In the ocean, diapycnal mixing governs the vertical exchange of mass, heat, salt, and tracers across density surfaces, thereby controlling ocean stratification. Through irreversible turbulent fluxes, diapycnal mixing provides also the mechanical energy dissipation required to sustain the upwelling branch of the overturning circulation . Although background mixing rates in the ocean interior are weak, observations consistently show that strongly localized enhancements near rough topography dominate the net diapycnal transport and water mass transformation . Multiple mechanisms contribute to topographically enhanced mixing, including internal hydraulic jumps , Ekman layer processes , internal wave generation and breaking , vertically sheared layered vortices , and overturning instabilities .

The efficiency of topographic mixing depends sensitively on regional circulation and bathymetric detail, and thus, in ocean models, on model resolution. While increasing computational power now permits global and basin-scale simulations at mesoscale-resolving and even submesoscale-permitting resolution, these models often produce counterintuitive diapycnal mixing relative to coarser configurations, largely because they retain vertical mixing parameterizations developed for much lower resolution systems . Here, we compare simulations spanning the range of submesoscale-permitting to mesoscale-resolving performed with a widely used ocean model to quantify how modeled diapycnal diffusivities and the underlying mixing processes depend on resolution in the Brazil Basin (BB). This region is particularly well suited for such an analysis, as it hosted the Brazil Basin Tracer Release Experiment (BBTRE), one of the first efforts to directly observe turbulent diapycnal mixing near fracture zones as part of the World Ocean Circulation Experiment. Understanding this dependence is especially important today, in light of ongoing efforts to develop the next generation of kilometer-scale climate and ocean models, whether based on explicit turbulence resolving dynamics , or emerging machine learning and AI-based parameterizations (e.g., ).

In summary, our analysis focuses on evaluating whether hydrostatic, terrain-following, mesoscale-resolving or submesoscale-permitting models realistically represent near-bottom diapycnal mixing over rough topography, and on identifying strengths and limitations across resolutions. The Brazil Basin offers a well-constrained testbed for this work due to its distinctive bathymetry and the availability of historical observations, allowing us to assess the relative roles of submesoscale circulations and tidal and wave-driven motions in shaping bottom boundary layer dynamics.

In the simulations, diapycnal mixing is modulated by the eddy field, with tides having a secondary role and not impacting the evolution of the eddy field whenever the Rossby deformation radius of the BBL is resolved (Figs. 2 and A3). However, both theory (e.g., ) and observations (e.g., ) identify internal waves generated by tide–topography interactions as an important driver of diapycnal mixing in the deep ocean in regions of steep topography. When the internal wave trajectories parallel the topographic slope, linear wave theory predicts that wave propagation would be limited, waves would break and, through this process, mixing in the BBL would be enhanced . The reason for such fundamental differences between theoretical predictions, observations and model outcomes can be understood considering how model resolution and bathymetric smoothing, which is required by models due to their discretization, affect the partition of energy among the mean flow, eddies, and internal waves.

The GIGATL6 is too coarse to represent the interactions between the steep bathymetry and the flow. As a result, eddies are very few and weak, and the internal wave field is strongly underestimated, with diapycnal mixing approximately constant across the water column, mostly controlled by the numerics.

Although the GIGATL1 and GIGATL3 simulations are at a resolution high enough to permit mesoscale and in part submesoscale dynamics, and they provide a reasonable representation of the small-scale topographic variability – GIGATL1 more so than GIGATL3 –, the topography remains too smooth to efficiently block and contract scattered internal tides, generating an intense eddy field instead.

We assess the consequences of this smoothing by considering the moments of the topographic height spectrum H(k) for GIGATL1, GIGATL3 and GIGATL6 and multibeam observations. The nth moment can be represented as 6∫0∞knH(k)dk

For abyssal hills, H(k) is commonly fractal, i.e. for high horizontal wavenumbers k, H(k)∝k-x with 2<x<3, see also Fig. 5.

Table 1 compares the moments associated with four data sets of the Brazil Basin bathymetry using a normalized spectral moment truncated at kcut: 7∫0kcutknHmb(k)dk∫0kcutknH…(k)dk

We considered multibeam data from nearby the tracer injection site in the Brazil Basin shown in Fig. 5a and the topographic height spectral density Hmb(k) shown in Fig. 5b, the SRTM_30 plus product Hsrtm(k), the GIGATL1 bathymetry H1km(k), the GIGATL3 bathymetry H3km(k) and GIGATL6 bathymetry H6km(k). The implication of our analysis is that the integral for the first moment converges, but not the second, or fourth. Linear wave kinematics prescribes a rate of energy transfer from the barotropic to baroclinic tide (generation) proportional to the first moment, while the energy density of the internal tide is proportional to the second moment and the shear variance, which relates to wave-breaking, is proportional to the fourth moment. Finescale parameterizations then connect turbulent dissipation to the square of this fourth moment. A prediction of infinite second moment implies infinite energy density, which is of course unfounded, and theoretically is avoided by using a quasi-linear model of wave generation which places the linear analysis in the advected coordinate of the barotropic tide. This effectively regularizes the integrals defining the moments (Eq. 6) by introducing an integration endpoint of approximately kcut=1/λh=σ/4U0, where kcut is set to be equal to the Nyquist wavenumber of the SRTM and model products. U0 represents the velocity amplitude of the barotropic tide and σ its frequency. λh is about 1 km in the Brazil Basin, significantly smaller than the 6–8 km distance between hill crests, and a velocity amplitude of U0 = 0.03 ms-1 maps well onto a peak in the observed near-bottom vertical wavenumber shear spectrum.

