the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Nov 2025
Impact of Surface Waves on Mixing and Circulation in a Summertime Lead
Abstract. Surface waves are becoming more prevalent in the Arctic as sea ice cover reduces. Here we use 3D turbulence-resolving simulations to explore how surface waves affect upper ocean dynamics, and hence surface conditions, as they propagate along summertime leads (narrow regions of open ocean between melting sea-ice cover). We separate the ocean dynamics into turbulent motions which dominate vertical kinetic energy, and a mean cross-lead circulation which drives near-surface downwelling within the lead. Without waves, along-lead winds create weak mixing and an asymmetric circulation where a sinking plume within the lead is balanced by upwelling that extends under the ice to the right of the wind vector. The presence of waves enhances both mixing and circulation by localizing, strengthening and deepening the downwelling plume and turbulent vertical velocities, increasing vertical buoyancy fluxes, and creating an upwelling cell to the left of the wind which significantly alters surface conditions beneath the left lead edge. Waves also drive a sharp front and convection within the lead. Physically-based scalings are proposed for the mixing and circulation changes to capture the effects of various system parameters including lead width, which has a leading-order impact on both turbulence and circulation. The wave-driven changes to turbulence and circulation are present even for relatively weak (developing) waves, although the biggest changes are seen for strong (equilibrium) waves.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-4239', Anonymous Referee #1, 21 Dec 2025
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AC1: 'Reply on RC1', Ara Lee, 08 May 2026
Reviewer Comments 1
In this manuscript, the authors discuss the impact of waves on mixing in conditions representative of the sea ice, where leads are present. I think this is an interesting work that falls well within the scope of TC and that, with a few minor updates, it should be suitable for publication.
Reviewer 1, thank you for your constructive feedback. We agree that these revisions will improve the manuscript and are ready to incorporate them into our next version. We provide our response to each of your comments below.
- Ice fixed or moving? (Pumping effect)
Reviewer: One point was not completely clear for me regarding the model setup: is the ice fixed, or moving? If it is fixed, then I suppose this means that effects such as the relative motion of ice floes and the associated "pumping" effect is missing (see for example https://doi.org/10.1029/2018JC014500 , https://doi.org/10.1063/5.0088953 )? This can typically generate quite a lot of mixing / eddies in particular when the floes and openings are quite small relative to the incoming wavelength? I think this could be made clearer and discussed, including discussing both i) can some additional mechanisms be present in the real world, ii) which regimes (wavelength to lead width / floe size for example) exist for which these would play a role.
Response: The ice is fixed in these experiments, as a deliberate choice to isolate the impact of surface waves on lead dynamics due to the spatial confinement of the waves. We agree that our idealized experiments do not include several processes and forcing complexities that can be significant under some realistic scenarios, particularly relating to relative ice motion (this comment) and wave-wind-lead alignment (your later comment). While we do mention the zero ice-ocean momentum fluxes in Line 80, the previous draft did not sufficiently discuss the limitations you mentioned (it currently reads: "There are no ice-ocean momentum fluxes, equivalent to stationary ice. This is a one-way coupling, where the ice conditions are imposed on the ocean, and the ice properties do not change over time.")
We acknowledge that relative ice-ocean motion and wave-ice interactions could modulate turbulence and circulation. Thank you for pointing out these two references on wave-ice interactions. We intend to discuss both in the context of vertical jet/pumping circulation mechanisms and alterations to turbulent dissipation, although we also note that these effects are only likely to be significant for leads that are much narrower than the wavelength of surface waves. For example, in Herman (2018), the spatial scale of ice floes ranges from 5% to 50% of the surface wavelength, which in our base experiments would correspond to ice floes with scales from 3m to 30m, which is much narrower than our lead widths.
In the enhanced discussion, we will also note that Bourgault et al. (2020) conducted LES experiments without wave effects which demonstrated that opposite moving ice on either side of a lead can drive turbulence and circulation within and around the lead.
