the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 09 Dec 2025
Idealized simulations of wind farm interactions with intermittent turbulence in stable boundary layer conditions
Abstract. Stable atmospheric boundary layer conditions typically correspond to low turbulence levels, but intermittent periods of elevated turbulence can occur during otherwise quiescent conditions. The interaction between intermittent turbulence and wind turbines is not well understood because of sparse observations, as well as the difficulty in realistically resolving small-scale turbulence during strongly stable conditions with numerical simulations. In this study, an explicit filtering and reconstruction approach for large-eddy simulation (LES) is used to simulate weakly and strongly stable conditions, with surface cooling rates of −0.2 and −2.0 K h−1, respectively. This approach can sustain resolved background turbulence at relatively coarse grid spacing and stronger stratification compared to conventional closures, resulting in more realistic intermittent stable boundary layer (SBL) turbulence. The idealized LES capability of the Weather Research and Forecasting model is employed with turbine rotors parameterized using generalized actuator disks to 1) determine how the presence of turbine wakes affects SBL evolution, and 2) examine the effect of intermittent turbulence on power production and wake recovery. Wakes increase mixing and therefore increase the height of the SBL, with this effect becoming more prominent as SBL strength increases. Intermittent turbulence does not have a significant impact on mean power generation and wake recovery because the relevant turbulent structures in this study only affect the bottom half of the rotor disk. Power production is, however, more variable during periods of elevated turbulence, demonstrating the impact of SBL intermittency. This study uses an idealized configuration, focusing on LES model performance and physical understanding, with the goal of informing future simulations of the conditions observed during the American Wake Experiment.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
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RC1: 'Referee Comment on wes-2025-246', Anonymous Referee #1, 02 Jan 2026
- AC1: 'Reply on RC1', Adam Wise, 15 Mar 2026
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RC2: 'Comment on wes-2025-246', Anonymous Referee #2, 04 Jan 2026
The authors investigate the interaction between wind farms and intermittency in the stable atmospheric boundary layer under weakly and strongly stable conditions, corresponding to weak and strong surface cooling rates. Two turbulence modeling approaches, the dynamic reconstruction model and the TKE-1.5 closure, are first compared. The dynamic reconstruction model is ultimately selected due to its better computational efficiency and its ability to capture backscatter, i.e., energy transfer from small to large scales. Intermittency is defined following the methodology of Coulter and Doran (2002), based on the sorted cumulative probability distribution of TKE (in this manuscript). Although the overall results suggest that intermittency has a little impact on mean wind-farm power production (primarily increasing power variability rather than the mean) this study provides a useful numerical framework for future investigations into the interaction between wind-farm performance and different intermittency mechanisms in turbulent flows.
The manuscript is generally well written, however, several critical issues arise concerning the treatment and interpretation of backscatter.
(1) In Figure 5, the total mean does not appear to equal the probability-weighted sum of the conditional means. For example, panel (a) at z=50 m is incorrect, whereas panel (c) at z = 80 m is correct...
(2) Also in figure 5, why conditioning on forward cascade is less smooth than conditioning on backscatter. I would expect the opposite due to much more samples for forward events. Any convergence study?
(3) It would be valuable/interesting to extend the discussion to the wind-farm region itself, including conditional statistics based on forward cascade and backscatter events in the presence of wind turbines.
Additional comments and suggestions are provided in the annotated PDF. Subject to satisfactory clarification and resolution of the issues outlined above, the manuscript could be recommended for publication.
- AC2: 'Reply on RC2', Adam Wise, 15 Mar 2026
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- 1
This work conveys a first attempt at investigating the effect of turbulence intermittency induced by stably-stratified conditions, on atmosphere-windfarm interaction. This involves exploiting an implementation of the DRM model from Katipodes-Chow(2005), permitting the 'backscatter' of turbulence from subgrid scales to larger resolved (though filtered) scales in LES.
[WRF-]LES is run for two cases roughly corresponding to the AWAKEN (CASES99?) campaign, though some details are lacking; it would be difficult for a reader to verify or repeat the study, as things like the explicit filter form are missing. Clarity and references are also lacking in some places, as noted further below.
Idealized simulations for two stable regimes, with a very shallow (rare) SBL having z_i=100m and LLJ below hub height (<80m) in the strongly-stable case, are conducted to study the impact of intermittency. The shallow inversion may be seen to dominate the heat flux, causing 6 times the surface value at z=z_hub; this could use some justification (e.g., many turbines nowadays are taller and larger, approaching or exceeding the inversion height, compared to the one used in the LES here), and\or be more clearly mentioned in the discussion\conclusion (also referring to literature finding such).
