For this study, all available satellite tracks of the TOPEX/Poseidon and Jason-1/Jason-2/Jason-3 missions are considered. We chose these satellite missions since they form together a time series of data from 1993 to 2025 with a revisit period of 9.9156 d. We select data from 1993 to 2020 to conduct a harmonic analysis. While tidal frequencies remain aliased due to the satellite sampling pattern, the length of our time series enables a reliable disentangling of the various tidal components, even when separating the data into two contrasted seasonal periods .

In order to retrieve the internal tides' signal on the region, the following processing steps have been applied :

Step 1: We conduct an harmonic analysis on the along-track Sea Level Anomaly (SLA) retrieved at each pass of the nadir altimeter according to the decomposition: h(x,t)=h0(x)+hT(x,t)+ϵ(x,t) where h is the Sea Surface Height (SSH) measured at the location x and time t, h0 is the mean SSH of the ocean at location x, ϵ is the residual signal including the non-coherent part of the baroclinic tides. hT is the contribution of barotropic and coherent baroclinic tides to the SSH: hT(x,t)=∑i=1NAi(x)cos⁡(ωit+ϕi) where Ai is the amplitude, ωi is the angular velocity, and ϕi is the phase of the ith∈[|1,N|] wave at the location x and time t. We focus here on the M2 component, characterised by ω=1.405189s-1. Hence, we recover the SSH linked to the M2 tidal frequency from altimetry.

In this study, track 137 of the TOPEX/Poseidon – Jason 1/2/3 mission is used to analyse the internal tide signal in the SSH. Hence, we use all other tracks of the mission crossing the track 137 to evaluate the uncertainty of the M2 baroclinic signal retrieved with our method. By computing the standard deviation of the differences in the M2 baroclinic amplitude at cross-over points, we estimate an uncertainty of about 0.3 cm, which represents a 10 % relative error on the amplitude.

We further evaluate the consistency of this processing method (Lanczos) with the High-Resolution Empirical Tide (HRET) model from for the baroclinic signal and with the FES2014 model for the barotropic signal . Both of these models are based on altimetric data. While HRET targets the modeling of internal tides, FES2014 provides a reconstructed field of the SSH through the resolution of the tidal barotropic equations. Therefore, these two models are relevant to evaluate our processing method relying on a simple filtering of altimetric data only.

We focus on the latitudes south of 20° S since we will study further the baroclinic flux propagating southwards. We display the comparison results on the track 137 flying over the ridge around 36° W, where internal tides are known to be the most intense (see Fig. ). We notice that the baroclinic signal retrieved by the Lanczos filtering is in reasonable agreement with the one derived in the HRET model, although the amplitudes appear slightly larger – sometimes with a difference of up to 30 %. While we process and keep nadir signal in this study, the HRET model produces a complete 2D map of the internal tides surface signature. It relies on the optimal interpolation of altimeters' nadir tracks. This method is known to smooth the overall signal, which may explain this slight difference in amplitude compared with our result . This difference could also be explained by some residual barotropic signal remaining in the baroclinic signal after applying the spatial filtering.

When we compare the barotropic signal retrieved from our spatial filtering (see Fig. ), we recover a signal close to the FES2014 model, thereby validating our processing method. As for the phase of the baroclinic signal, it encounters an inversion at 21° S, near the VTR. This confirms a propagation of the baroclinic tides in two opposite directions. A slight phase delay is observed between the Lanczos method and the models, but our results remain consistent with the phenomenology of the area. In addition, this filtering method is simple and computationally cost-effective and still provides sufficiently accurate results. These characteristics motivated its use in this study.

