We use version 2.01 of the hourly data set from the Global Drifter Program which includes 15 m-drogued and undrogued drifters. It is important to note that the positioning system used to track the drifters (Argos or GPS) can have an impact on the power spectral density of velocity. showed that the noise in the Argos positioning system adds high-frequency energy when compared to surface buoys equipped with GPS. In the NEATL domain (Fig. a), the database of undrogued (drogued) drifters, which was downloaded on 30 April 2025, can be divided into 27 134 (25 956) continuous 60 d segments, each associated with its mean position over the segment duration. Among these, 11 591 (14 933) are from GPS-tracked drifters. Of the segments of both Argos and GPS-tracked undrogued (drogued) drifters, 26 109 (23 704), corresponding to 96 % (91 %) of the total, are located in offshore waters, reflecting the sparse coverage of surface drifters in coastal regions. Because SHKE is defined at the ocean surface, we focus on undrogued drifters in the following analyses, as they more accurately sample surface velocities . Undrogued drifters are known to carry a larger wind-slip error than drogued ones, reaching 8.6×10-2 m s⁻¹ per 10 m s⁻¹ wind speed compared to 0.7×10-2 m s⁻¹ downwind per 10 m s⁻¹ wind speed for drogued drifters , but this slip has not yet been comprehensively disentangled from genuine oceanic surface variability across frequencies seefor a discussion of the limitations of using undrogued versus drogued drifters for model comparison. The number of undrogued drifter segments per 1°×1° cell in the offshore domain is shown in Fig. c. The spatial distributions of the other drifter datasets (drogued and undrogued, GPS-tracked and all) are provided in Fig S1 in the Supplement.

The NEATL HYCOM experiments, covering the Atlantic from 28° S to 80° N (Fig. a), are part of a suite of eddying and submesoscale-enabled numerical simulations performed with HYCOM v2.3.01 . These simulations were performed to study and quantify the impact of horizontal and vertical resolution on the large-scale circulation and water mass transformations in the Atlantic. In this paper, we analyze three 1/12° horizontal grid-spacing configurations (9 km at the equator, 6 km in the Gulf Stream region) and four 1/50° horizontal grid-spacing configurations (2.25 km at the equator, 1.5 km in the Gulf Stream region). Three of these configurations have been used previously in , while four simulations (NEATL12-T, NEATL12-M₂, NEATL12-T-HVR, and NEATL50-T-WD) are analyzed for the first time. The simulations are integrated for 18 months with tidal forcing of the eight largest tidal constituents (K₁, O₁, P₁, Q₁, M₂, S₂, N₂, and K₂) after spin-up as described in . The last 12 months outputs are used in the analysis.

These simulations are listed in Table , but are described in more details in the following:

NEATL12-T is the tidal 1/12° reference simulation with 6-hourly atmospheric forcing and 8 tidal constituents.

In the vertical dimension, the above simulations contain 32 or 96 hybrid layers with density referenced to 2000 m (σ2) (see and for details). The vertical coordinate is isopycnal in the stratified open ocean and makes a dynamically smooth and time dependent transition to terrain-following coordinates in shallow coastal regions and to fixed pressure levels in the surface mixed layer and/or unstratified seas . No inflow or outflow is prescribed at the northern and southern boundaries. Within a buffer zone of about 3° from the northern and southern boundaries, the 3-D modeled temperature, salinity, and depth of isopycnal interfaces are restored to the monthly Generalized Digital Environmental Model GDEM, climatology with an e-folding time of 5–60 d that increases with distance from the boundary. The initial conditions are derived from the GDEM climatology potential temperature and salinity and the atmospheric forcing is derived from the European Centre for Medium-Range Weather Forecasts reanalysis ERA40 with 6-hourly wind anomalies from the Fleet Numerical Meteorology and Oceanography Center Navy Operational Global Atmospheric Prediction System for the year 2003. The year 2003 is considered a neutral year over the 1993–present timeframe in terms of long-term atmospheric patterns, such as the North Atlantic Oscillation. The reader is referred to and for details on the parameterizations used in the model.

