We use a regional model configuration that consists of a host grid (TROPICO12, 1/12° horizontal resolution and 125 vertical levels) that covers the tropical and subtropical Pacific Ocean basin from 142° E–70° W and 46° S–24° N, introduced in Part 1. The oceanic reanalysis GLORYS2V4 prescribes initial conditions for temperature and salinity as well as the forcing with daily currents, temperature, and salinity at the open lateral boundaries. ERA5 produced by the European Centre for Medium-Range Weather Forecasts ECMWF, provides atmospheric forcing at hourly temporal resolution and a spatial resolution of 1/4° to compute surface fluxes using bulk formulae and the model prognostic sea surface temperature. The model is forced by the tidal potential of the five major diurnal (K1, O1) and semidiurnal (M2, S2, N2) tidal constituents. At the open lateral boundaries it is forced by barotropic SSH and barotropic currents of the same five tidal constituents taken from the global tide atlas FES2014 Finite Element Solution 2014,.

We build on hourly numerical simulation outputs from a higher-resolution horizontal grid refinement within the host grid in the southwestern tropical Pacific Ocean encompassing New Caledonia (CALEDO60). This nesting grid features 1/60° horizontal resolution or ∼ 1.7 km grid spacing initialized by Adaptive Grid Refinement in Fortran AGRIF,. Specifically, we make use of the three-dimensional velocity, temperature, salinity, and pressure fields as well as SSH. Coherent tidal harmonics are taken from Part 1 based on harmonic analysis and vertical mode decomposition. We refer the reader to Sect. 2.2 in Part 1 for more details. Both full-model variables and tidal harmonics are constrained to a full calendar year (model year 2014). Constraining the analysis to a full calendar year relies upon a compromise between high computational expenses and a time series long enough for a robust extraction of the coherent tide.

The model's capability to realistically simulate ocean dynamics that range from the large-scale circulation down to high-frequency motion using climatology, satellite altimetry, and in situ measurements was addressed in Part 1. Regarding the dominant semidiurnal M2 internal tide, confidence in the model's SSH signature is explicitly given by comparison with HRET, revealing reasonable amplitude and large-scale (interference) patterns (see Fig. 13a–d in Part 1). Furthermore, glider observations revealed the model's accurate representation of the spatiotemporal variability of the semidiurnal energy flux south of New Caledonia, including the location, magnitude, and vertical structure/extent of the westward internal-tide energy propagation characterized by narrow tidal beams .

Similarly to Part 1, the internal-tide life cycle, i.e., internal-tide generation, propagation, and dissipation, is studied using the depth-integrated baroclinic energy equation : 1∇h⋅Fbc-C+Dbc=0, where ∇h⋅Fbc is the baroclinic energy flux divergence with ∇h the horizontal gradient operator and Fbc=(Fx,Fy) the energy flux vector, C is the barotropic-to-baroclinic conversion term, and Dbc is the baroclinic energy dissipation. Dbc is computed as the residual of ∇h⋅Fbc and C. Further, we neglect the tendency of the total energy, i.e., ∂/∂t∫-H0(KEbc+APE)dz, where KE_bc is the baroclinic kinetic energy and APE available potential energy. Furthermore, Fbc consists only of contributions from hydrostatic pressure work, omitting contributions from KE and APE advection, nonhydrostatic pressure work, and diffusion . These simplifications were made since the given terms were found to be negligibly small in the above studies when averaged over a set of tidal periods.

