First, to examine the variability of IT responses to MEs, we explore all 25 h snapshots of IT energy flux from the AMAZON36 outputs during the SOND period. Following the method of Kelly et al. (2010), barotropic and baroclinic tidal constituents were separated. This separation is performed directly by the NEMO model to ensure accuracy, providing the total energy for all resolved propagation modes at a given tidal frequency (Tchilibou et al., 2022). Our analysis focuses solely on the M2 harmonic, the dominant tidal constituent in this region (Gabioux et al., 2005; Fassoni-Andrade et al., 2023).

The energy budget for IT can be expressed from the following equations (Wang et al., 2016; Buijsman et al., 2012; Kerry et al., 2013; Tchilibou et al., 2022; Siyanbola et al. 2024): 1∇h⋅F+D+R=C

In contrast to energy budgets decomposed into vertical modes, we refer to these as the undecomposed IT energy equations. Here, ∇h⋅F is the divergence of the depth-integrated energy flux, F=(Fx,Fy) the energy flux vector, C represents the depth-integrated barotropic-to-baroclinic energy conversion, and D is the depth-integrated energy dissipation term. The term R includes the energy tendency term, implicit horizontal dissipation, wave-mean flow and wave-wave interaction terms, and other offline computation errors. ∇h=(∂∂x,∂∂y) is the horizontal gradient operator.

In the following, a particular attention is given to depth-integrated and time-averaged energy flux term F, which was defined as (Tchilibou et al., 2022; Assene et al. 2024): 2[Fbc,Fbt]=∫-Hηubcpbcdz,ubtpbt, where u=(u,v) is the horizontal tidal velocity vector, and p the tidal pressure. Here, the subscripts bt and bc denote barotropic and baroclinic components, respectively. η is the sea surface height and H is the seafloor depth.

Second, to investigate whether the IT responses to MEs is mode-dependent and to examine potential inter-modal energy transfer, we project the M2 tidal constituent onto a set of vertical modes for selected 25 h snapshots that capture ME-induced IT responses. This selective approach substantially reduces the computational cost associated with processing high-resolution 3D data for all 25 h windows during the SOND period.

For each selected snapshot, we first extract the M2 harmonic via harmonic analysis. Although performing harmonic fits over short (25 h) segments may introduce frequency leakage from nearby tidal constituents (e.g., S2, N2, and K2) into the M2 signal, this effect is expected to be small in our case because the tidal regime is strongly M2-dominated, accounting for more than 70 % of the total tidal energy (e.g., Gabioux et al., 2005; Tchilibou et al., 2022; Fassoni-Andrade et al., 2023). This approach is consistent with previous studies that have successfully applied harmonic analysis to similarly short records to resolve semidiurnal constituents (e.g., 17–29 h M2 tidal observations in Waterhouse et al., 2018), demonstrating that dominant semidiurnal tides can be reliably estimated from short-duration data.

We then decompose the M2 tidal currents and pressure using a locally computed set of vertical modes. This method provides a more accurate separation of barotropic and baroclinic tides than simpler approaches (Kelly, 2016; Lahaye et al., 2020; Lahaye et al., 2024; Siyanbola et al. 2024).

The vertical modes are obtained by solving the standard Sturm–Liouville eigenvalue problem at each horizontal grid point, using the local mean stratification profile (based on the time-mean buoyancy frequency, N2‾), and assuming a flat bottom, a free surface, and no background flow (Gerkema and Zimmerman, 2008; Bella et al., 2024): 3∂z∂zΦnN2‾+Φncn2=0, with the boundary conditions: 4∂zΦn=0 at z=-H, and g∂zΦn+N2‾Φn=0 at z=η‾, where ∂z denotes the partial derivative in z-direction, Φn is the horizontal velocity/pressure eigenfunction for mode n, cn is the modal phase speed and g is the acceleration due to the gravity. The associated vertical velocity/buoyancy eigenfunction, φn, is given by: 5∂zφn=Φn, and ∂zΦn=-N2‾cn2φn.