To derive surface velocity from particles, and thus simulate the trajectories of surface drifters, we performed an OceanParcels experiment using the v2.3.2 Parcels Python package . This OceanParcels experiment (hereafter referred to as OP Seed 1/2°) was conducted offline using hourly 2D advecting velocity field (a combination of ocean current and wind-wave effects) outputs from the NEATL50-T-HB-HF numerical simulation. Particles were seeded every 30 d on a regular 1/2° × 1/2° grid between 15° S and 65° N in the NEATL domain and are advected with Parcels using a fourth-order Runge-Kutta scheme and no stochastic diffusion. The latitudinal restrictions were imposed to avoid proximity to the model open boundaries (located near 28° S and 80° N at the Fram Strait); the northern limit of 65° N also corresponds approximately to the Greenland-Scotland Ridge, which forms a natural boundary of the North Atlantic basin. Trajectories were then tracked for 60 d resulting in 11 seeding events over the one-year simulation and yielding 264 361 trajectory segments of which 244 632 (92 %) are located in offshore waters (Fig. b).

To assess whether differences between simulated and observed statistics could arise solely from the irregular spatial distribution of real drifter observations, we constructed a subset of the OP Seed 1/2° dataset that replicates the sampling characteristics of the undrogued surface drifter dataset (hereafter referred to as OP Seed Drifters; Fig. d). Specifically, for each 1° × 1° bin cell of OP Seed 1/2°, we randomly selected trajectory segments such that the number of simulated segments in each cell matches the number of undrogued surface drifter segments observed in the same cell (Fig. d). In a few cases, close to northern and southern limits, the OP Seed 1/2° dataset contained fewer segments than the undrogued drifter dataset for a given cell; in such cases, all available simulated segments were used. This approach keeps the spatial sampling density of the OP Seed Drifters as close as possible to that of the observational dataset, ensuring that any differences found in subsequent analyses cannot be attributed to sampling bias. The resulting subset contains 24 302 trajectory segments of 60 d each, of which 23 579 (97 %) are located in offshore waters (Fig. d).

Building upon the methodologies outlined in , , and , frequency rotary spectra at each model grid point (Eulerian) and along drifter trajectories (Lagrangian) are computed from surface horizontal velocity time series taken from the HYCOM simulation and surface drifter data. Rotary velocity spectra break down velocity variance into contributions from different frequencies and separate clockwise from counterclockwise components, thereby distinguishing anticyclonic from cyclonic energy. Following and , velocity variance is estimated and interpreted as kinetic energy; no factor of 1/2 is included in the calculations.

To compute spectra, hourly velocity time series (generated at each grid point for the Eulerian estimate and derived from particle velocities for the Lagrangian estimate) are segmented into 60 d periods with a 50 % overlap and linearly detrended. For both the model and drifter data, complex-valued fields (u+iv, where u and v represent zonal and meridional velocity components, respectively) are multiplied by a Hanning window before computing the 1-D discrete Fourier transform. Spectral estimates are obtained by multiplying the Fourier coefficients by their complex conjugates and averaged over segments. Finally, as per , the rotary frequency spectral densities are adjusted by a factor of 8/3 to account for the windowing operation . The resulting Power Spectral Density (PSD) of the rotary spectra corresponds to a 1-year period for the numerical products (both Eulerian and Lagrangian) and spans more than 30 years for the surface drifters (from the end of the 1980s to the beginning of the 2020s).

To decompose SHKE, the velocity rotary spectra are integrated over four frequency bands: high-frequency (<-0.5 and > 0.5 cpd, with cpd stands for cycles per day), near-inertial (±[0.9, 1.1]f cpd, excluding the ±5° latitude band around the equator, with f the Coriolis parameter), semidiurnal (±[1.9, 2.1] cpd), and diurnal (±[0.9, 1.1] cpd). In addition to these estimated SHKE components, the total SHKE (i.e., the time-mean of the instantaneous values squared) and low-frequency SHKE (total SHKE minus high-frequency SHKE) are computed. It is worth noting that in , SHKE maps from drifters were obtained slightly differently: the authors band-pass or low-pass filtered the drifter velocity time series and then computed the variance of the filtered velocities within bins. As stated by , both methods yield similar results. This allows us to use the same approach for both Eulerian and Lagrangian fields.

Finally, the spectra and SHKE are averaged within 1°×1° cells in the NEATL domain. Given that the vast majority of Lagrangian segments (96 % of undrogued drifters and 92 % of OP segments) are located in offshore waters, the Lagrangian analysis is constrained to the offshore domain, consistently with , , and . For the Eulerian fields, both subdomains are considered. The resulting gridded rotary spectra and SHKE partitions produced for this study are archived at SEANOE (NetCDF and associated README; ).