In Part 1, we estimated the coherent M2 internal-tide energy budget based on a harmonic analysis referenced to a full model calendar year. Here, in Part 2, our major objective is to deduce time variability from Eq. () for the semidiurnal frequency band (^D2, 10–14 h) through a bandpass-filtering technique following , , and . Specifically, time variability is inferred by decomposing the bandpass-filtered contribution in Eq. () into the coherent (^coh) and incoherent (^inc) parts for the horizontal velocity vector u and the pressure perturbation p: 2uD2=ucoh+uinc,pD2=pcoh+pinc. uD2 and pD2 can be further decomposed into their barotropic (_bt) and baroclinic (_bc) parts. The former is estimated by the depth average and the latter by the departure from the barotropic depth average: 3ubcD2=uD2-1H∫-HηuD2dz︸ubtD2,pbcD2=pD2-1H∫-HηpD2dz︸pbtD2, where H is the water column depth. The semidiurnal conversion term CD2 can then be written as 4CD2=1T∫T-∇hH⋅ubtD2pbcD2(-H)dt5=1T∫T(-∇hH⋅ubtcohpbccoh(-H)︸Ccoh-∇hH⋅ubtincpbcinc(-H)︸Cinc*-∇hH⋅ubtcohpbcinc(-H)-∇hH⋅ubtincpbccoh(-H)︸Ccross︸Cinc)dt, decomposed into the coherent (Ccoh) and incoherent conversion (Cinc=Cinc*+Ccross), averaged over a given time period T. Using least-squares fitting to extract the coherent component, the cross-terms Ccross=Ccross1+Ccross2, where Ccross1=-∇hH⋅ubtcohpbcinc(-H) and Ccross2=-∇hH⋅ubtincpbccoh(-H), are, by construction, considered incoherent. This classification follows from the orthogonality condition inherent in the least-squares framework: the residual (i.e., the incoherent component) is uncorrelated with the fitted coherent signal and lacks a consistent phase relationship with the tidal forcing. In other words, there is no preferred phasing between coherent and incoherent motions. As a consequence, bilinear products between coherent and incoherent fields tend to average out or remain negligibly small over the regression interval . However, as we show in the analysis below, these cross-terms can account for a substantial fraction of the variability on shorter timescales. We specifically focus on assessing their relative importance to better understand temporal variations in the conversion term and the physical mechanisms that drive them.

Similarly to CD2, the semidiurnal depth-integrated energy flux FbcD2 can be written as 6FbcD2=1T∫T∫-HηubcD2pbcD2dzdt7=1T∫T(∫-Hηubccohpbccohdz︸Fbccoh+∫-Hη(ubcincpbcinc+ubccohpbcinc+ubcincpbccoh)dz︸Fbcinc)dt.

The coherent terms ubtcoh, ubccoh, and pbccoh are taken from the harmonic analysis and vertical mode decomposition carried out in Part 1. Here, they are representative of the semidiurnal frequency band including the M2, S2, and N2 tidal frequencies. The barotropic part is equivalent to mode 0 and the baroclinic part to the sum of modes 1–9. The incoherent terms are computed as the difference between the above semidiurnal bandpassed and coherent time series, i.e., 8ubtinc=ubtD2-ubtcoh,ubcinc=ubcD2-ubccoh,pbcinc=pbcD2-pbccoh.

Semidiurnal energy dissipation DbcD2 is defined as 9DbcD2=1T∫T(-∇h⋅FbcD2+CD2)dt10=1T∫T(-∇h⋅Fbccoh+Ccoh︸Dbccoh)dt+1T∫T(-∇h⋅Fbcinc+Cinc︸Dbcinc)dt.

An important conclusion concerning the coherent internal-tide analysis in Part 1 was that Dbccoh may not be associated entirely with true energy dissipation. In fact, Dbccoh represents both energy dissipation and energy transfer to the incoherent tide. It also includes the energy transfer to higher harmonics (higher-frequency waves), which, however, is presumably expressed in numerical dissipation due to spatial resolution constraints . While DbcD2 accounts for actual energy dissipation, Dbcinc consists of both the fraction by which Dbccoh is mistakenly associated with true energy dissipation (or the error by which energy dissipation in Dbccoh is overestimated) and incoherent energy dissipation.

A ray-tracing method following is employed, which models the horizontal propagation of internal gravity wave modes in the presence of spatially varying topography, planetary vorticity, stratification, and depth-averaged currents. Here, the objective is to interpret the tidal beam's departure from tidal coherence in the far field, attributed to the refraction by mesoscale eddies. Specifically, we model semidiurnal ray paths for the first baroclinic mode for monthly varying stratification and currents. Note that the choice of depth-averaged currents is simplistic and relies on the assumption that vertically sheared background currents associated with mesoscale eddies do not alter the qualitative picture of ray trajectories that are obtained. To distinguish between mesoscale stratification and current effects, we consider three different scenarios: (1) monthly varying stratification and currents, (2) monthly varying stratification and annually averaged currents, and (3) annually averaged stratification and monthly varying currents. The reference ray path is given by annually averaged stratification and currents, representative of tidal coherence.

Internal gravity wave speeds are solved by the Sturm–Liouville problem for given stratification and bathymetry from CALEDO60. The semidiurnal rays are initialized at 167.75° E, 18.4° S and 167.65° E, 23.35° S within the two major internal-tide generation hot spots as identified in Part 1, i.e., the North (1) and South (2) domains (see Fig. ), and for a given propagation angle: northeastward (45°) and southwestward (210°), respectively. In an iterative procedure, the ray tracing considers for each step size (1 km) bathymetry, planetary vorticity effects, stratification, and currents.