It should be noted that the flat-bottom assumption could represent a limitation for higher-mode projections near steep topography such as the Ceará Rise seamount. The errors associated with this approximation are expected to be of a few percent for the dominant low modes (Kelly, 2016).

The vertical modes satisfy the orthogonality condition (Kelly, 2016; Lahaye et al., 2024; Bella et al., 2024): 6∫-Hη‾ΦmΦndz=Hδmn, where δmn is the Kronecker delta and η‾ is the time-averaged sea surface height.

We solved Eq. (3) for the first 11 modes (n=0,1,…,10) at each grid point, where n = 0 represents the barotropic mode. In this study, the analysis of energy flux focuses primarily on the first three baroclinic modes (n = 1,2,3), which are the most dynamically significant at the model's resolution (∼ 3 km). These three baroclinic modes account for 96.2 % (33.2 %), 96.8 % (37.9 %), and 97.2 % (26.3 %) of the total baroclinic energy flux (relative to the combined baroclinic and barotropic flux) in the NE, CEC, and CEE cases, respectively. They therefore capture the dominant share of the baroclinic energy, supporting their use as the basis of our analysis.

The horizontal tidal velocity u and pressure p fields are projected onto these modes to obtain the depth-independent modal amplitudes: 7[un(x,t),pn(x,t)]=1H∫-Hη‾[u(x,z,t),p(x,z,t)]×Φn(x,z)dz, with x=(x,y) denoting the horizontal direction.

The full 3D structure of un fields for each mode can be reconstructed as (Li et al., 2024): 8un(x,z,t)=un(x,t)Φn(x,z).

To analyze the inter-modal energy transfer/scattering and redistribution, we examine the terms of the modal energy budget of a given mode interacting with physical features such as topography and mesoscale flow (Fan et al., 2024; Bella et al., 2024; Kelly, 2016; Kelly and Lermusiaux, 2016): 9∇h⋅Fm+Dm+Ψm=∑n(Cmn+Amn+Hmn+Vmn+Bmn). Here:

Cmn is the nonlinear scattering (from mode m>0 into mode n) of energy by topography and stratification.

A previous seasonal-scale study by Bella et al. (2024) found the nonlinear coupling terms Cmn, Amn, Hmn, and Vmn to be dominant across the North Atlantic basin. For our investigation on a daily timescale, a preliminary analysis identified Cmn and Hmn as the dominant terms in our study region. We therefore focus on estimating these dominant couplings terms as defined by Bella et al. (2024): 10Cmn=〈Hpmun⋅Tnm-HpnTmn⋅um〉,11Hmn=〈-H(Umnhun)⋅um〉, With Tmn=1H∫-Hη‾Φm∇h(Φn)dz, (Umnh)ij=1H∫-Hη‾ΦmΦn∂U‾h,i∂xjdz.

Here, the angle bracket 〈⋅〉 denotes the average over a M2 tidal period, U‾h=(U‾,V‾) is the time-averaged total horizontal velocity vector. ∂U‾h,i∂xj is the tensor.

The modal horizontal kinetic energy (HKEn) of M2 IT is estimated as (Kelly et al., 2012; Fan et al., 2024): 12HKEn=ρ0H2〈un2+vn2〉, where ρ0 is the reference density.

The energy transfer matrices – including topographic scattering (Cmn) and (Hmn) – are decomposed into symmetric and antisymmetric components, following the established methodology (Savage et al., 2020; Bella et al., 2024). For any general transfer matrix (Xmn), the standard mathematical definitions are: the antisymmetric component, XmnA=12(Xmn-Xnm), and the symmetric component, Xmns=12(Xmn+Xnm).