We use regional simulations based on the forced ocean hydrodynamical model NEMO4.0.2. (Nucleus for European Modelling of the Ocean), which provides high resolution data . This regional model is named hereafter TAPIOCA-36. It benefits from an horizontal resolution of 1/36° (∼3 km), and 75 fixed z coordinates levels ranging from 0 to 5000 m depth. The grid resolution is finer in the first 100 m of the water column, counting 23 levels, while the thickness of the deepest model-level reaches 160 m. This configuration should be able to capture submesoscale phenomena, like meanders, jets, eddies and low-mode internal tides evolving in the upper layers of the ocean. A third-order upstream based scheme (UP3) with built-in diffusion is also implemented for momentum advection. The k–ϵ turbulent closure scheme constrains the vertical diffusion coefficients. Bottom friction is quadratic with a bottom drag coefficient of 0.0025, while we assume lateral wall free-slip boundary conditions. The temporal integration is achieved by an Asselin filter with a time step of 150 s. The time-splitting technique used in NEMO4.0.2. resolves the internal tides signal as it uses smaller time steps for the computation of the barotropic tides velocities. In this configuration, initial conditions for oceanic velocity fields, SSH, temperature and salinity, as well as open boundary conditions at the edges of the model domain, are given by the global ocean assimilative eddy-permitting GLORYS12v1 reanalysis in order to represent realistically the ocean large scale circulation . For similar reasons the model is forced during its time-integration by the surface atmospheric fluxes of the ERA-5 reanalysis . Eventually, FES2014 has been applied on the open boundaries to force the direction, elevation and barotropic currents of the 15 primary tidal components (M2, S2, N2, K2, 2N2, MU2, NU2, L2, T2, K1, O1, Q1, P1, S1, and M4) . We run the model over 2 years: 2008 is used for validation and 2009 for the rest of the study. For these two years, seasonal, monthly and daily outputs were computed for the following fields: temperature, salinity, SSH, oceanic horizontal and vertical velocities. An harmonic analysis is also computed on-line by the model to isolate and retrieve the 15 primary tidal frequencies, including M2. The method introduced by is used to separate barotropic and baroclinic tide constituents. This separation is directly performed at each time step by the model during the simulation. The baroclinic energy flux Fbc (Eq. ), the conversion C (Eq. ) and dissipation D (Eq. ) rates are then derived on-line, according to the following formulas: 1Fbc=∫-H0Vbcpbc‾dz(m3s-1)2C=∇zHVbtpbc‾(Wm-2)3D=C-∇Fbc(Wm-2) where H is the depth, Vbc is the baroclinic velocity, Vbt is the barotropic velocity, pbc is the baroclinic pressure.

To validate TAPIOCA-36 tidal forcing, we compare the M2 tidal signal contribution with the SSH over the spin-up year 2008 to the one of FES2014 (Fig. ). Figure  shows that the tidal amplitudes and phases are satisfactorily reproduced by TAPIOCA-36. The contribution of the M2 tidal frequency to the SSH of FES2014 refers only to the barotropic tide as a one-layer model, whereas TAPIOCA-36 merges both baroclinic and barotropic tides contributions by taking into account the stratification of the water column. It explains the stronger variability in the amplitude and phase of the tidal signal plotted for TAPIOCA-36. Subsequently, we validated qualitatively the stratification of TAPIOCA-36 against in situ data provided by the World Ocean Atlas (WOA) over the year 2008 . We average every available temperature and salinity profiles within a box extending from 20.5 to 29° S in latitude and from 40 to 33° W in longitude (see Fig. ). The mean temperature and salinity profiles of the first 500 m of the water column of TAPIOCA-36 show a good overall agreement with the ones reported by the WOA, although we note that TAPIOCA-36 is slightly saltier than the WOA data. This comparison provides a qualitative consistency check rather than a full validation of the model stratification. We refer the reader to for additional quantitative validation work of TAPIOCA-36 against ADCP data and GLORYS12v1 data.

We start with an overview of the internal tides' variability at the VTR. Altimetry and the TAPIOCA-36 simulation in 2009 provide complementary information to characterise the generation, the propagation and the dissipation of internal tides. On one hand, altimetry refers to internal tides which were actually observed over the past 27 years at the surface of the ocean. On the other hand, the TAPIOCA-36 product simulates internal tides using physical equations derived for this area. It therefore provides insights into the dynamics not only at the surface but throughout the water column.

The VTR is identified as a major generation site for internal tides, with conversion rates from barotropic to baroclinic energy reaching up to -0.3Wm-2, according to the model (see Fig. ). We note that the conversion from barotropic to baroclinic energy is not strictly negative in TAPIOCA-36. This does not mean that there is a transfer from baroclinic to barotropic energy, but rather indicates a phase shift between barotropic velocity and baroclinic pressure fields (see Eq. ), as explained by . We define 5 boxes surrounding the VTR for a finer local analysis and integrate the conversion rate within each box by summing the grid-cell conversion rates weighted by cell surface area. Conversion rates are expected to be the highest in box 3, as the VTR lens effect makes the energy converge at this location, following the study of . Our model quantitatively shows that box 3 accounts for nearly half of the conversion of barotropic energy into baroclinic energy. Moreover, the further away from box 3, the lower the conversion rate (see Fig. ).