Some nice statistics and visualizations of stably-stratified intermittency are shown for the two cases, including compelling evidence of the DRM-enabled backscatter (up-scale transfer of TKE) in Fig.4.
The abstract (and conclusions) should more clearly mention the context, that two flow regimes are prescribed: the more stable case being a rare one where the ABL depth is lower than the upper rotor tip, and associated jet being centered near\below hub height; and a weaker stable case with more commonly-found ABL depth. These 2 ideal cases logically exhibit two different sets of behavior, though all of this depends to some extent on the strength of prescribed free-stream temperature gradient (inversion strength, where there isn't really an inversion).
The intermittency is not found to affect power production, but rather production variability (it could be nice to see what happens in a typical 10-minute period instead of 1 hour).
This reviewer suggests revision, towards publication.
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I attach an annotated PDF that has many small corrections, along with detailed comments; the present text feedback gives the general overview.
The introduction is relatively solid, though there are a number of points where references are needed. This is also the case for section 2.1.
Section 2.2 on the DRM model appears to have (or at least cause) some confusion around how the filtering works; some clarification could help, especially since the referenced Chow et al.(2005) paper itself lacks details and points to previous papers by Xue and Chow for the notation.
One question which arises in eq.(1), for the explicitly filtered Navier-Stokes equations on the LES grid, is the non-commutativity of the discretization and filtering operators which arises for the body force term (see e.g. Finnigan et al papers on this) representing the actuator disks. Or, some mention should be made of how\why the explicit ("smooth") filtering is not applied to the final terms in eq.(1). Also, why does the resolved stress divergence term have an extra discretization operator applied (perhaps Bardina et al show this)?
What is the actual explicit spatial filter applied, in the horizontal and vertical directions?
The near-wall stress-correction of Brown et al, 20001 (similar to Moeng's) is used, but a "canopy" is mentioned with regard to setting the correction's vertical decay rate via shape parameter and cutoff-scale H_c, lacking some explanation (or removal of 'canopy'). Also in eq.(6) should the square not be on "cos"?
In §2.4, with the periodic domains, it appears that a WRF domain (and really WRF) is not used, rather a nested LES domain; this should be clarified.
The choice of d𝜃/dz=4K/km is a reasonable moderate value (see e.g. Kelly\Cersosimo\Berg2019), but the ABL depth prescribed via inversion height of 100m is quite rare. The latter should be mentioned, beyond "follows common approaches for...idealized SBL's". I.e., with such a choice you are testing cases where downward entrainment into the simulated windfarm will be quite significant.
Your chosen values of z_i and the inversion strength will dictate the strength of the jet (Pedersen et al.,2014) and downward heatflux (Kelly\Cersosimo\Berg,2019). Recall the inversion strength is simply the Brunt-Vaisala frequency corresponding to your 0.004K/m and your 𝜃~=300K there.
Note that you are using 13 hours of LES "spin-up" time, which might be ok; this needs to be checked, not just justified as "commonly done" as written (e.g. see Pedersen et al, 2014 on LES spinup of inversion-capped ABL).
In §3.2 mean stability values are calculated inconsistently; one must calculate the mean of 1/L, not L (nor the individual variables within it, due to their skewed distributions), as shown in Kelly&Gryning(2010).
The surface heat flux for the strongly stable regime could be compared to CASES-99 or AWAKEN values, for the reader \ connection to "real world".
Fig.6 is very nice, though the colors of the lines in plots (a) and (c) are quite similar; they should be made more dissimilar, and use different line styles as suggested by the WES journal.
Some mention of the lack (or narrowness) of the inertial range seen in the spectral plots should be made, as it implies a small Re without discussing the explicit filtering; perhaps the 5/3 line could be shifted to better compare against the z=50 spectrum, and the lack of inertial range at higher z discussed.
While shallower ABLs and the corresponding inversion-associated jets are often connected to more stable surface-layer conditions, note that you prescribed its strength and height via setting of the capping temperature inversion magnitude (inlet temperature profile) along with surface cooling rate, roughness, and G; one can reference Wyngaard's (2010) textbook, while on the LES side one has e.g. Pedersen et al (2014) and articles by Lanzilao and others.