The antisymmetric component, XmnA, represents the internal reallocation of energy – specifically, the scattering or transfer of energy among the various IT vertical modes. Critically, this process conserves the total energy of the IT field, as it analytically redistributes energy across the system modes and spatial scales without introducing a net gain or loss. For instance, the term Cmn is inherently antisymmetric and thus provides a canonical reference for conservative internal energy transfer.

Conversely, the symmetric component, Xmns, describes the net energy exchange between the IT and the low-frequency background flow. When integrated in a basin, this component acts as a source or sink for the IT system, quantifying the total energy gained from or lost to the slowly varying circulation (Bella et al., 2024).

The direction of energy transfer is interpreted from the sign of the matrix elements. Considering a specific mode m:

For the full matrix Xmn, a negative value indicates a net forward transfer of energy from mode m to mode n, while a positive value indicates a net backward transfer from mode n to mode m;

Third, to investigate whether the IT responses to MEs depend on the eddy encounter location, including the associated background conditions (currents and stratification), we detected and characterized eddies from 25 h mean snapshots of AMAZON36 outputs during the SOND period.

The mesoscale activity in this region during the 2015 ASOND period was previously assessed by Tchilibou et al. (2022). Their analysis, which compared the model's surface EKE with satellite data, showed reasonable agreement in both the spatial pattern and amplitude of the mean EKE, especially in regions dominated by the NECC.

Eddies were identified in our model outputs using the Okubo–Weiss parameter (W), chosen for its ability to detect coherent vortices on specific isopycnal surfaces or depths (Okubo, 1970; Weiss, 1991; Kurian et al., 2011; Xu et al. 2019). The W parameter is defined as: 13W=Sn2+Ss2-ζ2, where the normal strain (Sn) and shear strain (Ss), and the relative vorticity (ζ) are: 14Sn=∂u∂x-∂v∂y,   Ss=∂v∂x+∂u∂y,   ζ=∂v∂x-∂u∂y.

Regions where rotation (W<0) dominates over strain (W>0) indicate potential eddy cores.

The detection of eddies on selected isopycnal surfaces (between 23 and 27 kgm-3 isopycnals) following the procedure of Kurian et al. (2011) and Xu et al. (2019). First, the W fields were smoothed using a 50 km × 50 km half-power filter to suppress small-scale noise. For each 25 h mean snapshot, we then applied a constant threshold of W0 = -3 × 10⁻¹¹ s-2 to isolate vorticity-dominated regions (W<W0). Closed contours corresponding to W=W0 were identified, and each contour was subjected to a series of quality control criteria to be classified as an eddy: a shape error (deviation from a fitted circle) of less than 50 %, a mean azimuthal velocity greater than 5 cms-1, and a radius larger than 50 km.

For each identified eddy, its thickness was defined as the vertical extent of its W0 contours, and its center location was defined as the centroid of the closed W0 contour. Detected eddies were classified as cyclonic or anticyclonic based on the sign of their potential vorticity anomaly (PVA, positive for CEs and negative for AEs; Fig. 2a).

To analyze the eddy dynamical structure, we used the framework of rescaled potential vorticity (PVr). This method filters out high-frequency wave noise to isolate the balanced mesoscale signal. The PVr is derived from the classical Ertel (1942) potential vorticity, rescaled by a reference stratification at rest, ρ∗(z), following the approach of Morel et al. (2023, 2019) and subsequent studies (e.g., Delpech et al., 2020; Aguedjou et al., 2021; Ernst et al., 2023).

Its expression is: 15PVr=(∇×U+f)⋅∇Z(ρ)=∇⋅[(∇×U+f)Z(ρ)], where U=(U‾,V‾,W‾) is the time-mean total velocity vector, and f is the local Coriolis parameter. Z(ρ) is a rescaling function of time-mean potential density ρ, defined using the reference density profile ρ∗ so that Z(ρ∗(z))=z. ρ∗ is defined by the adiabatically rearranged state of minimum potential energy, following the concept of Lorenz (1955) as formalized by Nakamura (1995) and Winters and D'Asaro (1996). An eddy dynamical core is then identified by its anomaly from the background planetary vorticity, PVA=PVr-f, within a layer bounded by two isopycnals.