In Fig. , only the GPS-tracked drifters were used to minimize the noise . In contrast, all undrogued drifters are included in Fig. , as restricting the analysis to GPS-tracked drifters would lead to insufficient spatial coverage in parts of the domain (e.g., the equatorial South Atlantic; see Fig. S1 in the Supplement).

The zonally averaged rotary spectra of OP Seed Drifters and undrogued drifters are shown in the first row of Fig. . Before contrasting the two datasets, we note that, near 30° N, the inertial frequency (grey dashed line) coincides with the diurnal tidal frequency (±1 cpd), making it difficult to disentangle their respective contributions. This latitude corresponds to the diurnal critical latitude (e.g., 27.6° for O₁ and 30° for K₁; ), defined as the latitude where the inertial frequency equals the tidal frequency e.g.,. According to linear internal wave theory, it marks the poleward limit of wave propagation so, poleward of 30°, diurnal internal tides become evanescent. The critical latitude for the semidiurnal (±2 cpd) band is much higher, around 75° (e.g., 74.5° for M₂ and 85.7° for S₂; ), allowing semidiurnal internal waves to propagate across most of the global ocean.

The pattern of the zonally averaged PSD of rotary spectra is similar between the observed and numerical drifters (Fig. a and b). However, the observed drifters show more energy in the high-frequency band, while the semidiurnal and diurnal peaks are, at most latitudes, more pronounced in the NEATL50-T-HB-HF numerical drifters. As discussed by , this high-frequency content in the observed drifters may originate from the drifter tracking system and/or from artifacts in the estimation of drifter positions and velocities . Overall, the numerical drifters contain less total SHKE than the observed undrogued surface drifters (Table ). Yet, they contribute to a significantly higher fraction to the low-frequency band, storing 83.3 % of the total SHKE (87.8 % of OP Seed 1/2°). In comparison, the undrogued drifters store 75.3 % in the low-frequency band (64.3 % for GPS-tracked drifters). In absolute and relative terms, the numerical particles exhibit more energy than observed in the semidiurnal and near-inertial bands.

The normalized ratio (right column in Fig. ) reveals clear spatial contrasts between the numerical simulation and the observations. Indeed, there is a striking bipolar pattern in the diurnal band (Fig. i) that is more pronounced in the observations with higher SHKE poleward of the diurnal critical latitude and less equatorward of it. This observed poleward diurnal energy is consistent with , who reported that diurnal motions are driven not only by tides, but also by the day/night solar heating cycle. At low frequencies, the model indicates higher SHKE in energetic regions such as the Gulf of Mexico and the Gulf Stream whereas the surface drifters show the opposite (Fig. f). In the semidiurnal and near-inertial bands, the pattern reverses, with observations exhibiting higher SHKE in these energetic regions, whereas the model distributes energy more broadly (Fig. l and o). The effect of temporal coverage mismatch, resulting from the difference between the 30-year observational record and the single-year OP drifter simulation, is also weakly discernible in the near-inertial band. Indeed, the two narrow bands of enhanced near-inertial energy between 20 and 30° N in panel (m) of Fig.  for the 1-year numerical OceanParcels simulation correspond to the tracks of Hurricanes Fabian and Kate of the 2003 season (the atmospheric forcing year of the simulation), a feature that is even more apparent in the Eulerian fields (Fig. m).

Overall, the undrogued surface drifter data contains more total SHKE than NEATL50-T-HB-HF numerical particles, with the model over-representing the fraction of energy in the near-inertial and tidal reservoirs. Regionally, the sign of the model–observation discrepancy depends on the frequency band. At low frequencies, the modeled energy exceeds the observed one in the western boundary currents, whereas the reverse holds elsewhere. By contrast, in the semidiurnal and near-inertial bands, the observed energy exceeds the modeled one in these same energetic regions. The largest discrepancy is in the diurnal band. South of the diurnal critical latitude, where internal tides radiate freely, the modeled diurnal energy exceeds the observed one while observations exceed the modeled one poleward, where only non-tidal mechanisms can sustain diurnal energy. Whether these discrepancies reflect genuine model biases or arise partly from the Lagrangian sampling framework is examined in the following subsection.