The results summarized in Table 1 imply an energy transfer from barotropic to baroclinic tides. Even in the higher resolution GIGATL1 case, there is nearly an order of magnitude difference in the second moment (energetics) and an even greater underestimation for the model fourth moment (shear variance). Our interpretation is that the smoothing of the bathymetry in the GIGATL runs, and more generally in ocean models, alters both the generation of the eddy field and the pathways through which its energy can be transferred toward smaller scales. Smoothed topography generates reliefs that retain the key features at scales larger than 3–4 km but removes small-scale roughness, allowing isopycnal spreading over the ridge and an appreciable velocity curvature Uzz. The resulting flow facilitates baroclinic and submesoscale instabilities which convert available potential energy into eddy kinetic energy, supporting the generation of strong eddies. Rough topography in the real ocean, on the other hand, provides an important pathway through which geostrophic and tidal motions can transfer energy into the internal-wave field, ultimately feeding small-scale shear and turbulent dissipation . With a smoothed topography, CROCO generates less of these waves than the real ocean, the eddy field loses a principal energy sink and the result is a more energetic flow field. Eddies persist at higher amplitude and contribute to an elevated diffusivity that extends to the ocean interior, and to an overall barotropization of the water column, as found near the surface as well . Bathymetric smoothing therefore has the potential to affect both sides of the eddy–internal-wave energy partition.

To confirm our interpretation of the results and further quantify the role of bathymetric representation, we performed an additional sensitivity experiment using the bathymetry of the GIGATL3T run in a regional simulation at the resolution of 1 km. This experiment develops substantially fewer coherent deep eddies and weaker relative vorticity than GIGATL1T (Fig. A6), and the resulting circulation more closely resembles GIGATL3T. Thus, increasing horizontal resolution alone is not sufficient to reproduce the energetic eddy field found in GIGATL1T. Together with the consistency with geostrophic mean circulation among GIGATL1, GIGATL3, and GIGATL6, the sensitivity experiment points to the representation of the underlying topography as a primary control on the differences in the simulated eddy field.

The energy exchange diagnostics introduced in further illustrate how the generation of an intense eddy field modifies the abyssal energy partition. Following , we diagnose the horizontal exchange between the eddy and internal-wave fields from the covariance between internal-wave stresses and eddy strain (Table 2). Averaged between 3000 and 5000 m, eddy kinetic energy in GIGATL1T is approximately nine times that in GIGATL3T, while the RMS eddy strain is nearly five times larger. The diagnosed eddy-to-internal-wave energy conversion also increases strongly, by approximately a factor of 21. However, the resolved internal-wave kinetic energy increases by only about 30 %. Thus, the higher-resolution bathymetry in GIGATL1 facilitates stronger coupling between the eddy and internal-wave fields, while the resulting increase in the resolved internal-wave reservoir remains far smaller than the increase in eddy energy. This is consistent with the 1 km bathymetry still being too smooth to support internal-wave generation and scattering sufficient to act as an effective sink of energy.

The sensitivity run confirms that at the first order bathymetrical detail, and not resolution per se, controls the energy conversion.

The key differences in bottom roughness between model and observations can be further assessed considering the differences in the vertical wavenumber spectra. The vertical wavenumber spectrum and horizontal KE spectra for the deep Brazil Basin in the GIGATL1 runs and in the observations are compared in Fig. 5c and d. The model captures the observed near-inertial peak. In horizontal wavenumber space, the modeled and observed spectra agree reasonably well at low wavenumbers, yet the energy in CROCO decays too fast at high wavenumbers. The model vertical wavenumber bandwidth (i.e. j∗) is also slightly smaller than the observations, speaking to the impacts of CROCO finite spatial resolution, which, in combination with the smoothed topography, acts on the representation of the generation and scattering processes. The more rapid spectral roll-off compared to observations suggests an inefficient forward cascade of energy to fine scales in the simulation. Indeed, the model retains much of its energy in long-lived, coherent mesoscale eddies.

The vertical wavenumber spectra for both the model and the observational data document relatively low KE to PE ratios at the largest resolved vertical wavelengths, increasing at 500 m wavelength. We interpret such increasing ratios as a result of parametric subharmonic instability transfers from the semi-diurnal internal tide to near-inertial waves. The model near-inertial field, however, is less developed than in the observations. At subinertial frequencies, the model spectra indicate decidedly greater eddy variability at periods of 10 d, which we attribute to the submesoscale field. The field record extends to nearly two years and documents the presence of longer periods that we cannot presently assess.