In the annual mean, the semidiurnal barotropic-to-baroclinic conversion is largely dominated by the coherent component. Meanwhile, it is the coherent tide that is associated with a substantial amount of variability due to the spring–neap cycle, driven by the interaction of M2 and S2 tidal constituents (Fig. ). Note that the N2 tidal constituent adds a low-frequency component to the modeled variability with a period of ∼ 9 months. Specifically, on timescales of ∼ 2 weeks conversion linked to the coherent tide may vary on average by a factor which ranges between 3 and 7 among the subdomains between spring and neap tides. This is in agreement with recent findings over the Reykjanes Ridge . The coherent conversion explains in the area integral most of the semidiurnal variability (γcoh= 0.90–0.99) within the internal-tide generation hot spots (Table ). The remaining fraction is explained by the incoherent tide (γinc= 0.01–0.10).

We explicitly show the spatial contribution to semidiurnal conversion variability by the coherent and incoherent parts for the South (2) domain (Fig. ). The South (2) domain represents the most prominent internal-tide generation site with conversion rates well above 1 W m⁻² across steep slopes such as Pines Ridge (Fig. a). Even though it is the coherent tide and, thus, the spring–neap cycle which dominate semidiurnal variability, certain regions stand out with increasing contributions of the incoherent tide (Cinc). This is the case close to the lagoon and to the southeast around seamounts, notably Antigonia, Jumeaux Est, Jumeaux Ouest, and Stylaster (Fig. c). In these regions, the incoherent tide can explain well above 50 % of the semidiurnal conversion variability. However, it is worth mentioning that they are generally associated with reduced values of CD2 compared to the overwhelmingly strong generation at Pines Ridge. This is crucial knowledge for the design and interpretation of in situ observations at fixed locations such as moorings (see Sect. ).

To better understand the origin of Cinc, we further decompose it into a purely incoherent term (Cinc*) and two cross-terms (Ccross1, Ccross2) following Eq. (). Across all internal-tide generation hot spots, Ccross1 dominates (γcross1> 0.73; Table ). This implies that semidiurnal conversion variability (apart from the tidal-forcing-induced spring–neap variability) is driven by the work of the coherent barotropic tide on incoherent baroclinic bottom pressure variations pbcinc(-H). Ccross2, linked to temporal variations of the barotropic forcing, can account for up to γcross2= 0.23. Cinc* tends to play a negligible role. We note that Cinc* and Ccross2 can have compensating effects (see Norfolk Ridge (3) in Table ), but the mechanisms underlying this compensation remain unclear.

Similarly to the analysis above, we show for the South (2) domain the contribution of the different terms that make up Cinc (Fig. ). The annual means for Cinc*, Ccross1, and Ccross2 are shown in Fig. a–c. Note that the color bar range is an order of magnitude smaller than in Fig. a–c and that the overall contribution to the annual mean remains small. While the three terms feature similar amplitudes, their spatial patterns differ. Based on the area-integrated explained variance in Table  (γcross1= 0.91), alongside high standard deviations, Ccross1 dominates Cinc (Fig. e, h). Ccross2 plays a minor but non-negligible role (γcross1= 0.09) in the incoherent variance, with an elevated contribution particularly above steep bathymetry (Fig. f, i).

To summarize, incoherent conversion averages approximately to zero in the annual mean. Temporally, though, it features marked positive and negative contributions to the semidiurnal conversion at shorter timescales (see Fig. ). Decomposing Cinc allows for a more detailed view of the origin of conversion variations not linked to spring–neap tide variability. As expected, the work of the coherent barotropic tide on incoherent baroclinic bottom pressure variations pbcinc(-H), expressed by Ccross1 is the most important. Interestingly, conversion variability induced by temporal variations of the barotropic forcing (Ccross2) is non-negligible. Temporal variations of the barotropic tide are generally known to exist through seasonal and climatological stratification changes. It may also be possible that these temporal variations represent the energy transfer from the internal tide to the barotropic tide due to pressure work . However, to our knowledge it remains to be quantified to what extent they may drive conversion variability. Also, we can not fully exclude uncertainties linked to the applied methodology, i.e., the bandpass filter and depth average to extract the semidiurnal barotropic tide. In the following, we focus on the governing processes that drive pbcinc(-H).