Proposed Changes in Revised Manuscript: We will expand the model description in Section 2.1 to explicitly state this assumption. Furthermore, we will add a paragraph in the Discussion/Conclusions highlighting that the relative motion of ice floes and "pumping" effects would act as an additional source of mixing in real-world scenarios, and noting the role of ice motion in cross-lead dynamics following the LES experiments of Bourgault et al. (2020).
- Role of the Coriolis force
Reviewer: It is interesting that you choose to keep the Coriolis force - given the spatial and temporal scales that are considered here, does it really play a role, or is it present just as a "carry over" from the base model used?
Response: Thank you for this question; the Coriolis force plays a significant role across the simulations presented in the manuscript, and you have highlighted that we need to better discuss the impact of the Coriolis force. All the wind and wind/wave forced simulations have significant cross-lead anisotropy, which is driven entirely by the combined effects of the Coriolis force and the directional wind and wave forcing. Cross-lead anisotropy is apparent in many of the figures demonstrated by differences between cross-lead circulation and turbulence structure on the left side of the lead vs. the right side of the lead. This anisotropy is not present in buoyancy forced simulations where the system has rotational symmetry (Figure C1; we will also make clear that this simulation has non-zero f in the text of Appendic C). Simulations with wind and waves, but no Coriolis force produce systems that are symmetric in the cross-lead direction (not shown in the manuscript). The significant effect of the Coriolis force is consistent with LES of even narrower leads in Bourgault et al (2020), with these Coriolis force effects resulting primarily from the wind stress curl in the system at the lead edges (in our experiments) or across the lead (in their experiments). We will address this in both the text and in the schematic (Figure 3) where the wind stress curl term will be multiplied by f to emphasize the role of the Coriolis force in this circulation, and to avoid misleading readers who may want to apply this to Southern hemisphere systems.
In terms of the role the Coriolis effect plays in the scaling we produce, we demonstrate in our sensitivity tests (Figure 14 and Table 3) that the Coriolis parameter affects the depth and strength of mixing and circulation within the lead, albeit to a lesser extent than some other system parameters (e.g., wave strength and lead width).
In terms of timescales, the high latitude means the Coriolis adjustment timescale is relatively fast (proportional to 1/f). In terms of spatial scales, the along-lead dimension is assumed to be infinitely long (periodic domain), while the cross-lead dimension is narrow. The long along-lead dimension allows the Coriolis force to play a meaningful role in the dynamics of the system.
Proposed Changes in Revised Manuscript: We will add text to the Results and Discussion sections explicitly discussing the active role of the Coriolis parameter (f). We will draw more attention to the sensitivity tests (Figure 14 and Table 3), highlighting how varying f significantly affects the depth, strength, and anisotropy of the cross-lead circulation.
- Wind and wave direction
Reviewer: If I understand correctly, you only look at one particular case of relative wind and wave direction - basically wind and waves propagating alongside the lead. Is this understanding correct? I think it is only named "in passing" in a sentence in 2.1. Actually, I think this is a quite "strong" / "limiting" hypothesis - I do not see a reason a priori for the wind and waves to propagate alongside the leads, and results may look quite different if wind and waves propagate for example perpendicular to the leads, or at an angle with each other. Of course, doing LES for a wide range of relative wind and waves orientation with respect to the leads may be too much work for a single paper, so it is fine to pick up a specific case as you do here - but this should be made very clear, and highlighted / discussed more in my opinion.
Response: The reviewer is right that we assume wind and waves are aligned along the lead. This idealized setup allowed us to identify the first-order impact of waves on cross-lead circulation by connecting with the open-ocean literature where wave-driven upper-ocean dynamics are heavily studied and a long fetch is assumed. It also avoids two numerical challenges of setting up LES experiments with waves propagating across the leads. First, the horizontal convergence/divergence of Stokes drift near the lead edges combined with incompressibility would require the imposition of a vertical Stokes drift component, but this vertical Stokes drift has not been studied previously. Second, cross-lead winds would create a wave field that grows across the lead width as waves are energized, and waves that propagate a significant distance under the ice. It would be difficult to define a physically realistic spatial field describing wave growth and decay across the lead and sub-ice region respectively.