To distinguish subsurface eddies from surface-intensified ones, we classified them based on the isopycnal level of their core of PVA. Following the method of Kouogang et al. (2025), we used the base of the pycnocline (defined by ∼ 26.5 kgm-3 isopycnal) as the boundary of the lower pycnocline depth. Eddies with their PVA core on isopycnals less dense than 26 kgm-3 were classified as surface-intensified eddies (Fig. 2b), while those with their core on denser isopycnals (> 26.5 kgm-3) were classified as subsurface-intensified eddies as formalized by Aguedjou et al. (2021) in the tropical Atlantic Ocean. This classification scheme was applied to all eddies detected during the SOND period. This study focuses specifically on these surface-intensified eddies.

We first analyse the tidal energy diagnostics for the NE case to establish an eddy-free propagation baseline. Figure 6a–c maps the energy flux propagation and HKE for the first three modes, revealing distinct patterns for each one.

Mode-1 energy propagation is highly dominant. The fluxes, generated from sites A and D, constructively form a notably coherent beam that converges and propagates northeastward (∼ 37° azimuth) for over 1100 km with minimal deviation (Fig. 6a). This long-distance propagation maintains a relatively constant HKE of 150–200 Jm-2, with a wavelength (λ1) estimated between 90–125 km. In contrast, the Mode-2 flux propagates a significantly shorter distance (500–600 km, λ2: 60–85 km) and terminates abruptly at the seamount (Fig. 6b). Mode-3 forms no coherent beams but appears as scattered patches extending only 50–100 km (λ3: 35–50 km; Fig. 6c). Along their respective beams, Mode-1 and Mode-2 exhibit stronger energy flux amplitudes (> 200 Wm-1) compared to Mode-3 (< 200 Wm-1). The spatial distribution of these modal energy fluxes is consistent with the vertical structure of the corresponding baroclinic velocity profiles (Appendix B, Figs. B1 and B2). A sharp Mode-2 damping is clearly visible over the seamount, while Mode-3 energy appears trapped over the seamount and ridge where the Mode-1 flux diminishes, suggesting that topographic features drive scattering to higher vertical modes.

To quantitatively assess the mechanisms responsible for this energy loss, we compute intermodal energy transfer terms (Eqs. 9–11) and map only the dominant terms in Fig. 5d–o. These dominant terms, of order of magnitude comparable (O(10-8Wmkg-1)), are topographic scattering term (Cmn, Eq. 10), and the horizontal shear term (Hmn, Eq. 11) of background flow. They then are separated into its antisymmetric and symmetric part for the analysis. All other background flow-induced energy transfer terms, such as advection and vertical shear, are negligible in comparison (O(10-10Wmkg-1)); figures not shown).

The analysis reveals a primary pathway of intermodal energy transfer driven by topographic scattering term (Cmn), which is antisymmetric by construction. Along the IT path from generation sites A and D, a dominant forward energy cascade (|Cmn|∼ 4 × 10⁻⁸ Wmkg-1) occurs near major bathymetric features – the shelf break and seamount. Specifically, energy is sequentially transferred from Mode-1 to Mode-2 IT for C12 (Fig. 6e, blue patches), and then from Mode-2 to Mode-3 IT for C23 (Fig. 6f, blue patches). For C13, however, energy exchanges between Mode-1 and Mode-3 IT are bidirectional – energy is both lost and gained – and spatially confined to the vicinity of topographic features (Fig. 6d, blue and red patches). This could stem from the background conditions, particularly the notable effect of the horizontal stratification gradient in the coupling term Cmn (Appendix A, Fig. A1), or the influence of shear in the background flow (NBC, NECC), the effect of which is discussed in detail below.