The previous subsection established the differences between OP Seed Drifters and undrogued surface drifters. The effect of drifter sampling density on the 60 d segments and corresponding spectra was found to be small and spatially incoherent (see comparison between the high density OP Seed 1/2° and subsampled OP Seed Drifters in Fig. S2 and Sect S3 of the Supplement). Restricting the undrogued drifter statistics to the OP Seed Drifters footprint (between 25° S and 65° N, not shown) yields nearly identical frequency distributions (to within 0.1 percentage points), with only a modest increase of total SHKE from 137.8 to 144.4×10-3 m² s⁻². This confirms that the spatial coverage of the OP experiments is not the main driver of the frequency-distribution mismatch between the model and the observations.

The zonally averaged PSD is overall similar between the native Eulerian fields and OP Seed Drifters (Fig. a and b), but the tidal peaks are broader and increasingly indiscernible at higher frequencies in the Lagrangian spectra (e.g., the ±4 cpd peaks are barely discernible in the Lagrangian but prominent in the Eulerian). This spectral broadening redistributes energy away from peak centers toward neighboring frequencies, as shown by the ratio in Fig. c and consistent with observations from earlier work . Above approximately ±2.5 cpd, the Eulerian spectrum shows clear mirror images of the inertial ridge at -f±1 cpd that appear as a surplus of Eulerian over Lagrangian energy (Fig. c), while these features are barely discernible in the OP Seed Drifter (Fig. b) and undrogued drifters spectra (Fig. b). Their presence in our Eulerian fields corroborates the interpretation by , namely that such mirror images, previously identified in global surface drifters and in both Eulerian and Lagrangian global tide-resolving simulations , reflect genuine oceanic processes. However, the attenuation of these mirror images in the Lagrangian spectrum suggests that the undrogued drifter sampling in the NEATL domain, although adequate for the frequency bands considered here, may under-resolve these weaker high-frequency features. Domain-averaged energy in specific frequency reservoirs (Tables  and S1) shows that the different velocities (Lagrangian vs. Eulerian) have minimal impact on total SHKE and in low, diurnal, and near-inertial bands. However, significant deviations occur in the semidiurnal frequency band with Eulerian velocities containing up to 50 % more energy than Lagrangian velocities. The SHKE maps (Fig. ) confirm comparable levels of energy for low, diurnal and near-inertial frequencies. In the semidiurnal band, OP Seed Drifters show less energy over most of the domain with a notable exception at the Amazon shelf (Fig. j), a well-known hotspot of semidiurnal barotropic and internal tides e.g., where Lagrangian particles are advected across strong velocity gradients at each tidal cycle, likely amplifying the apparent tidal energy relative to Eulerian estimates.

The comparison of Lagrangian and Eulerian estimates (Fig. ) shows that the differences observed between OP Seed Drifters and undrogued surface drifters (Fig. ) cannot be attributed to the Lagrangian sampling alone. In particular, the lower (higher) energy poleward (equatorward) of 30° N and the deficit of high frequency energies in the model relative to observations are not visible when comparing OP Seed Drifters to the Eulerian fields, confirming that these are genuine dataset differences rather than an outcome of the Lagrangian sampling. Note that the high-frequency deficit in the simulations could partially be the result of drifter tracking and position-estimation artifacts or wind slippage instead of real oceanic motions. Similarly, the higher observed SHKE in strong low-frequency flow, seen in the near-inertial and semidiurnal bands of the observation compared to the numerical drifters, is not recovered as a Lagrangian/Eulerian difference in our twin-simulation experiments. This contrasts with , who reported a Lagrangian underestimation of low-frequency and diurnal KE relative to the Eulerian field in regions of strong low-frequency flow. This apparent disagreement may be a consequence of a difference in experimental design as their analysis relied on a very large ensemble of particles distributed throughout the same simulation, providing the statistical power to isolate small Lagrangian sampling effects on energetic mesoscale regions. As in and , the main effect of the Lagrangian sampling is the spectral broadening of tidal peaks which has a negligible impact on the frequency distribution of low, diurnal and near-inertial bands (Table ). In the semidiurnal band, however, the broadening is more pronounced, with the Eulerian fields storing 2.6 % of total SHKE compared to 1.7 % in the Lagrangian experiment, implying that part of any semidiurnal discrepancy between observations and Eulerian model output may reflect the Lagrangian/Eulerian framework itself.