Proposed Changes in Revised Manuscript: We will highlight this limitation more notably in Section 2.1. We will also add a discussion point in the Conclusions regarding the potential impacts of wind/wave angles and misalignment.
- 4. LES grid size/resolution adequacy
Reviewer: I am used to LES in aerodynamics as a way to model (without resolving them) the smallest scales (for example mm / sub-mm scales) but resolving the larger eddies. I am less familiar with LES in ocean sciences, so my understanding may be a bit off. Still, I am surprised that one can "just" pick up such a large mesh size (1x1x0.5 m3). I think you may need to discuss more why / if the LES grid size / resolution is adequate (in particular, what are the smallest scales expected, what is the LES cutoff, and is it appropriate). If I understand correctly, this should be validated by comparing the different scales in the turbulent cascades, and determining what needs to be resolved vs. what can be modeled.
Response: Our choice of resolution is aimed at resolving the turbulences of the OSBL. We conducted a domain and resolution sensitivity test in Appendix D (Lines 465-475), which showed that large-scale circulation patterns are robust across different grid setups.
Proposed Changes in Revised Manuscript: To reassure the reader early on, we will add a text to Section 2.1 clearly referencing Appendix D such as: “To ensure that our grid resolution (1 x 1 x 0.5 m^3) adequately captures the essential OSBL turbulent dynamics without excessive dampening, a domain and resolution sensitivity test was conducted (detailed in Appendix D), which confirms the robustness of the simulated large-scale circulation patterns.
- Figure 3 confusion
Reviewer: Fig. 3 may be a bit confusing - each arrow should have a clear reason for being here, at present it seems like there are "many, decorating" arrows. Consider taking an iteration through the figures to make sure all elements are necessary / meaningful / explained.
Response: We appreciate this feedback. We agree that the current schematic may be visually overwhelming.
Proposed Changes in Revised Manuscript: We will re-illustrate Figure 3. We will remove any redundant arrows and explicitly label the remaining arrows with their corresponding physical forcing terms from Equations 6 and 7 to make the physical mechanisms and balances much more intuitive. We will also add a Coriolis parameter that multiplies the wind stress term to make the role of the Coriolis effect clearer.
- Trustworthiness of results
Reviewer: If one trusts the simulations and the fact that the LES is properly applied and models an appropriate range of scales, then the results should be also trustworthy and the discussion / analysis parts which use quite standard analysis techniques, hence, should be generally robust. Therefore, I have no major comments on the results per se, and these seem anyways quite well aligned with what one would expect a priori.
Response: We thank the reviewer for their confidence in our methodology and analysis techniques.
Citation: https://doi.org/10.5194/egusphere-2025-4239-RC1
Citation: https://doi.org/10.5194/egusphere-2025-4239-AC1
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AC1: 'Reply on RC1', Ara Lee, 08 May 2026
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RC2: 'Comment on egusphere-2025-4239', Anonymous Referee #2, 07 Apr 2026
Review of "Impact of Surface Waves on Mixing and Circulation in a Summertime Lead"
The paper presents an idealised numerical model study of the impact of waves on the mixing and circulation in leads. The topic is an important one, and one that is well suited to the audience of The Cryosphere. The paper is well written and well presented. It is interesting and potentially important that the waves are able to modify the circulation in the leads quite profoundly. A question that I find hard to answer from this study, though, is to what extent we can efficiently parameterise the effect of waves on the melting of summer ice. The authors briefly mention this, but provide no real way forward to a parameterisation which could be of use for forecast systems and climate models. It would be very useful if the authors would expand the discussion to at least point toward how such parameterisations could be implemented with a spectral wave model coupled to an ice-ocean model.Minor comments:
L 35: "climates" is poor EnglishL 60: Please explain that the density $\rho$ is absorbed into $p$ here and in the following
Fig 4: Panels (e) and (f) are mentioned in the caption but appear to be missing from the figure.F
ig 5: Units of panels (c) and (f) should be m/s. Please explain.
Fig 11: Ditto for panels g-l. I believe you mean $\langle w'b' \rangle$ under the colour bar.