Decomposing the horizontal shear term Hmn (Fig. 6g–i) into its antisymmetric (Fig. 6j–l) and symmetric (Fig. 6m–o) components shows that its net influence (|Hmn|∼ 4 × 10⁻⁸ Wmkg-1) is more due to the symmetric part. This latter facilitates energy exchanges between the background flow and the IT modes along the IT path from the most energetic sites. Indeed, before the seamount, the symmetric terms H12S and H13S are both strongly dominant in their net effect, while H23S is weakly dominant in H23. In this region, energy is strongly transferred from the Mode-2 and Mode-3 background flow to the Mode-1 IT (Fig. 6m and n, red patches). Over the seamount, the symmetric part of Hmn becomes notable. Here, energy transfers are weak overall, but a notable transfer occurs from the Mode-2 IT to the Mode-3 background flow (Fig. 6o, blue patches).

In essence, in the NE case, coherent energy flux from sites A and D converges and propagates until encountering major topographic features (seamounts and ridges). While Mode-1 IT energy propagates over long distances with amplitudes exceeding 200 Wm-1, the higher modes behave differently. Mode-2 IT energy, despite having a comparable amplitude to Mode-1, is effectively damped. In contrast, the weaker Mode-3 IT energy (< 200 Wm-1) becomes trapped by the topography. The interaction with topographic features, potentially enhanced by the background flow, triggers significant intermodal energy transfer on the order of 10⁻⁸ Wmkg-1. This transfer is governed by two primary mechanisms: (1) topographic scattering drives a dominant forward energy cascade through the IT modes (Mode-1 → Mode-2 → Mode-3), and (2) the horizontal shear of the background flow facilitates a direct energy scattering from the Mode-2 and Mode-3 background flow to Mode-1 IT.

We next examine IT responses when the energy flux from sites A and D encounter the core of a surface-intensified CE (CEC case, Fig. 2b). The CE, centered at 4.9° N, 44.4° W above the localized mid-seamount, has a radius of 157 km, maximum velocity 1.35 ms-1, and a core bounded by 23–25.5 kgm-3 isopycnals extending ∼ 150 m within the pycnocline.

Prior to interaction, the incident mode-1 IT energy fluxes converge and interfere. Upon encountering the CE core, this energy is refracted into a single beam (Fig. 7a), which emanates from the eddy center and propagates northward at approximately 35° from their northeastward incident direction. Both incident and refracted beams maintain comparable HKE of 150–200 Jm-2 (Fig. 7a), though the refraction process locally confines the energy, leading to a reduction in HKE (25–50 Jm-2) in the northwestern lee of the eddy. Concurrently, the Mode-2 IT energy flux is blocked at the southern edge of the CE and seamount (Fig. 7b), while Mode-3 appears as scattered patches in the regions where Mode-2 is trapped (Fig. 7c), indicating active intermodal energy scattering. As in the NE case, Mode-1 and Mode-2 IT exhibit higher energy flux amplitudes (> 200 Wm-1) along their beams than Mode-3 (< 200 Wm-1) (Fig. 7a–c). The  vertical structure of the along-transect baroclinic velocity further supports these results (Appendix B, Figs. B1 and B3).

An analysis parallel to that conducted for the NE case identified the topographic scattering term (Cmn) and the horizontal shear term (Hmn) of the background flow as the dominant mechanisms responsible for the active energy scattering observed.