NEATL12-T and NEATL12-M₂ differ only in the number of tidal components forcing the model (eight largest tidal constituents and M₂ only, respectively). Their zonally averaged rotary spectra are broadly similar (Fig. a–c), but NEATL12-T has greater energy in the vicinity of the tidal peaks. This is particularly evident in the normalized ratio (Fig. c), except at the exact position of the M₂ frequency (around ±2 cpd) and its pure second harmonic (around ±4 cpd, see ), where the tidal peak of NEATL12-M₂ is comparable to that of NEATL12-T (i.e., normalized ratio near 0.5 in Fig. c). Globally, the total SHKE remains essentially unchanged between the two runs (Table ), with a slight decrease offshore and a more notable increase on the shelf in NEATL12-T. When fewer constituents are retained, the low-frequency component contains a slightly larger fraction of the total SHKE (i.e., 91.8 % offshore and 45.7 % inshore in NEATL12-T against 92.4 % offshore and 48.7 % inshore in NEATL12-M₂) while the near-inertial bands contain a slightly smaller fraction. There is also an increase in the semidiurnal fraction of total SHKE in NEATL12-T compared to NEATL12-M₂ but the diurnal band concentrates the strongest contrast, with NEATL12-T more energetic both offshore and inshore but the largest differences are on the coast (a factor of three in both absolute and relative terms).

Regionally (Fig. ), no clear contrast between the two experiments emerges in the low-frequency, semidiurnal, and near-inertial bands with NEATL12-T being slightly more energetic in most of the domain. The diurnal band tells a different story with a clear separation at 30° N. Poleward of 30° N the two experiments are comparable offshore, whereas equatorward of 30° N NEATL12-T is significantly more energetic. On the shelves, the NEATL12-T excess of diurnal SHKE is present at all latitudes, including north of 30° N.

Overall, adding more tidal components increases, as expected, the energy at the added frequencies, with the largest increase on the continental shelves where, through tidal shoaling, the barotropic tidal amplitudes are largest . In the semidiurnal band, the slightly smaller fraction found in NEATL12-M₂ might reflect the absence of S₂, N₂, and K₂ constituents, which together contribute a non-negligible share of the global semidiurnal signal. Offshore and poleward of 30° N, the diurnal signal is nearly identical in both runs, highlighting that, as discussed by , a large fraction of the diurnal flow is non-tidal. Possible sources for this non-tidal diurnal SHKE are the wind variability (further discussed in Section 5.6) and/or aliasing of mesoscale variability . By contrast, the diurnal energy is substantially larger near the equator and on the shelves in NEATL12-T than in NEATL12-M₂, showing that the diurnal tidal constituents (K₁, O₁, P₁, Q₁) dominate the local diurnal variability in these regions.

NEATL50-T and NEATL12-T differ only in horizontal resolution (1/50° and 1/12°, respectively). The zonally averaged rotary spectra (Fig. a–c) show that NEATL50-T is significantly more energetic at nearly all frequencies (see Fig. 2 of for a comparison of the time evolution of the domain-averaged total 3D kinetic energy where 1/50° has approximately 70 % more energy than 1/12°). This is confirmed by examining the ratio in Fig. c and particularly true for frequencies whose absolute value exceeds 2 cpd. However, NEATL50-T and NEATL12-T have close levels of energy at tidal peaks close to ±2 cpd. The only exception to the rule that higher resolution yields higher energy is that NEATL12-T has more energy in the -[0.9, 1.1]f cpd frequency band, which corresponds to near-inertial motions in the northern hemisphere but to the cyclonic side of the spectrum in the southern hemisphere. Table  quantifies that the SHKE in the deep ocean increases by around one-third when the horizontal resolution increases from 1/12 to 1/50° horizontal grid-spacing; however, the differences are less pronounced on the continental shelf. The excess of energy is, roughly, well distributed across the different reservoirs, as the percentage of the total SHKE stored in each compartment is comparable between the two experiments. In detail, the most noticeable difference occurs in the deep ocean where the percentage of total SHKE stored in the near-inertial band decreases by one-third (from 6 % to 4 %) as the resolution increases.

