For model validation of tidal simulations, this study uses velocity observations from the AnSlope (Cross-slope exchanges at the Antarctic Slope Front) project. The dataset comprises Acoustic Doppler Current Profiler (ADCP) and Rotor Current Meters (RCM) records from 17 mooring stations deployed at the mouth of DT (yellow dots in Fig. 1), spanning multiple periods from March 2003 to March 2004 (for more details, see Table 1 in Gordon et al., 2009).

Mooring motion can contaminate velocity measurements (Kalvaitis, 1974; Langlois and Maze, 1990; Harding et al., 2017). During the AnSlope project, strong currents exerted considerable drag on the mooring lines, causing significant blow-down (Padman et al., 2009) and compromising some of the collected data (Gordon et al., 2009). To mitigate this, we only use data measured by the deepest ADCP or RCM at each station, as such instrument is closest to the anchor, where line tension is greatest, and thus experiences the least vertical and horizontal displacement (Susanto and Gordon, 2005). Our validation adopts a point-to-point comparison, matching the deepest observed point to the horizontally nearest model grid cell, then selecting the nearest valid cell within that column. While this introduces minor spatial mismatches, the dominant barotropic tidal scales far exceed grid spacing, making horizontal offsets of a few kilometers negligible. Furthermore, local baroclinic tides are bottom-trapped, non-propagating waves that affect amplitude but not the barotropic phase. Thus, a single depth suffices. Semi-diurnal and diurnal tidal constituents are extracted using the t_tide harmonic analysis package (Pawlowicz et al., 2002) for both observations and model output.

The interaction of tidal currents with sloping topography can generate a rectified mean flow (Garreau and Maze, 1992; Chen and Beardsley, 1995; Pérenne et al., 2000); therefore, comparing observed and simulated mean currents provides indirect validation of the tidal simulation. However, the mean flow varies strongly with height within the bottom boundary layer, and in steep areas, the model's bottom depth is likely not the same as the actual one, making the same absolute depth incomparable between the model and observations. This issue is compounded by mooring blow-down, which introduces time-dependent instrument depths and complicates fixed-depth assessments. To address this, we select several deep observation points at each station, specifically those least affected by mooring motion, and vertically average their time-mean velocities to define the observed mean flow. The corresponding model mean flow is derived by applying the same vertical and temporal averaging over the equivalent depth range and time period at the nearest grid cell. This procedure reduces sensitivity to vertical mismatches between observed and modelled depths.

For comparison with previous studies, we calculated the two key diagnostic parameters defined by Padman et al. (2002, 2003): the root-sum-square of tidal harmonic amplitude and the time-averaged tidal flow speed. The spatial patterns shown in our Fig. 2 are consistent with those presented in Fig. 2 of Padman et al. (2003), whose results were derived from both “forward” (dynamical) and “inverse” (data assimilation) models.

The model's performance in simulating tides is further validated by comparing the time series and power spectral density (PSD) of tidal currents between the model output and observational data. For brevity, only the comparison for central mooring station cc1 is presented in the main text (Fig. 3); the results for the remaining 16 moorings are shown in the Supplement (Figs. S1–S16). Notably, a mismatch is found at station adp1 (Fig. S1), where the observed stronger semi-diurnal signal likely stems from the advective effects of the diurnal tides (Bell, 1975), as the slope there may exceed the resolving capability of the model's vertical grid.

As shown in Fig. 3c, the simulated tidal current energy shows peaks at diurnal and semi-diurnal frequencies matching the observations, although its magnitude is somewhat underestimated (especially for the Mf constituent). The good agreement between model and observations in the filtered time series (Fig. 3a and b) validates that the model correctly captures the phase of the predominantly diurnal current, and also reproduces the spring-neap cycle well. This lends credibility to studying the tidal dynamics and energetics in the Ross Sea using the model output.

The comparison between simulated and observed mean currents is presented for 13 mooring stations (Fig. 4). Although current velocity observations are available from 17 stations, some are located close enough to map to the same horizontal model grid cell. For each such group, only the station with the closest match between observed and modelled seafloor depth was retained. The model agrees well with observations at most stations, capturing the mean flow in both magnitude and direction, though a few individual stations exhibit discrepancies. It should be noted that the observed mean flow likely reflects the background Antarctic Slope Current rather than purely tidally rectified flow. Nevertheless, the overall consistency demonstrates the model's ability to reproduce the mean circulation, thereby lending indirect support to the reliability of the tidal simulation. Additionally, we compare the modelled cross-slope temperature section with observations from the PRISM project (Fig. S17 in the Supplement). The model reproduces cross-slope thermal structure, revealing the extension of CDW from the deep ocean onto the continental shelf. This provides further independent validation of the model's representation of water-mass properties. Overall, these results reinforce confidence in our subsequent estimate of tidally driven cross-slope heat transport.