The analysis of the term Cmn in the CEC case reveals a distinct coupling pattern modulated by the CE core in conjunction with the seamount along the IT path from sites A and D. A dominant forward energy transfer (|Cmn|∼ 4 × 10⁻⁸ Wmkg-1) from Mode-1 to Mode-2 occurs near the shelf break for C12 (Fig. 7e, blue patches), consistent with the NE case (Fig. 6e). A significant shift occurs near the southern edge and core of the CE, where a dominant backward energy transfer is observed (with the exception of Mode-1 to Mode-3 IT). Here, energy is sequentially gained by Mode-1 from Mode-2 for C12 (Fig. 7e, red patches near the southern edge and core of the CE) and by Mode-2 from Mode-3 for C23 (inverse cascade, Fig. 7f, red patches), while energy is simultaneously lost from Mode-1 to Mode-3 for C13 (direct forward transfer, Fig. 7d, blue patches). These patterns could be due to either the horizontal stratification gradient in the coupling term Cmn associated with the CE (Appendix A, Fig. A1), or shear in the background flow (NECC/CE).

Analysis of the background flow horizontal shear term (Hmn) shows that its magnitude (|Hmn|∼ 4 × 10⁻⁸ Wmkg-1) is comparable to the topography scattering term as in NE case. In the CEC case, along the energy flux from sites A and D, the net effect of Hmn (Fig. 7g–i) is primarily due to its symmetric part (Fig. 6m–o), except for term H13. Between the shelf break and the southern edge of the CE, both the symmetric terms H12S and H23S are both strongly dominant in their net effect. In this region, energy is both lost and gained between the Mode-1 IT and the Mode-2 background flow, and between the Mode-2 IT and the Mode-3 background flow (Fig. 7n and o, blue patches). This bidirectional transfer is spatially confined to this region and more pronounced between the Mode-1 IT and the Mode-2 background flow, a pattern also present in the NE case (Fig. 6h and n). Near the CE center and seamount, the terms H13A and H13S weakly combine to form H13 (Fig. 7j and m, blue and red patches), while H12S and H23S both remain dominant in their net effect. These patterns coincide with the region where energy fluxes are deflected. Here, energy transfer is stronger for H12S than for H23S. Specifically, the background flow loses energy to the IT modes: the Mode-2 background flow energizes the Mode-1 IT (Fig. 7n, red patches), and the Mode-3 background flow energizes the Mode-2 IT (Fig. 7o, red patches). These overall patterns indicate a deflection of Mode-1 and Mode-2 IT, and provide strong evidence for a dominant energy pathway from the background flow to the IT modes driven by horizontal shear. This latter is coupled with direct forward energy transfer between IT modes driven by topographic scattering previously observed.

In summary, in the CEC case, the interaction with the CE core dictates distinct fates for IT modes. Mode-1 IT from sites A and D is not freely propagating but is primarily refracted into a single northward beam. In contrast, Mode-2 IT is blocked, and Mode-3 IT is scattered at the eddy edge and seamount. Energy flux amplitudes for Modes 1 and 2 exceed 200 Wm-1 along their beams, whereas Mode-3 remains below this threshold. This interaction facilitates a significant energy transfer (O(∼10-8Wmkg-1)) governed by a complex interplay of two mechanisms: (1) a dominant backward energy cascade, where horizontal shear transfers energy from the Mode-3 background flow to Mode-2 IT, and from the Mode-2 background flow to Mode-1 IT; and (2) a forward scattering, where topography directly transfers energy from Mode-1 to Mode-3 IT.

Finally, we assess IT interactions with the edge of a surface-intensified CE centered at 5.3° N, 45.0° W (radius 143 km, maximum velocity 1.23 ms-1, core bounded by 23–25.5 kgm-3 isopycnals extending ∼ 100 m above the pycnocline).

This interaction yields a different kinematic response. The incident Mode-1 energy fluxes from sites A and D converge and, at the eddy edge, clearly diffract into two distinct beams (Fig. 8a): one propagating northward (∼ 39°) and the other eastward (∼ 35°) relative to their northeastward incident direction. The northward-refracted beam maintains high HKE (150–200 Jm-2), while HKE is sharply reduced (25–50 Jm-2) in the northeast lee of the CE (Fig. 8a). Separately, the eastward-refracted beam, less energetic (HKE < 100 Jm-2) than the northward beam, passes near the eastern edge of a small AE. Mode-2 flux is sheared at the CE edge with limited directional change (Fig. 8b), and Mode-3 becomes trapped along the northeastern CE edge and near the ridge (Fig. 8c). Consistent with previous cases, Mode-1 and Mode-2 exhibit higher energy flux amplitudes (> 200 Wm-1) than Mode-3 (< 200 Wm-1), and the energy flux patterns is supported by the vertical structures of the baroclinic velocity (Appendix B, Figs. B1 and B4).