Over most of the domain (Fig. ), the NEATL50-T simulation has significantly more energy than NEATL12-T at low, diurnal, and semidiurnal frequencies. However, the opposite is true for the near-inertial frequency. By contrast, near 30° latitude in the diurnal band, NEATL12-T has more energy than NEATL50-T, but this corresponds to the latitude where energy stored in the near-inertial band overlaps with that in the diurnal band .

Overall, increasing the horizontal resolution leads to a substantial increase in total SHKE across most of the energy spectrum, consistent with previous studies. showed that high horizontal-resolution simulations have much higher values of kinetic energy for low frequency motions compared to low-resolution simulations. For tidal frequencies, found that increasing the horizontal resolution in realistic HYCOM simulations from 8 to 4 km increased the semidiurnal barotropic-to-baroclinic tidal conversion by half, and more baroclinic modes were resolved. also found that decreasing the horizontal grid spacing leads to more realistic internal wave frequency spectra. The increase in horizontal resolution also leads to a better representation of the submesoscale field, and increases wave-mean and wave–wave interactions, explaining the filling of the high-frequency continuum between the tidal peaks in the 1/50° simulations when compared to the 1/12° simulations (Figs.  and c). There are two exceptions to this overall increase in SHKE. First, the semidiurnal fraction of the inshore SHKE decreases from 48.0 % to 43.4 % while the offshore fraction barely changes (1.9 % to 2.0 %; Table ). A possible explanation is that over continental shelves, where the semidiurnal signal is predominantly barotropic and a large fraction of the global M₂ energy is dissipated , enhanced barotropic-to-baroclinic conversion redistributes energy away from the barotropic tide, while the generated internal tide radiates seaward and is not retained locally. also suggested that insufficient horizontal resolution could enhance the semidiurnal peak by inhibiting scattering of tidal energy into the wave continuum . Second, the near-inertial band is weaker on average at the higher horizontal resolution. One possible interpretation could be a more efficient vertical transport of near-inertial kinetic energy into the ocean interior through the resolved mesoscale and submesoscale fields in the 1/50° simulation e.g.,. However, the spatial pattern in near inertial SHKE reduction does not straightforwardly support this view, since the reduction is not systematically concentrated in the most energetic regions of the domain (Fig. d), where mesoscale activity is strongest, but rather appears in the basin interior.

NEATL12-T-HVR and NEATL12-T differ only in vertical resolution (96 and 32 isopycnal layers, respectively). The zonally averaged rotary spectra (Fig. a–b) show no clear differences in total SHKE, tidal peaks or harmonics. However, the normalized ratio indicates slightly more energy in the northern high latitudes with more vertical levels and less energy in the low latitudes. As seen in Table , increasing the vertical resolution from 32 to 96 levels results in approximately a 10 % to 15 % increase in total SHKE, with the increase being higher over the continental shelf. Because the fraction of total SHKE in each band is largely unchanged (Table ), this additional energy is distributed broadly across the frequency domain. The most remarkable difference seen here is that, by increasing the vertical resolution, around 2 % less of the total SHKE is stored in the near-inertial frequencies over the continental shelf.

The maps in Fig.  confirm the domain-averaged picture. Surface kinetic energy increases slightly across most regions and frequency bands when vertical resolution is refined, with no strong spatial pattern. The main exception lies offshore north of 40° N, where the increase appears spatially uniform in the diurnal band. This signal reflects the general increase of the total SHKE, which stands out visually in this otherwise low-energy region, rather than a diurnal-specific enhancement. Another exception regards regions of intense mesoscale activity, with elevated low-frequency energy in the corridors of North Brazil Current rings , Gulf of Mexico Loop Current eddies , and Gulf Stream meanders/rings, largely masked by the high background energy in the ratio panel (Fig. f), but evident when comparing the pathways in panels (d) and (e).

Overall, vertical refinement increases the total SHKE, distributed broadly across the frequency domain (see also Fig. ), with a coherent enhancement at high latitudes. This is consistent with various studies that show that tidal energetics vary with the number of vertical layers provided that horizontal grid spacing is not the limiting factor. showed that the modeled internal wave frequency spectra are improved with increased vertical resolution only when the horizontal resolution is also increased. In an idealized 1/100° HYCOM configuration forced solely by semidiurnal tides, found that increasing the number of isopycnal layers increases tidal-induced vertical velocities and available potential energy, while tidal kinetic energy remains largely unchanged. The energetics increase up to 48 layers and change little thereafter. Here, at 1/12° horizontal grid-spacing, the tidal SHKE changes only weakly between 32 and 96 layers, and the tidal SHKE fraction even decreases slightly, suggesting that the horizontal grid-spacing is the limiting factor in our configuration. The dominant effect of vertical refinement is therefore an increase of low-frequency SHKE, also visible in total KE (not shown), in the already energetic meso- and large-scale flow regions, consistent with the primary role of the vertical grid in resolving horizontal flows via improved representation of their baroclinic structure .

