the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Jun 2026
Wave-phase-aware model implementation in WRF-LES v3.8.1 for turbulence-resolving simulations of turbulent flow over monochromatic waves
Abstract. In simulations of turbulent marine atmospheric flows, wind-wave interactions are commonly represented using bulk, wave-phase-averaged parameterizations, which can introduce errors across different wave conditions due to their inability to capture phase-dependent processes. In scale-resolving large-eddy simulations (LES) or direct numerical simulations (DNS), wave-phase-resolved approaches explicitly represent wave geometry, but at a substantial computational cost. To bridge this gap, recent developments in wave-phase-aware models incorporate phase-dependent effects at reduced cost, often by leveraging canopy-stress analogies originally developed for atmospheric boundary layer flows over rough surfaces. However, differences in model implementation across numerical frameworks have hindered direct comparison of the predictions from these different wave representations in LES. In this study, we implement two wave-phase-aware models, the Wave Drag Model (WDM) and the Windward Potential Flow Model (WPM), within a unified LES framework using WRF-LES, and compare them against a wave-phase-resolved moving-wave (MOW) model under identical forcing conditions, enabling a consistent assessment of the trade-offs between computational efficiency and physical fidelity. The wave-phase-aware models reproduce mean velocity profiles with typical deviations of 𝒪(8 %–11 %), with best agreement for low steepness (ak = 0.10) across all wave ages, while discrepancies increase for steeper waves at high wave age. They capture key momentum transfer behavior, including momentum reversal from the waves to the airflow, but underestimate wave-induced velocity fluctuations by about one order of magnitude relative to the wave-phase-resolved model. The wave-phase-aware models implemented in WRF-LES v3.8.1 are made publicly available to facilitate reproducibility and broader community use.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2292', Oliver Fringer, 08 Jul 2026
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RC2: 'Comment on egusphere-2026-2292', Anonymous Referee #2, 26 Aug 2026
General Comments
In the manuscript, the authors implement in WRF and conduct an assessment of three models for representing waves in marine atmospheric boundary layer (MABL) simulations: a wave-phase-resolved model and two wave-phase-aware models (one from Princeton and one from Johns Hopkins). The implementation of these models in WRF is an invaluable contribution to the community. However, the manuscript in its current form falls somewhat short on analysis and assessment, and further efforts are required in revision, both in terms of model formulation, presentation, and simulation set-up.
Specific Comments
1. The abstract is light on drawing any conclusions regarding comparisons between the two phase-aware models. The results indicate that they are similar, and this would be an important point to note.
2. The notation in Eq. 2 is confusing with the use of overbars. In the paragraph above, the authors state that this corresponds only averaging, which is clearly not the case for the subfilter stress tensor.
3. The formulations of the models are difficult to follow due to differences in the notation. Looking at the references, the authors seem to use the notation from the original works, but it must be presented here in a consistent unified manner (e.g., relative velocity is different definitions and symbols).
4. The authors state in Sec. 2.2.2 that the wave phase is not resolved in WDM (and WPM). This is not the case. The waves are horizontally (so phase) but not vertically resolved. The nomenclature should be tightened up.
5. The mathematical notation is poor. In Eq. 19, there is a mix of tensor (LHS) and vector (RHS) notation. In Eq. 24, the RHS is nonsense with a vector velocity and a height gradient; the RHS must be a vector so a correction required. Exactly what correction is made to WDM in Eq. 24 is unclear given this vector notation inconsistency. (The alignment correction in Eq. 24 is unneeded for these 1D cases anyway...)
6. A major opportunity is missed to compare the formulations of WDM and WPM. My impression is that, beyond the drag coefficient formulation, there is difference in the dependence on flow velocity in WDM compared to a dependence of relative velocity times height gradient in WPM (difficult to tell exactly from the vector inconsistency in Eq. 24). Is this indeed the sole difference? Which is correct?
7. WDM and WPM use different formulations for the wall model. How much does this influence the results? Would WDM be improved by using the WPM wall model formulation rather than the empirical exponential damping?
8. For WDM, in the 2024 paper, the authors have an additional factor to deactivate the model when the waves are faster than the flow speed. Is this included? (This might fix the drag; see below.)
9. The comparisons between LESGO and WRF are very confusing and incomplete. WPM is implemented in LESGO, so why is this also not included in the comparisons? For WDM, since this is not the original implementation, is the comparison with LESGO really verification? Why not just compare with the results in the Aiyer paper? The verification should either be systematic and complete (all models) or removed.
10. For the comparison simulations, the number of grid points for the phase-resolved simulations is only 32 compared to 22. However, the vertical grid spacing near the wall is nearly 10x smaller! The grid in the phase-resolved simulations must be highly stretched. How so? Are the results grid independent for both phase-resolved and phase-aware?
11. The models should be run with the same time step, and the models should be run with the same wall models.
12. In the verification results in Fig. 2, why does the total stress indicate an oscillation near the surface in WRF?
13. For the verification results in Fig. 3, the only meaningful conclusion is that the values closest to the surface are roughly the same, so the model must be correct. I note that the grids near the surface are also different. Are these differences due to a model error, discretization error, etc.? I would not really call this exercise "verification"; it is really a sanity check to make sure that the implementation is more or less ok and need not appear in the manuscript without more rigor.
14. In Fig. 4, the main issue is the large negative drag predicted by WDM. Those authors already acknowledge this in the 2023 paper; the model was reformulated in the 2024 paper to deactivate when the waves are fast, which might address the large negative drag. Have the authors implemented the most recent WDM?
15. The first full paragraph on page 19 is somewhat redundant with the previous.
16. The main event of the analysis is Fig. 6. However, the commentary on the utility of the phase-aware models compared to the phase-resolved model is rather limited. Please expand to provide guidance to the community on when to use each model when. There is some of this in the conclusions but is missing from the main text.
17. The wave-induced velocities are very different quantitatively and qualitatively. I do not see how any claim could be made that they are similar. More text is devoted to trying to make this claim then to a systemic discussion of Fig. 6.
Citation: https://doi.org/10.5194/egusphere-2026-2292-RC2
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