Citation: https://doi.org/10.5194/egusphere-2025-4239-RC2 -
AC2: 'Reply on RC2', Ara Lee, 08 May 2026
Reviewer Comments 2
We would like to thank Reviewer 2 for their encouraging words and for recognizing the importance of this topic. We greatly appreciate the suggestion to provide a clearer pathway toward parameterization, as well as the attention to detail in the minor comments.
1. Major Comment
Reviewer: The paper presents an idealised numerical model study of the impact of waves on the mixing and circulation in leads. The topic is an important one, and one that is well suited to the audience of The Cryosphere. The paper is well written and well presented. It is interesting and potentially important that the waves are able to modify the circulation in the leads quite profoundly. A question that I find hard to answer from this study, though, is to what extent we can efficiently parameterise the effect of waves on the melting of summer ice. The authors briefly mention this, but provide no real way forward to a parameterisation which could be of use for forecast systems and climate models. It would be very useful if the authors would expand the discussion to at least point toward how such parameterisations could be implemented with a spectral wave model coupled to an ice-ocean model.
Response: Thank you for pointing this out. We agree that our manuscript would be improved by better linking our results to potential parameterization development (and hence model improvement). Despite our study being focused on a mechanistic understanding of this type of system, potential parameterization linkages helped direct our study (including the properties we targeted for scaling development) but we did not make that clear.
Proposed Changes in Revised Manuscript: We will add a sub-section to the Discussion detailing the conceptual framework outlined above. This section will explicitly make a link between our scalings and plume-based parameterizations and discuss the transition from monochromatic to spectral wave applications in coupled models. We outline some new discussion points below.Information from the manuscript, particularly the proposed scalings for vertical turbulent kinetic energy (VKE) and circulation downwelling maxima averaged across the lead (W-down), could be used to augment various upper-ocean mixing parameterizations with varying degrees of applicability and appropriateness. For example, many parameterizations assume that turbulence mixes properties down-gradient (from high to low value regions), and these schemes prescribe or prognose an eddy viscosity/diffusivity to describe the strength of turbulent mixing. Physically, the eddy viscosity/diffusivity are proportional to the VKE multiplied by a turbulence timescale, so our VKE scaling could be applied to modify the viscosity/diffusivity parameters in these types of system to account for the lead-weakened mixing.
Some schemes may be more amenable to using both the turbulence (VKE) and circulation (W-down) pieces of our scaling. For example, Garanaik et al. (2024; https://doi.org/10.1029/2023MS003846) presented an upper-ocean mixing parameterization where the flow is decomposed into downwelling and upwelling plumes, and the distinct properties of each plume are used to estimate turbulent fluxes. The scheme accurately reproduced VKE for multiple open ocean systems, and the scalings used here could be used to modulate those open-ocean VKE values to capture the VKE of lead-like systems where waves and winds only force a sub-region of the ocean. This type of scheme can also be generalized to an arbitrary number of plumes (Firl & Randall, 2015; https://doi.org/10.1175/JAS-D-14-0192.1), so it is possible that the equations could be reframed to include a “circulation-scale” plume type that downwells within the lead, and weakly upwells over a broad area under the ice, with a vertical downwelling speed estimated using the W-down scaling and the circulation W profiles shown in the manuscript. This is something we are already thinking about as part of future work.
On the topic of implementing these parameterizations when coupling a spectral wave model to ice-ocean models, this is something we expect to be a natural application of any augmented parameterization that leverages these results. Our simulations are forced by monochromatic waves rather than wave spectra, but the scaling results should be applicable to arbitrary wave fields aligned with the wind, perhaps with the caveat that delta terms in Eq. 15 would need to be adapted to represent TKE budget terms integrated across all wave numbers or decay depths of the wave spectrum. Our use of monochromatic wave forcing in the LES was driven by the difficulty of imposing complex wave spectra in numerical simulations (LES) due to the concentration of Stokes drift within the top grid cell(s) and the associated poor resolution of Stokes drift and shear associated with high frequency components of the wave spectrum.