Generally speaking, Ccross1 is driven by incoherent baroclinic bottom pressure variations, which can be due to local and remote effects through local stratification changes and remotely generated internal tides, respectively. The former are expressed by pressure amplitude variations (dPA) only, whereas the latter is expressed by both dPA and pressure phase variations (dPϕ) . Here, dPA and dPϕ are representative of the amplitude and phase difference between the semidiurnal and coherent tide, determined by complex demodulation of pbcD2(-H) and pbccoh(-H). We start by focusing on Pines Ridge in the South (2) domain before generalizing our findings (Fig. ). The monthly time series of conversion anomaly expressed by the ratio of Ccross1/CD2 reveals two distinct events around April/May and November 2014, during which conversion is decreased by more than 10 % in the domain average. Note that this anomaly can be much higher locally. Here, conversion variability through Ccross1 is largely driven by incoherent baroclinic bottom pressure amplitude variations (correlation coefficient r=0.80 with a 90 % confidence interval [0.50, 0.93] assuming N=12 samples) (Fig. a). Moreover, there is no correlation with baroclinic bottom pressure phase variations (r=-0.02 [-0.51, 0.49]). Ccross1 does not follow a seasonal cycle. Rather, the modeled variability on monthly to intraseasonal timescales is highly suggestive of mesoscale variability.

The monthly time series of bottom stratification N2(-H) (extracted from the bottom most grid cell), mesoscale sea level anomaly (SLA), and mesoscale eddy kinetic energy (EKE; similarly computed to Sect. 3.2 in Part 1) suggest that conversion variations through dPA are linked with mesoscale-eddy-induced stratification changes (Fig. a and b). Particularly around April/May and November, negative conversion/baroclinic bottom pressure amplitude anomalies are associated with negative bottom stratification anomalies and negative mesoscale SLA. The latter is further associated with elevated mesoscale EKE. Mesoscale SLA including the surface geostrophic velocity field is exemplarily shown in Fig. c for a 5 d mean snapshot on 26 April, revealing a cyclonic eddy approaching Pines Ridge.

Pressure perturbations and stratification changes are directly linked assuming a second-order Taylor expansion of pressure around depth z0: 11p(z)∼p(z0)+∂p∂zz0(z-z0)+∂2p∂z2z0(z-z0)22.

In hydrostatic balance (∂p∂z=-ρg), expressed via stratification (∂2p∂z2=ρ0N2), this can be written as p(z)∼p(z0)-ρg(z-z0)+ρ0N2(z-z0)22. By taking the time derivative and assuming adiabatic motion (∂ρ∂t=0), we obtain the relation 12∂p∂t∼ρ0∂N2∂t(z-z0)22.

In practice, this translates to decreasing (increasing) stratification, which corresponds to more widely (closely) spaced isopycnals, leading to weaker (stronger) baroclinic pressure anomalies. Here, negative and positive stratification anomalies above the seafloor are likely associated with the upward and downward pumping of isopycnals by cyclonic (CE) and anticyclonic (AE) eddy activity, respectively (see also Fig. ). In phase with the local tidal forcing, pbcinc(-H) induced by AE adds constructively to pbccoh(-H), whereas pbcinc(-H) induced by CE is in opposite phase and has a destructive effect. This is supported by positive correlations of pressure amplitude variations with bottom stratification (r=0.84 [0.59, 0.94]) and mesoscale SLA (r=0.57 [0.10, 0.83]) in Fig. b.

Generalizing our results for the whole region is far from being straightforward. We calculate the probability density function of the correlation coefficients for the monthly time series of Ccross1 with dPA, dPϕ, N2(-H), and mesoscale SLA for each subdomain (Fig. ). The correlation coefficients for the domain-integrated/averaged quantities (filled circles) including their 90 % confidence intervals are also given. Generally, pressure amplitude variations are very pronounced, suggesting that local effects play an important role (Fig. a–d). Correlations with pressure phase variations tend to be less pronounced or more randomly distributed. Exempt therefrom is Norfolk Ridge (3), where pressure phase variations are strongly positively correlated, suggesting that remote effects are important (Fig. c). Note that pure correlations do not provide information about the amplitude of Ccross1. High correlations indicate that the temporal patterns of variability are consistent, but they do not imply that the magnitude of the conversion is equally significant across all regions.