After their generation, internal tides propagate away from the ridge, mostly southwards. We analyse their pattern of propagation and assess the consistency between the TAPIOCA-36 simulation and altimetry data along the track 137. To achieve this, we co-located the TAPIOCA-36 data with the trajectory followed by the satellite on track 137. In Fig. , we display the elevation of the SSH linked to the M2 baroclinic tide according to altimetry and our simulation. This comparison indicates that the baroclinic signal varies with the same order of magnitude both in the altimetric data and in the model, even though TAPIOCA-36 tends to amplify the signal, with a M2 baroclinic amplitude peak of 4 cm at the VTR (∼20.5° S) symbolised by a blue line on the Fig. . We notice that the altimetric signal is slightly offset from the TAPIOCA-36 simulation output. It is important to recall here that the harmonic analysis of altimetry has been conducted over 27 years of data, whereas the harmonic analysis of TAPIOCA-36 has been computed on one year only. Note that some holes remain in the TAPIOCA-36 product because of the presence of islands and seamounts. No interpolation has been applied to keep the baroclinic signal intact from any smoothing. At 22° S, the behavior of the model and of the altimetric data appear disparate as their baroclinic signals are not completely in phase anymore over a few hundreds of kilometres. In the next sections, we will see that interactions between internal tides and the background circulation are likely to happen at these latitudes and can alter the internal tides signature.

Besides, the spectral analysis displayed in Fig.  shows that the first mode of propagation is the most energetic. More precisely, the spectrum indicates a wavelength of approximately 140 km. The second mode is also observable, with a wavelength of around 65 km. As the altimetric track crosses the internal tides flux at an angle of about 20°, the actual wavelengths of the first and second mode of propagation are respectively 131 and 61 km. Nonetheless, there is a slight difference of around 5 km between the altimetric and the TAPIOCA-36 signals. This difference remains acceptable and is in agreement with the study of .

Despite this variability in the baroclinic signal between altimetry and TAPIOCA-36, the reflection beams of the baroclinic signal captured by altimetry fit the ones of the model, hence supporting the consistency between our different datasets. A reflection beam refers to a beam of internal tide energy that results from the reflection of a primary beam on the surface in our case. After being reflected, this beam propagates away from the reflection point following the direction imposed by the internal wave dispersion relation. In our analysis, these reflection beams are identified as coherent structures in the SSH signal, corresponding to regions where baroclinic energy remains concentrated along preferential directions. In particular, the first reflection beam happens at around 100 km away from the ridge. It corresponds approximately to the order of magnitude of the wavelength of the first mode of propagation (right panel of Fig. ). The second reflection beam also happens around 100 km away from the first beam. This indicates that the propagation of internal tides might be dominated by the first mode of propagation. The elevation of the SSH reaches its peak in the region south of the VTR at the second reflection beam, translating the presence of a more energetic signal, before decreasing. From this point, the following reflection beams are much closer to each other, separated by about 50 km only, which likely corresponds to the wavelength of the second mode of propagation (see Fig. ).

Once generated, internal tides are known to have a usual lifespan of a few hours to a few days until they dissipate . As in , we define the harmonic dissipation as the energy residuals between the conversion and the baroclinic flux (Eq. ). Therefore, we assume that the baroclinic energy which has been generated and isn't propagating has been dissipated.

Part of the dissipation of the M2 baroclinic tide may occur locally and also along the propagation path. From the dissipation map derived with TAPIOCA-36, we find that almost 45 % of the dissipation occurs locally, close to the ridge (Fig. ). Dissipation is still intense until 22° S with around 40 % of the dissipation happening before reaching the seamount located at this latitude. A bit more than 150 km separate the VTR from this seamount, corresponding approximately to the wavelength of the first mode of propagation of internal tides. As a consequence, we infer that most of the baroclinic energy is dissipated during the first beam of reflection.

This first analysis shows an intense generation of internal tides mostly located in the arc shape of the VTR. With an along track analysis, we deduce that the propagation of internal tides is dominated by the first mode of propagation, at a wavelength of around 131 km, followed by a second mode of propagation with a wavelength of 61 km. The harmonic dissipation mostly refers to the energy contained in the first mode of propagation, which loses most of its energy during its first beam of reflection. Considering that internal tides are fine scale processes, we now aim to further investigate the intra-annual variability of this region and how it may influence internal tides.

