \delta \theta / \theta_0 (e.g., Jiang, 2014, JAS), where \theta_0 is ~300, and \delta \theta potential temperature difference between the surface and the top of the boundary layer, then a reasonable value of the reduced gravity for conditions relevant for an operating wind farm is between 0 (neutral stratification) and 0.03 (weakly to moderately stable). Notice that the reduced gravity of 0.1 would mean that the potential temperature difference between the surface and the top of the boundary layer is 30 K. Such strong stability of an atmospheric boundary layer is achievable when the winds and therefore shear are weak. Under such conditions wind turbines do not generate power and therefore there are no wakes. Finally, the treatment of turbulence mixing induced by the presence of a wind farm is very simplistic and does not account for the stronger mixing and momentum entrainment induced by the shear at the top of the wake.

Taking all the above into account I do not recommend the manuscript for publication in the present form. The authors should attempt to put their work in proper context of a realistic conditions under which a wind farm operates. An analysis unconstrained by realistic conditions yields unrealistic results and leads to false conclusions.

Specific remark

• Line 109 – It is stated that “The vertical mixing process is difficult to model.” This statement should be qualified – it is difficult to model in simple models like the one presented in the manuscript.
• Line 110 – Two occurrences of the word “may” should be omitted and/or replaced with “is.”
• Line 112 – It is not clear why is Barstad (2016) cited here when the concpets are fundamental textbook concepts.
• Equation (9) – The second term on the left-hand-side should be FRR not FRC.
• Line 177 – “Understanding infinitely wide windfarms” is of no real value, since such a wind farm is unrealistic.
• Line 274 – Periodic solutions always wrap around from the exit to the entrace of the domain – the question is how the outflow impacts the inflow and the part of the domain that is of specific interest.
• Line 301 – Instead of “warm” it should be “farm.”
• Table 2 – Instead of “Inversion strength” better would be “reduced gravity.”
• Table 3 – The values of “reduced gravity” are not relevant for an operating wind farm, a more realistic values should be chosen.
• Equations (42) and (43) – instead of “Deficit(y)” a symbol representing deficit should be defined and used.
• Line 489 – However, the model does not include ABL turbulence and its effects, e.g., under convective conditions. This is a serious omission.
• Line 516 – Symbol “H” should be defined before it is used.
• Table 4 – It is not clear why would a reduced gravity value be dependent on the fram size (FS). In particular, the value of 0.1721 is likely unrealistically large for an operating wind farm.
• Line 540 – It is not clear what is meant by “low wind,” turbines do not operate below 3 m/s.