Assuming that local effects dominate overall, the probability density functions for the correlation of pressure amplitude variations with bottom stratification and mesoscale SLA are shown in (Fig. e–h). In Fig. f and g (representative of the South (2) and Norfolk Ridge (3) domains), the slightly negatively skewed probability density functions are statistically robust with the hypothesis that conversion variations are linked with mesoscale-eddy-induced stratification changes. This becomes more evident when considering the correlation coefficients based on the area-integrated/averaged time series (see the filled circles above the panels). There are good correlations with bottom stratification (South (2): r=0.89 [0.71, 0.96]; Norfolk Ridge (3): r=0.80 [0.49, 0.93]) and mesoscale SLA (South (2): r=0.45 [-0.06, 0.78]; Norfolk Ridge (3): r=0.49 [-0.02, 0.79]). In these regions, mesoscale-eddy-induced stratification changes can induce semidiurnal conversion anomalies by up to 20 % relative to the coherent conversion (see also Fig. ). These correlations (based on the area-integrated/averaged time series) can largely differ from the regional probability distributions, as the former may give greater weight to regions of enhanced conversion influenced by mesoscale variability. In contrast, the probability density functions represent the correlations at every grid point. We only choose grid points where |CD2|> 0.2 W m⁻² to emphasize areas of strong conversion. We note that as the threshold increases, the probability distributions become more negatively skewed, indicating increasingly positive correlations of dPA with N2(-H) and mesoscale SLA (not shown).

North (1) and Loyalty Ridge (4) show no clear correlations between pressure amplitude variations with bottom stratification and mesoscale SLA (Fig. e and h). Several explanations are possible. First, the assumption of depth-independent or weakly baroclinic structure may not be valid. Particularly, conversion at Loyalty Ridge (4) takes place in deeper waters (1000–3000 m compared to < 1000 m in the South (2) domain) and is, thus, considerably deeper than the eddies' vertical extent. Mesoscale eddies near North (1) are generally less numerous and much less energetic than south of New Caledonia . There are many other factors which can alter conversion such as seasonal stratification changes. Seasonal stratification changes have recently been reported to drive conversion variations on global scales . In our study region, they seem to play a secondary role and are at best superimposed on mesoscale variability (see also Fig. ). Other local processes include the direct influence of background currents, which induce asymmetries in internal-tide generation, being enhanced on the upstream side of bathymetric obstacles . Nonetheless, remote effects can play an essential role in local conversion variations, too. They primarily include the remotely generated internal tides, which undergo phase modulations as they propagate through the open ocean before impinging on bathymetric slopes; these are subject to local internal-tide generation. They are usually out of phase with the local tide forcing, though they can theoretically be in phase or in opposite phase as well, making it hard to distinguish local from remote effects. However, remote effects seem to be of relatively small importance around New Caledonia except at minor internal-tide generation sites, which lie in the propagation direction of the major tidal beams. Moreover, there are no major remote sources of internal tides which potentially shoal on the New Caledonia ridges.

We conclude that mesoscale variability can be an important source of conversion variations by enhancing/reducing semidiurnal energy conversion within the internal-tide generation hot spots around New Caledonia. Generalizing our findings is challenging since the relative importance of the underlying dynamics can strongly vary among the generation sites. Furthermore, many processes may be superimposed. Nonetheless, on monthly to intraseasonal timescales we attribute 10 %–20 % of semidiurnal conversion variations to mesoscale-eddy-induced stratification changes.

We extend the analysis in Sect.  by decomposing semidiurnal SSH into its coherent and incoherent parts (Fig. ). The overall signature resembles the semidiurnal energy flux in Fig. d–f with the predominant beams to the north and south of New Caledonia, clearly visible in SSH with root mean square (rms) > 6 cm and dominated by the coherent tide (Fig. a–b). The SSH manifestation of the incoherent tide is characterized by an overall smaller but important rms (1–2 cm; Fig. c). The incoherent SSH is less confined to the tidal beams and seems more widespread in the domain, which suggests that the dispersion of internal waves occurs all along their propagation through the domain.

In Part 1, we calculated annually averaged SSH wavenumber spectra along the beam direction for two transects: (i) a northern transect and (ii) a southern transect (see Fig. a). The objective was to investigate the underlying dynamical regimes and assess the relative importance of balanced and unbalanced motions. The analysis revealed that the coherent internal tide strongly dominates SSH variance within the mesoscale band, limiting SSH observability of balanced motions to large eddy scales. By applying a correction for the coherent internal tide, it was shown that this observability can be increased by shifting the transition scale to smaller wavelengths.