NEATL50-T-WD and NEATL50-T differ only in the inclusion of internal wave drag in NEATL50-T-WD. The zonally averaged rotary spectra (Fig. ) show that the inclusion of wave drag reduces energy across the majority of the frequency domain. The reduction is less pronounced at frequencies below the near-inertial band, where it becomes almost negligible. Table  confirms that the inclusion of wave drag leads to a slight decrease in energy across all the frequency bands analyzed. The most pronounced impact is in the semidiurnal band, where the fraction of total SHKE drops by about 0.4 %–0.5 % both inshore (from 43.4 % to 42.9 %) and offshore (from 2.0 % to 1.6 %). While this represents a small relative change inshore, offshore it corresponds to a relative reduction of about 1/5.

The SHKE maps (Fig. ) confirm that incorporating wave drag leads to an overall reduction in surface SHKE across the frequency bands studied. In the low-frequency band, a clear reduction is visible in the tropical band equatorward of around ±15° (Fig. d–f). In the diurnal band, the reduction is most apparent equatorward of 30° N, while no clear signal emerges poleward of this latitude. In contrast, the decline in semidiurnal energy is more pronounced in the deep ocean at nearly all latitudes, with the exception of the western boundary current pathway from the Gulf of Mexico into the Gulf Stream (Fig. j–l). Finally, in the near-inertial band, no clear signal emerges.

Overall, the inclusion of wave drag reduces the energy in each frequency band over the latitudes where the corresponding motions can propagate, that is, equatorward of about ±15° for the low-frequency band (below ± 0.5 cpd), ±30° for the diurnal band, and across nearly the entire domain for the semidiurnal band, except along the western boundary current pathway. By construction, wave drag dissipates propagating tides, which explains the absence of a clear difference poleward of these critical latitudes, where the motions become evanescent. reported that the MITgcm tends to overestimate semidiurnal SHKE compared to surface drifters and, following and , attributed this bias partly to the absence of topographic internal wave drag in the MITgcm simulations. Our results support this interpretation, with lower semidiurnal energy when wave drag is included.

NEATL50-T-HB and NEATL50-T differ only in bathymetric resolution, with NEATL50-T-HB using a native 1/50° bathymetry rather than the 1/12° product interpolated onto the 1/50° grid . Overall, the higher-resolution bathymetry reduces the SHKE across most of the frequency domain (see Fig. a–c and Table ). There are, however, notable exceptions in the semidiurnal and higher-frequency tidal peaks and in the latitudinal band between 20° N and 30° N, where the SHKE is higher in the high-resolution bathymetry simulation. The low-frequency fraction of SHKE is only marginally reduced (from 92.2 % to 91.4 %), whereas in shallow regions it drops more noticeably, from 49.7 % to 45.0 % (Table ). There are minimal changes in the diurnal and near-inertial components, but enhancing the bathymetry resolution leads to increased energy in the semidiurnal frequency band. The percentage of KE contained in the semidiurnal band increased from 43.4 % to 48.0 % in the shelf domain, and from 2.0 % to 2.5 % in the offshore domain when high-resolution bathymetry was used.

The SHKE maps (Fig. ) do not show clear regional differences in the low-frequency and near-inertial bands. A noteworthy exception is the enhancement (diminution) of low-frequency SHKE below (above) the equator off the the Amazon shelf (Fig. f). In the diurnal frequency bandWith, there is a reduction of energy in the higher-resolution bathymetry experiment, with the exception of the 30° N latitude and a few specific regions such as the Adriatic Sea. By contrast, in the semidiurnal band, the increase in bathymetry resolution increases the surface SHKE, with a few exceptions, mainly at high latitudes. There is also a clear increase in the SHKE associated with semidiurnal internal tides in the Amazon shelf.