Since most of the Ross Sea lies poleward of both the diurnal (∼30° S) and semi-diurnal critical latitude (∼74.5° S) and its tidal regime is diurnal-dominated, internal tides generated by the barotropic tide-topography interaction are bottom-trapped, leading to an intensification of the near-bottom flow and shear (D'Asaro and Morison, 1992). As shown in Fig. 10a and b, both the baroclinic kinetic energy and squared vertical shear are intensified within the bottom tens of meters. This bottom-intensified tidally modulated shear is consistent with trapped internal tides. The vertical extent of these waves varies with the tidal cycle, increasing significantly during spring tide and shrinking or even vanishing during neap tide. Note that the term “bottom-trapped” refers to an energy maximum near the bottom, not the absence of baroclinic flow above it. These waves form through constructive interference of individual modes (Falahat and Nycander, 2015). It is also worth noting that similar near-bottom enhancements can arise from frictional boundary layer dynamics, nonlinear tidal rectification over rough topography (which also produces spring-neap variability), and topographic scattering or critical reflection.

To map the distribution of bottom-intensified energy, we introduce a non-dimensional parameter, RKE, defined as: 23RKE=〈EK〉100/〈EK〉H, where 〈EK〉100 and 〈EK〉H denote the kinetic energy averaged over the bottom 100 m and the full water column, respectively. The 100 m layer thickness is taken as a representative scale of the bottom-intensified layer, as revealed in Fig. 10a. The value of RKE exceeds 1 indicates the presence of bottom intensification. To ensure the identified bottom-trapped signals are significant, we applied RKE calculation only when the barotropic kinetic energy ranked in the top 10 % of the time-mean barotropic kinetic energy, equivalent to a velocity of 5 cms-1. The regions beneath ice shelves are excluded from the calculation.

The spatial pattern of RKE in Fig. 10c reveals significant bottom intensification over the continental slope and topographic features such as banks and troughs, while it is minimal over the slope east of Houtz Bank (HoB). The bottom-trapped waves cause vertical displacement of bottom water particles, which peaks north of DT at meter-scale amplitudes (Fig. 10d). This is much smaller than the hundred-meter amplitudes of freely propagating internal tides (e.g., in the Bay of Biscay, see Pairaud et al., 2010), highlighting the bottom-trapped nature of Ross Sea internal tides.

A potential concern regarding the modal decomposition of Tanaka (2023) is that it assumes SSH is determined only by the surface mode, whereas in regions with strong stratification, SSH may also be affected by bottom-trapped waves. To test this, we evaluate the baroclinic pseudo sea level ζbc (Fig. S20a in the Supplement) with density, following McWilliams et al. (2024, their Eq. 17). Figure S20 shows that ζbc is negligible throughout the Ross Sea, even in the Drygalski and Joides Troughs where stratification is strongest. The mean amplitude of ζbc is less than 2 cm, more than an order of magnitude smaller than that of the barotropic SSH (Fig. S20b), thus the modal decomposition of Tanaka (2023) is valid in the Ross Sea.

The energy conversion between the surface and topographic tidal modes is shown in Fig. 11a. A positive value denotes energy transfer from the surface to the topographic mode, and vice versa. As expected, the conversion is concentrated over topographic features, with the magnitude of 1 Wm-2, much greater than the BT-BC energy conversion rate (Fig. 11b). The pattern reveals large alternating positive and negative patches, which are associated with the eddy-like structures in the topographic mode (Fig. 7a and b). The conversion rate varies in sign along the slope because the eddies' velocities are alternately aligned with or against the surface mode (Fig. 7). In addition, smaller-scale patches are found along the coast, which are likely related to coastal trapped waves.

Energy conversion from barotropic to baroclinic tides in the Ross Sea mainly occurs over the slope and peaks near the mouth of DT (Fig. 11b), with a rate of approximately 10-2 Wm-2. The BT-BC conversion rate in the Ross Sea is considerably lower than those reported in other ocean regions, such as the ∼0.1 Wm-2 estimated in Monterey Bay (Kang and Fringer, 2012) and the ∼1 Wm-2 over the Luzon Ridge (Han and Eden, 2019), indicating weaker internal tide energy. This order of magnitude is consistent with the estimates of Müller (2013), who applied a global model and used a methodology similar to ours. It also agrees with the estimates derived from the method of Falahat and Nycander (2015), in which the rate is obtained by dividing the baroclinic energy density (Fig. 12b and d) by a decay time of 2–3 d. However, the model of Müller (2013) produces higher conversion rate near the Iselin Bank (IB) than our model. This discrepancy is likely due to the difference in horizontal and vertical resolution (Niwa and Hibiya, 2011). The energy conversion from barotropic to baroclinic tides is separated into contributions from the surface (Fig. 11c) and topographic modes (Fig. 11d), respectively. It is evident that the topographic mode dominates the conversion to baroclinic tides in most of the region. Notably, the surface mode appears to extract energy from the baroclinic tides, especially near the mouth of DT (negative values in Fig. 11c). This implies a cyclic energy pathway there: from the surface to the topographic mode, then to the baroclinic tides, and back to the surface mode.

