the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Jun 2026
Diapycnal Mixing in Submesoscale Permitting Simulations of the Deep Brazil Basin
Abstract. Modeling diapycnal mixing in the deep-ocean is challenging, particularly in regions with complex topography. Here we diagnose the relative roles of sub-inertial motions and tidal forcing focusing on the deep Brazil Basin in four simulations using a hydrostatic, high-resolution regional model (CROCO), at 1 km and 3 km horizontal resolution, in presence or absence of tides. Tracer particles are released at multiple depths to investigate the variability of modeled mixing estimates. In the model, horizontal resolution exerts the primary control on diapycnal mixing, while tidal forcing plays a secondary and resolution-dependent role. Increasing resolution significantly increases number and intensity of eddies and enhances diapycnal mixing across the water column. The comparison with the in-situ observations indicates that the simulated diffusivities near the bottom boundary layer are comparable in value to observational estimates. However, diffusivities in the stratified interior are overestimated due to bathymetric smoothing, which causes an underestimation of high-mode internal tides and allows eddy-driven motions to dominate.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-2869', Anonymous Referee #1, 07 Jul 2026
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AC1: 'Reply on RC1', Yonglin Huang, 25 Aug 2026
We thank the reviewer for the positive assessment and helpful comments. We have reviewed the manuscript and revised the manuscript accordingly.
Comment 1. l.102 depth / Fig. 1a:
Response: Figure 1a shows the water depth of the Brazil Basin study region. The seafloor depth over the ridge region is approximately 3000 - 4500 m, while the adjacent off-ridge abyssal plain has a mean depth of approximately 5500 m. We will revise Fig 1 and show model bathymetry more explicitly.Comment 2. BTC/BCC at 4000 m and other depths
Response: BTC (energy transfer for KE between the eddy field and mean flow) is consistently about one order of magnitude larger than BCC (energy transfer for APE between eddy and mean flow). We extended the BTC and BCC calculations to additional depths (3000 m and 5000 m) in the deep water column. We find that the relative magnitudes of the two conversion terms remain similar to those at 4000 m.Comment 3. Missing units
Response: We thank the reviewer for pointing this out. We have carefully checked all figures, colorbars, and captions. Missing units will be added where appropriate, and the figure captions will be revised for consistency.Citation: https://doi.org/10.5194/egusphere-2026-2869-AC1
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AC1: 'Reply on RC1', Yonglin Huang, 25 Aug 2026
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RC2: 'Comment on egusphere-2026-2869', Anonymous Referee #2, 17 Jul 2026
The authors compare several high-resolution model simulations, with and without tides, to understand how diapycnal mixing changes between those simulations. This manuscript is very well written, with nice figures, but I'm struggling to get excited since this is just a comparison between very similar simulations and I'm not quite sure what to learn from this.
- Why 1km vs 3km? Both are submesoscale permitting; what about including e.g. a coarser eddying simulaton to see what actually changes when we allow for submesoscale, or a very high-resolution simulation to see if diffusivities actually converge?
- There's a lot of talk in the paper about bathymetric smoothing; why not run a simulation with more/less smoothing to actually show the difference? Theoretical arguments are one thing, but simulations to back up these arguments would be very useful.
- What would the authors expect if these simulations were non-hydrostatic?
The authors put so much effort into writing a nice manuscript but could have done so much more to produce exciting research with very little extra effort. At an absolute minimum I think the authors will have to explain why they ended up with the model resolution they chose. In addition, the authors definitely need to tone down their comments of the role of bathymetric smoothing or provide numerical evidence by running further simulations.
Citation: https://doi.org/10.5194/egusphere-2026-2869-RC2 -
AC2: 'Reply on RC2', Yonglin Huang, 25 Aug 2026
We thank the reviewer for these thoughtful comments, which helped us clarify the central message and strengthen the physical framework of the manuscript. We appreciate the concern regarding the broader significance of the comparison and we have carefully revised the manuscript accordingly.
Comment 1. Choice of resolution
Response: We thank the reviewer for this comment. Based on the scale and effective resolution of the represented bathymetry, we view the 1 km and 3 km configurations as distinct dynamical regimes in the Brazil Basin. The 3 km simulations could only marginally permit some smaller-scale motions with an effect resolution of approximately 7.5 km, while the GIGATL1 runs are indeed submesoscale-permitting in the Brazil Basin.
Nevertheless, we understand the reviewer’s broader concern. To address this point, we have extended the analysis to include a 6 km horizontal resolution case, GIGATL6T, including tides. Also, for this case we performed the corresponding Lagrangian particle experiment. The 6 km case provides a coarser comparison and shows the expected progression with resolution: coherent deep eddies are largely absent, and bathymetric smoothing prevents the formation of a bottom boundary layer where mixing increases because of energy conversion when the currents interact with the topography. As a result, the diagnosed diapycnal diffusivity is lower than in the 3 km and 1 km simulations and nearly constant throughout the water column. We will add and discuss this case as integral to the revised manuscript (Supplement Fig.1).
Performing an even higher resolution run (which would require a nonhydrostatic configuration) is beyond the scope of the current work, which aims at quantifying with a very specific example why simply increasing model resolution to km scale and/or developing AI-based parameterizations from submesoscale permitting simulations may not reduce (global) ocean models structural uncertainty.