The reduction in the total SHKE of NEATL50-T-HB when compared to NEATL50-T is consistent with the enhanced lateral and bottom dissipation due to the increase in bathymetric resolution , both of which are more accurately represented in the finer bathymetric resolution. This reduction is achieved through a transfer of energy toward higher-frequency motions via flow–topography interactions and internal wave generation e.g.,. This mechanism is consistent with the observed reduction of low-frequency SHKE, which occurs in both subdomains, but it is much more pronounced on the continental shelf than in the deep ocean, likely reflecting the enhanced coupling between surface and bottom processes in shallow waters, where the bottom is closer to the surface and more directly shapes the surface kinetic energy. However, changes are spatially heterogeneous, with local increases and decreases in low-frequency energy, in agreement with bathymetry-induced modifications of the large-scale circulation as, for example, on the Amazon shelf near the North Brazil Current retroflection. In the semidiurnal band, there is an energy increase almost everywhere and we surmise this is due to a better representation of local internal wave generation with better-resolved bathymetry . This is supported by the more pronounced signature observed over the Amazon shelf (Fig. i), consistent with the strong M₂ barotropic-to-baroclinic conversion documented in that region . In contrast, the higher bathymetry resolution tends to reduce the diurnal energy, especially equatorward of its critical latitude, possibly reflecting enhanced dissipation of propagating internal waves.

NEATL50-T-HB-HF and NEATL50-T-HB differ only in the temporal frequency of the wind forcing, with NEATL50-T-HB-HF using hourly wind stress rather than 6-hourly. Increasing the wind-forcing frequency leads to a rise in SHKE across all frequency bands (Table S1 in the Supplement). However, this does not necessarily imply an increase in all bands when when expressed as fractions of total SHKE (Table ). For example, there is a reduced percentage in the low frequencies in the offshore domain (86.7 % instead of 91.4 %) while it remains comparable inshore (44.8 % instead of 45.0 %) (Table ). The near-inertial band on the shelf shows almost no net change in total SHKE (Table S1 in the Supplement), because the overall increase of total SHKE is compensated by a reduction in the near-inertial fraction at higher temporal frequency (Table ). At high frequencies, the energy in the diurnal band (offshore and inshore) and in the offshore near-inertial band shows a large increase, by more than 50 %. This is also visible in Fig. a–c where zonally averaged rotary spectra are compared. We find that an increase in wind frequency increases the energy in nearly all the frequency domains at all latitudes, with the exception of low and semidiurnal frequency motions where the level of energy is comparable. Spatially, the increase in energy for higher wind frequency is mostly uniform for the low frequency, diurnal and near-inertial frequency bands (Fig. ). However, in the semidiurnal frequency band, the increase is only confined to specific regions, e.g, the Gulf of Mexico, Mediterranean Sea, Baltic Sea, Norwegian Sea and Greenland Sea.

Overall, the increase in wind forcing frequency raises the total SHKE across most of the domain through a gain of high-frequency energy. A strong amplification occurs in the near-inertial band, consistent with the known role of the wind in driving near-inertial motions . As noted by several authors , this near-inertial response is less pronounced in tropical and subtropical regions than at mid-latitudes (Fig. o). A more unexpected feature is the strong amplification in the diurnal band almost everywhere and in the semidiurnal band in regions of weak semidiurnal energy such as semi-enclosed basins. This behavior likely reflects the diurnal and semidiurnal cycles of the wind itself . In particular, estimated globally that the diurnal cycle accounts for 30 %–40 % of the daily wind variance over the ocean, whereas the semidiurnal cycle accounts for only 15 %–25 %. The dominant diurnal share explains why the wind-forced signal covers most of the domain in the diurnal band. The semidiurnal share, by contrast, is small enough that the directly wind-forced response can only emerge clearly where the background astronomical semidiurnal tide is itself weak, which is precisely the case in the semi-enclosed basins where we observe the amplification in the ratio maps. Consistently, no such amplification appears in regions known for resonant astronomical semidiurnal tides, such as the North Sea e.g.,, the English Channel and Irish Sea e.g.,, Hudson Bay e.g.,, and the Bay of Fundy–Gulf of Maine system e.g.,, where the strong astronomical signal is expected to mask the wind-forced response. Note that the diurnal amplification appears weaker near 30° in Fig. i.