As in prior cases, the analysis identified topographic scattering (Cmn) and horizontal shear (Hmn) of the background flow as the two dominant mechanisms driving intermodal scattering in the CEE case.

The analysis of the term Cmn reveals a pattern modulated by the CE edge and seamount along the IT path from sites A and D. A dominant forward energy transfer (|Cmn|∼ 4 × 10⁻⁸ Wmkg-1) from Mode-1 to Mode-2 for C12 (Fig. 8e, blue patches) and from Mode-1 to Mode-3 IT for C13 (Fig. 8d, blue patches) occurs near the shelf break. Near the eastern edge of the CE and the southern flank of the seamount, inter-modal IT energy transfers – between Mode-1 and Mode-2 IT, and between Mode-2 and Mode-3 IT – are both strong and bidirectional (i.e., forward and backward transfers coexist; Fig. 8e and f, blue and red patches), and remain spatially confined to this region. An exception is the Mode-1 to Mode-3 IT transfer (Fig. 8d), which is weak in this area.

These overall patterns indicate that the CE edge inhibits the forward energy cascade observed in the NE case and instead initiates a dual mechanism: a potential flow shear-induced energy transfer between the background flow (NECC/CE) and IT modes, and a topographically-driven energy scattering between IT modes.

As in previous cases, the horizontal shear term (Hmn) in the CEE case is of comparable magnitude (|Hmn|∼ 4 × 10⁻⁸ Wmkg-1) to the topographic scattering term. The net effect of Hmn (Fig. 8g–i) is primarily dominated by its symmetric part (Fig. 8m–o), except for term H13. Along the IT path from sites A and D, terms H12S and H23S are both strongly dominant in their net influence, while H13A and H13S weakly combine to form H13 (Fig. 8g, j, and m) – a pattern also present in the CEC case (Fig. 7g, j, and m). The energy transfer pattern along this path is characterized by alternating bands of energy loss and gain (blue and red patches), reflecting bidirectional transfers between the background flow and IT modes. These alternating bands are particularly striking and spatially extended for H12S (Fig. 8h and n). They are distinct from those observed in the previous cases, appearing both upstream and downstream of the seamount and near the eastern CE edge. These patterns could result from an interference structure associated with the IT field. For H23S, however, forward energy transfer dominates: the Mode-2 IT energizes the Mode-3 background flow near the CE edge (Fig. 8o, blue patches), coinciding with the region where energy fluxes are deflected. These overall patterns provide strong evidence for a dominant energy pathway between the background flow and IT modes driven by horizontal shear, coupled with a topographically-driven energy transfer between IT modes.

In summary, in the CEE case, upon interacting with the CE edge, each IT mode meets a distinct fate. Mode-1 IT from sites A and D splits into two energetic beams, propagating northward and eastward with energy fluxes exceeding 200 Wm-1. In contrast, Mode-2 IT is sheared apart, while Mode-3 IT is scattered by the eddy edge and seafloor topography, its energy flux remaining below 200 Wm-1. During this encounter, a significant energy transfer (∼ 10⁻⁸ Wmkg-1) occurs through dual mechanism distinct from that observed in the CEC case: (1) a dominant bidirectional energy transfer between the background flow and the IT modes (Mode-1 ↔ Mode-2 ↔ Mode-3) driven by horizontal shear, which can act to suppress the topographically-driven downscale energy, and (2) a bidirectional energy transfer between the IT modes driven by topographic scattering.