Figure 12 presents the depth-integrated, period-averaged tidal energy densities in the Ross Sea. The total baroclinic energy densities (Fig. 12b and d) are of the same order as the theoretical estimates of Falahat and Nycander (2015), which are based on barotropic tidal velocities and topographic gradients. Overall, BTKE exceeds BCKE by an order of magnitude, which is supported by the low energy BT-BC conversion rate shown in Fig. 11b. Furthermore, the total tidal potential energy is itself an order of magnitude smaller than the kinetic energy, and within it, APE is an order of magnitude smaller than BTPE. The enhancement of BTKE along the slope is modulated by the topographic mode (Fig. 7a and b). Specifically, it is strongest where three eddy-like structures are present (Fig. 12a). Meanwhile, the enhancement of BTPE over the slope is associated with the surface mode of the diurnal tide (Fig. 12c). The APE reaches its maximum over the DT, corresponding to the vertical displacement shown in Fig. 10d. Although BCKE is relatively small in the depth-integrated sense, it is significant near the seafloor because baroclinic tides in the Ross Sea are predominantly bottom-trapped waves. Unlike freely propagating super-inertial internal tides that disperse energy into the ocean interior, these sub-inertial waves are trapped at the topography, confining their energy to the bottom boundary layer. This confinement of energy intensifies near-bottom velocity shear (D'Asaro and Morison, 1992), which promotes shear instabilities and turbulent dissipation, thereby enhancing local diapycnal mixing (Falahat and Nycander, 2015; Musgrave et al., 2017).

The barotropic and baroclinic energy fluxes exhibit remarkable differences in both magnitude and spatial pattern. For clarity, only the high-tide snapshots are displayed in Fig. 13. The complete figure set, covering time-average values, high-tide snapshots, and low-tide snapshots, is shown in Fig. S21 in the Supplement. The barotropic tidal energy flux is dominated by the pressure work (Fig. 13a), with the advective component being two orders of magnitude smaller (Fig. 13b). Both barotropic components are significantly shaped by the topographic mode but respond differently to tidal phase. The simultaneous sign change of sea surface perturbation and tidal velocity causes the pressure-work-induced energy flux to maintain a consistent direction over the slope (Figs. 13a and S21c). The advective flux, however, reverses direction between flood and ebb (Figs. 13b and S21f). Consequently, the time-averaged energy flux from pressure work retains eddy-like patterns along the slope (Fig. S21a), whereas the advective component is largely cancelled out (Fig. S21d).

The baroclinic energy fluxes from pressure work and advection are comparable in magnitude, peaking around the DT and IB (Fig. 13c and d) in a pattern consistent with the BCKE distribution (Fig. 12b). Moreover, the magnitude is consistent with that reported by Müller (2013) in the Ross Sea. The pressure-work-induced baroclinic energy flux exhibits a disorganized directional pattern (Fig. 13c). This disorder arises because bottom-trapped internal waves differ fundamentally from free-propagating waves, which radiate internal tide energy in coherent beams. In contrast, the velocity and pressure structures of bottom-trapped waves are governed by the topographic gradients and the distance from the generation site (Falahat and Nycander, 2015). Consequently, the irregularity of the topography induces a complex interference pattern as waves generated at sites overlap, ultimately leading to this disordered state.

Figure 14 shows the spatial distribution of total tidal energy dissipation, which is strongest along the continental slope, especially west of Cape Adare. Pronounced dissipation also occurs near the southwestern grounding line of the Ross Ice Shelf and over shelf regions with complex topography. A dedicated calculation of the baroclinic dissipation was not performed, owing to numerical constraints. Near the steep slope, C-grid staggering and partial bottom cells interact to treat some near-bottom velocity points as land, so that bottom cells over the slope often hold only one horizontal velocity component. Accordingly, bottom-intensified velocities may not be fully represented. This limitation affects the estimate of baroclinic energy flux divergence far more than baroclinic energy itself. Because the thin layer of bottom-intensified flow occupies only a minor portion of the 500–2000 m water column, the omission of one velocity component may lead to a slight underestimate of depth-integrated energy, with an uncertainty typically below 20 %. However, the baroclinic energy flux over upper layers of water column may partially cancel during vertical integration (as illustrated in Fig. S22 in the Supplement), and the near-bottom flux is comparatively strong and coherent. The integrated flux is therefore overwhelmingly determined by the lowest few partial cells and is highly sensitive to their velocity components. Missing either u′ or v′ in these cells projects the local flux vector onto a single direction, distorting both magnitude and orientation. Accordingly, diagnosing baroclinic dissipation as the residual would introduce significant numerical uncertainty that we do not report it separately. The estimated barotropic-to-baroclinic energy conversion is an order of magnitude smaller than the total dissipation shown in Fig. 14. Even if fully dissipated locally, this converted energy would represent only a minor fraction of the regional tidal energy budget. Thus, the conclusion that barotropic tides dominate the regional dissipation remains valid.