The VTR is located at a sub-tropical latitude. Therefore we can expect two contrasted seasons to likely influence the stratification of the water column, mostly due to the Sun radiative forcing variability. In the TAPIOCA-36 simulation outputs, the density profile appears really smooth from May to October, with a density variation of 2 units in 500 m (see Fig. ). We consider that a permanent pycnocline is located at a depth of around 150 m, where the profile slope breaks slightly. At this depth, we also notice a small bump on the Brunt–Väissälä frequency profile (right panel of Fig. ). In contrast, from November to April, a seasonal pycnocline appears around 50 m down. During this period, the ocean is strongly stratified: the Brunt–Väissälä frequency reaches a maximum of 0.0006 Hz at 50 m depth. This seasonal stratification has been evidenced recently with in situ observations in . Based on these profiles, we define hereafter two contrasted seasons:

A season spanning from May to October with a permanent pycnocline at 150 m, also named the winter season hereafter;

In the following subsections, we will analyze if and how these two contrasted seasons may have an impact on internal tides generated over the bathymetric slope of the VTR.

We have seen that the seasonal pycnocline was associated with higher conversion rates from barotropic to baroclinic energy. How does it reflect on the propagation of internal tides? We assess the baroclinic tide propagation by the computation of the baroclinic flux (see Eq. ), performed by the numerical model. We notice that the baroclinic flux is slightly more energetic during the so-called summer season, consistent with the more intense generation of internal tides from November to April. The baroclinic flux follows the same pattern during both seasons: starting from the VTR, internal tides propagate mainly towards the south until 27° S, that is to say more than 500 km away from the ridge (Fig. ). Nonetheless, from 23° S the flux is deflected eastward along its course. This deflection could be correlated with the presence of a seamount around 22.2° S or might be influenced by the background circulation, investigated hereafter.

The medium of propagation of internal tides in this region is influenced by a seasonal pycnocline, introducing abrupt changes of the physical properties in the water column near the surface. We investigate if these seasonal changes have an impact on the wavelength of internal tides by using altimetry (see Fig. ). We conduct a seasonal spectral analysis on the track 137 of the TOPEX/Poseidon mission, presented previously. We take advantage of the 27-year long time series to divide our dataset into two different periods, by gathering the data belonging to the winter (resp. summer) season of each year from 1993 to 2020, reducing the impact of aliasing . In Fig. , we note that the first mode of propagation keeps the same wavelength over the year, being around 131 km when corrected by the angle at which the altimeter overpasses the internal tides flux. However the second mode of propagation experiences a change: in May–October, the wavelength of the second mode is about 5 km longer than during November–April along the chosen track. On this spectrum, we also notice that the mode-2 of internal tides is more energetic in winter than in summer, with a higher Power Spectral Density. This seasonal variability and its impact on the internal tides' behavior will be discussed in the following section.

The shape of the baroclinic flux and the spatial chaotic pattern of the internal tides dissipation lead us to investigate the role of the background meso- to submesoscale dynamics, using the TAPIOCA-36 simulation. We plot the daily mean relative vorticity computed at the pycnocline depth and visualize it jointly with the baroclinic flux, in order to evaluate whether the internal tides could interact with other ocean processes in this turbulent region.

By looking at snapshots over the year 2009, we spot a mesoscale anticyclonic eddy entering the propagation area of the main baroclinic flux on the 13 February 2009. The center of this eddy is arriving from the open sea and evolving westward to the Brazilian coast along the 23.5° S parallel, where we highlighted a peak of dissipation between November–April (see Fig. ). We follow the course of this anticyclonic eddy by selecting four key moments, corresponding to similar tidal regimes. On the 27 February, the baroclinic flux starts to be deflected by about 25° towards the east when crossing the eddy at its center, as if the energy was trapped and concentrated by the anticyclonic eddy. On the 13 March 2009, the eddy is located directly south of the internal tide generation hotspot. The associated baroclinic flux mainly propagates southwards but is also slightly deflected towards the east and the west. On the 12 April 2009, the eddy finally escapes the main internal tides propagation area and deflects the flux by about 25° towards the west.