Here, we revisit this analysis by addressing the incoherent internal tide to understand its impact on transition scales and potentially for SSH observability of balanced motions. Similarly to Part 1, we investigate SSH wavenumber spectra with regard to different dynamics that are separated in terms of frequency bands: subinertial frequencies (ω<f, SSHsubinertial) for mesoscale and submesoscale dynamics, as well as superinertial frequencies (ω>f, SSHsuperinertial) for internal gravity waves, while distinguishing between the coherent internal tide (SSHcoh), incoherent internal tide (SSHinc), and supertidal frequencies (ω> 1/10 h, SSHsupertidal). Note that the incoherent internal tide is determined by applying a bandpass filter in the full semidiurnal–diurnal tidal range (10–28 h). As such, it also comprises contributions from near-inertial, non-tidal internal gravity waves and short-lived submesoscale features, but we assume that they are negligibly small.

Seasonally averaged SSH spectra for Southern Hemisphere summer (January–March, JFM) and winter (July–September, JAS) are shown in Fig. . By definition, the coherent internal tide is the same in both seasons. The seasonality of the transition scale corrected for the coherent internal tide (Ltcorr) is, thus, generally attributed to seasonal variations of subinertial motions, i.e., mesoscale to submesoscale dynamics, and unbalanced wave motions. First, we point out that the incoherent internal tide (SSHinc) predominantly governs motions at superinertial frequencies if corrected for the coherent internal tide – at least down to 100 km independent of the season for both transects.

Along the southern transect, seasonal modulations of the SSH spectra become evident for all wavelengths < 300 km (Fig. c–d). In summer, it features a more flattened wavenumber slope in the mesoscale to submesoscale range with a characteristic k-2 slope corresponding to superinertial motions (internal wave continuum) (Fig. c). In winter, it becomes more continuous, characterized by a k-4 slope (Fig. d). This can be attributed to subinertial motions such as mesoscale to submesoscale processes that undergo seasonal variability. This was explicitly shown for New Caledonia in and , in which increasing importance of mixed layer instabilities and frontogenesis was attributed to more available potential energy in the Southern Hemisphere winter months. Seasonal modulations of SSH spectra can also be linked to unbalanced wave motions, which are amplified in summer months, particularly for higher vertical modes due to increasing stratification . Superinertial processes dominate subinertial motions in both seasons at scales below 180 km. However, the relative importance of superinertial over subinertial motions is more pronounced in summer months. This can be explained by the seasonality of superinertial and subinertial motions being out of phase; i.e., superinertial motions are enhanced in summer, while subinertial motions are considerably reduced and vice versa in winter. The transition scale (Lt) does not feature strong seasonality between summer and winter (Fig. c, d), though the transition scale is not well-defined in winter, where subinertial and superinertial signals have similar variance at wavelengths 90–180 km (Fig. d).

Important conclusions are made when correcting for the coherent internal tide. In summer, the transition scale (Ltcorr) is only slightly reduced from 175 to 156 km (Fig. c). This is linked to the seasonally enhanced incoherent internal tide, which is still contained in the signal featuring equal SSH variance with subinertial signals at 90–180 km wavelength (Fig. c). At scales below 90 km, the incoherent tide even dominates SSH variance over subinertial motions and is equally important to the coherent tide. In winter, the transition scale is largely reduced from 165 to 78 km (Fig. d). This is primarily linked to the fact that subinertial motions are energized in winter, while the SSH signature of motions at superinertial frequencies are less energetic. We note a significant contribution of motions at supertidal frequencies for scales smaller than 100 km.

The northern domain differs from the southern domain in that SSH variance of subinertial motions is generally reduced and the seasonal cycle less pronounced (shown by the white lines in Fig. a–b). Motions at superinertial frequencies largely dominate over motions at subinertial frequencies throughout the year, dominated by the coherent internal tide. As for the southern transect, the incoherent contribution features seasonality and increases in summer but remains weaker than the coherent signal. Increasing SSH observability of mesoscale and submesoscale motions by correcting for the coherent internal-tide signal proves overall to be more efficient since the incoherent internal-tide signal is largely reduced in SSH variance compared to the southern transect (Fig. a–b). Specifically, the transition scale is reduced from 211 to 146 km in summer (Fig. a) and from 207 to 85 km in winter (Fig. b). Contributions by motions at supertidal frequencies appear to have larger importance in the northern domain compared to the southern domain. In fact, at scales below 146 and 85 km for summer and winter, respectively, SSH variance is governed by equal contributions from the incoherent internal tide and motions at supertidal frequencies.