Comment 2. Bathymetric smoothing
Response:
We thank the reviewer for this comment. We agree that a direct numerical sensitivity test would provide a stronger assessment of the role of bathymetric smoothing. We are currently running a 1 km test simulation with downscaled 3km bathymetry which will be added when ready. Unfortunately, through the summer semester our supercomputer was under maintenance for a prolonged time, and the simulation is not yet completed.
This comment, though, prompted us also to revisit the physical framework underlying this part of the manuscript. Energy stored in the mean flow can be transferred to the eddy field through barotropic and baroclinic instabilities, while eddy–internal-wave interactions can provide a sink of eddy energy and a source of internal-wave energy. Polzin (2010) showed that internal waves propagating through a three-dimensional mesoscale strain field can exchange energy with the eddies through correlations between wave stresses and the mesoscale rate of strain. Both oscillatory tidal flows and slowly varying geostrophic currents interacting with rough bathymetry can radiate internal waves and exert topographic form drag (Bell, 1975; Nikurashin and Ferrari, 2010). Then nonlinear transfers toward smaller vertical scales enhance shear and ultimately support wave breaking and turbulent dissipation.
The geostrophic mean flow in the simulations is broadly consistent across the runs (very similar between GIGATL1, 3 and 6, and from a very preliminary analysis in agreement with ARGO-derived estimated), suggesting that strong eddy fields in the simulations are not primarily associated with a bias in the mean-flow reservoir. In contrast, GIGATL1T exhibits substantially larger EKE and shear than GIGATL3T. The diagnosed horizontal energy conversion from the eddy field to the internal-wave field and the internal-wave energy also increase in GIGATL1T, consistent with the enhanced interaction between the eddy field and the higher-resolution topography. However, the enhancement in internal wave energy in GIGATL1T is much smaller than the increase in EKE. This supports our interpretation that, although the higher topography resolution in GIGATL1 allows more energy transfer from the eddy field to the internal-wave field relative to GIGATL3, internal-wave generation remains strongly limited even at 1 km resolution. As a result, the internal-wave pathway cannot provide a sufficiently efficient sink, especially for the enhanced eddy energy in GIGATL1.
3000–5000 m mean
GIGATL1T
GIGATL3T
GIGATL6T
Unit
Eddy Strain RMS
1.1175e-05
2.3041e-06
1.1341e-06
s⁻¹
Eddy Kinetic Energy
2.8746e-03
3.0936e-04
1.6540e-04
m2 s⁻2
Internal Wave Kinetic Energy
6.3305e-04
4.8929e-04
4.3792e-04
m2 s⁻2
Eddy → Internal Wave energy conversion
1.0512e-10
4.9923e-12
1.1227e-15
W kg⁻¹
Table. Eddy deformation and diagnosed horizontal energy conversion to the internal-wave field in GIGATL1T and GIGATL3T, averaged over 3000–5000 m in the subregion (17-20°W, 20-22°S)
We have also considered tempering our statements and strengthening the theoretical framework of the manuscript by diagnosing energy transfer and the physical mechanisms in Section 4 and 5.
Comment 3. What would happen in non-hydrostatic simulations?
At the resolution considered, we would not expect the hydrostatic approximation alone to qualitatively change the large-scale conclusions of this study. The dominant eddies analyzed here have horizontal scales much larger than their vertical scales, so their dynamics are expected to remain largely hydrostatic. Nonhydrostatic effects would be most relevant for localized near-bottom processes, which occur at scales that are only marginally resolved, or unresolved, in the present configurations, and are further limited by the bathymetric smoothing required by the terrain-following grid. Thus, nonhydrostatic simulations would be valuable for future process studies, but we do not expect nonhydrostatic dynamics alone to change the results too much at the present resolutions. We will add this consideration to our revised discussion.
Reference:
Polzin, K. L. (2010). Mesoscale eddy–internal wave coupling. Part II: Energetics and results from PolyMode. Journal of Physical Oceanography, 40(4), 789–801. https://doi.org/10.1175/2009JPO4039.1
Bell, T. H., Jr. (1975). Topographically generated internal waves in the open ocean. Journal of Geophysical Research, 80(3), 320–327. https://doi.org/10.1029/JC080i003p00320
Nikurashin, M., & Ferrari, R. (2010). Radiation and dissipation of internal waves generated by geostrophic motions impinging on small-scale topography: Theory. Journal of Physical Oceanography, 40(5), 1055–1074. https://doi.org/10.1175/2009JPO4199.1
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AC2: 'Reply on RC2', Yonglin Huang, 25 Aug 2026
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The manuscript investigates diapycnal mixing in the deep Brasil basin using hydrostatic model simulations. The analysis compares runs at different resolutions, with or without tidal forcing. The authors estimate a variety of metrics to discuss the role of mixing and diffusivity terms at the bottom boundary layer and in the water column interior. As a whole, the manuscript reads very well and I have just a few comments. Therefore, I would suggest minor revision.
Minor comments:
l.102: what is average depth of the seafloor on and off the ridge? Is fig1a bathymetry?
l.145: are the BTC and BCC components at 4000m depth balanced in magnitude? How would they compare at other depths?
Please double check figures, in some instances the units are missing on colorbars or in the captions