Again, this analysis supports the hypothesis that the smoothed model bathymetry limits the transfer of energy toward the high-wavenumber internal-wave field. Although the higher-resolution GIGATL1 bathymetry permits stronger eddy-internal-wave coupling than GIGATL3, the model still lacks the finescale internal-wave energy observed over the rough Brazil Basin topography. The resulting internal-wave pathway therefore remains an insufficient sink for the energy with the generation of an energetic eddy reservoir instead. The coherent eddies, in turn, contribute to elevated diffusivity in the ocean interior.

The genesis of enhanced turbulent mixing above rough topography has been discussed extensively in recent decades . Given the role that diapycnal mixing plays in shaping the distribution of heat and carbon and the overall overturning circulation, it is paramount to capture its variability in time and space. Observations remain limited and model simulations are strongly constrained by resolution, vertical discretization choices, approximations adopted – most commonly the hydrostatic assumption – and parameterization schemes implemented, or, in the case of direct numerical simulations, size and realism of the integration domains. The contribution of each dynamical process involved with diapycnal mixing in the BBL remains unconstrained, especially in regions characterized by very rough topography. This is the case of the Brazil Basin, where topographic features are of order O(1) km.

Diapycnal mixing in the deep Brazil Basin is known to be significantly elevated over rough bathymetry and decline when moving into the ocean interior . The GIGATL simulations at 1 and 3 km horizontal resolution, with and without tide, reproduce this trend: K peaks near the bottom and declines with height, and in the BBL is broadly consistent in magnitude with that observed during the BBTRE campaign. If eddies do not form (GIGATL6 runs) then K is approximately constant in the water column and controlled by the numerics (parameterization and parameterization coefficients). However, at 1 km horizontal resolution modeled diffusivities are overestimated in the ocean interior. This discrepancy suggests that CROCO fails to suppress excessive mixing in the stratified interior, and mesoscale eddies emerge as critical in the abyssal Brazil Basin. The instabilities that occur over rough topography as represented by the model facilitate the generation of eddies that extend from the BBL into the water column, displacing isopycnals. Localized increased vertical mixing is found around and within these eddies, which are stronger and more numerous in the GIGATL1 simulations because the scale of the instabilities responsible for their generation is better resolved. At the resolutions considered in this work, the enhanced eddy reservoir can outpace the model's ability to transfer energy toward the internal-wave and ultimately dissipative pathways, contributing to overestimated diffusivities in the ocean interior. At the same time, the model underestimates the high-wavenumber energy because the smoothed topography precludes a realistic internal wave generation. In summary, two non-exclusive processes explain the eddy–wave partitioning in the model simulations: on one hand, buoyancy anomalies favorable to baroclinic instability are amplified relative to reality; on the other, the absence of a realistic internal-wave field removes an energy sink that would otherwise damp the eddy field.

As note of caution, we stress that beyond eddy dynamics, vertical mixing parameterizations and the numerical schemes employed also contribute to the biased interior diffusivity. The GIGATL runs employ the k-ε parameterization. Compared to the widely used KPP parameterization, the k-ε is more sensitive to background settings and to the imposed vertical–mixing value , which in our runs attains a minimum value of turbulence kinetic energy (TKE) (tkemin = 10⁻⁶).

Also, the numerically induced contributions to mixing relevant to the terrain-following coordinates need to be considered. showed in CROCO that numerical diapycnal mixing can become substantial over steep slopes, even when rotated tracer-advection schemes are used, because the rotation of the diffusive operator is constrained by the grid geometry. Their results also highlight that additional topographic smoothing reduces numerical mixing, but simultaneously removes small-scale bathymetric structure that is dynamically important for flow–topography interactions.

In closing, the comparisons among the five simulations considered and the observations highlight that in mesoscale-resolving/submesoscale-permitting ocean models, horizontal resolution modulates vertical diapycnal diffusivity and mixing more than tidal forcing. Even at 1 km, the smoothing applied to the bathymetry removes high-wavenumber roughness. As a result, the high-mode internal-tide shear and the consequent wave-breaking contributions are underestimated, causing the energy to remain concentrated inside the eddies, which are likely more numerous and intense in the model runs than in the real ocean. The outcome is that over rough topography increasing model resolution to a submesoscale-permitting regime may produce unrealistic, overestimated diffusivities in the ocean interior, and, counterintuitively, more so than in simulations that cannot resolve the submesoscale instabilities responsible for the eddy generation.

In summary, in the case of ocean diapycnal mixing, resolution alone is not the answer, and further research is needed to improve the realism of traditional ocean models and of the emerging machine learning based ocean emulators, often trained on submesoscale-permitting runs. Furthermore, nonhydrostatic model simulations are needed at finer horizontal and vertical resolution, which would be valuable for future process studies to advance our understanding of the interactions between internal waves, rough topography, submesoscale instabilities and their impact on the diapycnal mixing and buoyancy transformations in and above the BBL. Moving forward, observational constraints are required to establish how often and by how much the relative contributions of the eddy versus internal wave fields in the BBL are misrepresented in state-of-the-art ocean models. These constraints would also allow us to better validate the residence time of heat and carbon across the water column.