2. Minor comments:
L 35: "climates" is poor EnglishWe will correct this to "climate" in the revised text.
L 60: Please explain that the density $\rho$ is absorbed into $p$ here and in the following
We will clarify this in the text by explicitly stating that p represents the kinematic pressure (standard pressure normalized by the reference density rho_0).
Fig 4: Panels (e) and (f) are mentioned in the caption but appear to be missing from the figure.
We apologize for this oversight. Figure 4 will be updated in the revised manuscript to include the missing panels (e) and (f), which show the cross-sections of the along-lead averaged turbulent vertical buoyancy flux.
Fig 5: Units of panels (c) and (f) should be m/s. Please explain.
Thank you for catching this typographical error. We will update the x-axis labels in panels 5(c) and 5(f) to correctly display the units as m/s.
Fig 11: Ditto for panels g-l. I believe you mean $\langle w'b' \rangle$ under the colour bar.
You are completely correct. The color bar for panels (g-l) was incorrectly labeled. We will fix the label to <w'b'> and ensure the corresponding units are correctly displayed as m^2/s^3 in the revised figure.
Citation: https://doi.org/10.5194/egusphere-2025-4239-RC2
Citation: https://doi.org/10.5194/egusphere-2025-4239-AC2
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AC2: 'Reply on RC2', Ara Lee, 08 May 2026
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- 1
In this manuscript, the authors discuss the impact of waves on mixing in conditions representative of the sea ice, where leads are present. I think this is an interesting work that falls well within the scope of TC and that, with a few minor updates, it should be suitable for publication.
- One point was not completely clear for me regarding the model setup: is the ice fixed, or moving? If it is fixed, then I suppose this means that effects such as the relative motion of ice floes and the associated "pumping" effect is missing (see for example https://doi.org/10.1029/2018JC014500 , https://doi.org/10.1063/5.0088953 )? This can typically generate quite a lot of mixing / eddies in particular when the floes and openings are quite small relative to the incoming wavelength? I think this could be made clearer and discussed, including discussing both i) can some additional mechanisms be present in the real world, ii) which regimes (wavelength to lead width / floe size for example) exist for which these would play a role.
- It is interesting that you choose to keep the Coriolis force - given the spatial and temporal scales that are considered here, does it really play a role, or is it present just as a "carry over" from the base model used?
- If I understand correctly, you only look at one particular case of relative wind and wave direction - basically wind and waves propagating alongside the lead. Is this understanding correct? I think it is only named "in passing" in a sentence in 2.1. Actually, I think this is a quite "strong" / "limiting" hypothesis - I do not see a reason a priori for the wind and waves to propagate alongside the leads, and results may look quite different if wind and waves propagate for example perpendicular to the leads, or at an angle with each other. Of course, doing LES for a wide range of relative wind and waves orientation with respect to the leads may be too much work for a single paper, so it is fine to pick up a specific case as you do here - but this should be made very clear, and highlighted / discussed more in my opinion.
- I am used to LES in aerodynamics as a way to model (without resolving them) the smallest scales (for example mm / sub-mm scales) but resolving the larger eddies. I am less familiar with LES in ocean sciences, so my understanding may be a bit off. Still, I am surprised that one can "just" pick up such a large mesh size (1x1x0.5 m3). I think you may need to discuss more why / if the LES grid size / resolution is adequate (in particular, what are the smallest scales expected, what is the LES cutoff, and is it appropriate). If I understand correctly, this should be validated by comparing the different scales in the turbulent cascades, and determining what needs to be resolved vs. what can be modeled.
- Fig. 3 may be a bit confusing - each arrow should have a clear reason for being here, at present it seems like there are "many, decorating" arrows. Consider taking an iteration through the figures to make sure all elements are necessary / meaningful / explained.
- If one trusts the simulations and the fact that the LES is properly applied and models an appropriate range of scales, then the results should be also trustworthy and the discussion / analysis parts which use quite standard analysis techniques, hence, should be generally robust. Therefore, I have no major comments on the results per se, and these seem anyways quite well aligned with what one would expect a priori.