Briefly summarized, the dominance of unbalanced motions in the mesoscale to submesoscale band strongly limits SSH observability of geostrophic dynamics around New Caledonia, especially in summer. In other words, SSH observability of mesoscale dynamics is limited to large eddy scales even after a correction for the coherent tide in numerical simulation output. It is to a large extent the incoherent internal tide and non-tidal internal gravity waves at scales < 100 km which may eventually constrain SSH observability of mesoscale and submesoscale dynamics.

The SSH wavenumber spectra in Fig.  and the associated conclusions for transition scales are only valid for a one-dimensional transect in the tidal beam propagation direction, in which the internal-tide signature is well-captured. Here, we mimic SSH wavenumber spectra from satellite altimetry by interpolating SSH from CALEDO60 (similarly to Sect. ) onto realistic altimetry tracks, which are not aligned with the tidal beam propagation direction (Fig. ). Further, the SSH wavenumber spectra are averaged for the region south of New Caledonia (Fig. a).

South of New Caledonia and along the tidal beam propagation direction, the coherent tide was found to clearly dominate over subinertial motions or to be of comparable importance, regardless of the season (see Fig. c–d). However, averaged SSH wavenumber spectra along given altimetry tracks reveal a different picture. Spectral peaks associated with tidal motions are less pronounced (Fig. b–c). Lt is generally decreased from 175 to 115 km in summer months and from 165 to 41 km in winter months. This reduction is linked to the anisotropic nature of the (coherent) internal tide. Along the altimetry track direction, only a fraction of the internal-tide energy is captured, causing the SSH wavenumber spectra to emphasize the more isotropic balanced flow regime. Moreover, the incoherent internal tide becomes increasingly important, dominating over the coherent tide across all spatial scales. This shift reflects the larger isotropy of incoherent SSH compared to the coherent SSH. Consequently, in along-track spectra, the dominance of balanced motions and the incoherent internal tide renders corrections for the coherent tide ineffective. This is evident when comparing Lt and Ltcorr in Fig. b and c (from 115 to 107 km in summer months and 41 to 40 km in winter months).

We conclude that the orientation of altimetry tracks has important implications for the interpretation of transition scales computed on along-track SSH wavenumber spectra. This effect is particularly pronounced in regions with prominent internal-tide motion and well-defined propagation beams, such as around New Caledonia. In such cases, transition scales may lead to erroneous estimates of the wavelength at which unbalanced motion becomes dominant over balanced motion, as anisotropic motions like internal tides are not effectively captured in the along-track direction. Separating balanced from unbalanced motions is critical for the dynamical interpretation of SWOT SSH, particularly for accessing the mesoscale to submesoscale flow regime and derived quantities such as surface geostrophic velocities.

In the annual mean, semidiurnal barotropic-to-baroclinic conversion is largely dominated by the coherent tide, which in turn explains a large part of the semidiurnal variability (90 %–99 %) through the spring–neap cycle. The incoherent tide is negligibly small in the annual mean, suggesting that incoherent contributions cancel out in the long-term average, though locally and on shorter timescales, it can explain a notable fraction of semidiurnal variability. Our objective was to identify the underlying mechanisms responsible for conversion variations not linked to the tidal forcing.

Generally speaking, sources of conversion variations are numerous and difficult to distinguish due to the unpredictable nature of local and remote effects. To clearly distinguish between these dynamics, we separated the incoherent conversion Cinc into its purely incoherent term (Cinc*) and two cross-terms (Ccross1, Ccross2) (see Eq. ). Our analysis suggests that the work done by the coherent barotropic tide on incoherent baroclinic bottom pressure variations dominates incoherent conversion (71 %–90 %), expressed by Ccross1. The dominance of baroclinic bottom pressure amplitude variations (over phase variations) implies that local effects dominate over remote effects. Locally and on monthly to intraseasonal timescales, mesoscale-eddy-induced stratification changes through upward (CE) and downward (AE) pumping of isopycnal surfaces can induce negative and positive conversion anomalies by more than 20 %, respectively. This is supported by positive correlations of incoherent baroclinic bottom pressure amplitude variations with bottom stratification and mesoscale SLA. Seasonal variability seems to play a minor role or is superimposed on the dominant mesoscale variability. The importance of conversion variations through changes in the barotropic tide forcing remains to be investigated, but we showed that they can explain an important fraction of up to 23 % in the incoherent conversion term.

Semidiurnal tidal energy propagating towards the open ocean follows at first order the spring–neap tide cycle, closely coupled to semidiurnal conversion variability. However, it features elevated levels of tidal incoherence, which increases with increasing distance from the generation sites. Close to the generation sites, tidal incoherence explains up to 20 % of the semidiurnal variability. In the far field, it can account for up to 90 % (in 500–1000 km distance from the generation site). Tidal incoherence is generally of higher importance south of New Caledonia, corresponding to enhanced mesoscale activity, leading to dispersion in the far field alongside increasing phase variability. Further, it is associated with the refraction of the tidal beams in the propagation direction. This is in agreement with a simplified ray tracing, which tracks the horizontal propagation of inertia-gravity modes at semidiurnal frequency with varying background stratification and/or currents. Tidal beam refraction occurs through varying group and phase speeds as the semidiurnal rays interact with the mesoscale eddy field. Changing orientation is primarily dominated by background currents accounting for twice as much refraction along the propagation path as stratification. North of New Caledonia, the semidiurnal rays closely align with the theoretical propagation direction for a semidiurnal ray in annually averaged stratification and currents.

The dynamical interpretation of SSH in regions where balanced and unbalanced motions feature similar SSH variance at comparable wavelengths is challenging. By revisiting Part 1, we computed SSH wavenumber spectra in the tidal energy propagation direction and extended the analysis by investigating the relative importance of the incoherent tide in SSH variance. A correction of the coherent tidal signature in SSH is only partly effective in accessing scales toward smaller wavelengths due to seasonal modulations of superinertial and subinertial motions, which are in opposite phase; i.e., superinertial motions are enhanced in summer, while subinertial motions are considerably reduced and vice versa in winter. Ultimately, it is the incoherent tide which limits SSH observability of balanced and unbalanced motions to scales above 150 km in summer and above 80 km in winter.

SSH wavenumber spectra computed along altimetry tracks lead to several conclusions. The altimetry tracks are not oriented in the tidal energy propagation direction, and therefore the spectra capture only part of the internal-tide energy. The incoherent tide dominates over the coherent tide across all wavelengths, reflecting its more isotropic nature compared to the coherent tide. Moreover, transition scales derived along altimetry tracks are generally reduced compared to those determined in the tidal energy propagation direction since the SSH wavenumber spectra emphasize the more isotropic balanced flow regime. Relying on these transition scales in regions where balanced and unbalanced motions coexist may result in a distorted view of the governing dynamics as anisotropic processes such as internal tides are not properly sampled. However, knowing at which wavelengths balanced and unbalanced motions dominate is particularly crucial for SWOT in order to disentangle the different flow regimes in SSH measurements.

This study provides several routes for future work to better understand the internal-tide life cycle. One open question arising from our analysis is how variability in barotropic-to-baroclinic energy conversion influences both the outward propagation of internal-tide energy and local dissipation. According to the baroclinic energy budget (Eq. ), dissipation is defined as the residual between conversion and energy flux divergence. We therefore ask the following question: do variations in conversion directly translate into proportional changes in energy flux divergence – and, by extension, in dissipation – or are they partially decoupled? For instance, does increased conversion always imply stronger outward flux and higher dissipation ? Monthly anomalies of CD2, ∇h⋅FbcD2, and DbcD2 relative to the annual mean are shown in Fig. . Energy flux divergence anomalies generally follow those of conversion, with positive conversion anomalies typically resulting in increased energy flux divergence, and vice versa. In contrast, dissipation anomalies are less variable. Nevertheless, periods exist when energy flux divergence anomalies are either more or less pronounced than conversion anomalies, leading to reduced or enhanced dissipation, respectively. The processes governing whether an excess or a deficit of tidal energy conversion is balanced primarily by outward energy propagation or by local dissipation (or other terms in Eq. ) remain to be fully understood.

This highlights the need for further investigation into the mechanisms controlling energy partitioning between these pathways. Those findings could have important implications for parameterizations of internal-tide dynamics such as tidal mixing and dissipation for climate and ocean general circulation models, which do not resolve tidal processes. Current parameterizations consider geographically varying tidal mixing . However, temporal variations induced by the spring–neap cycle, mesoscale variability, and seasonal changes are not taken into account.

Further insight is expected from an extensive in situ experiment (SWOTALIS, ) that was carried out in March–May 2023. It was inter alia dedicated to the deployment of full-depth oceanographic moorings and located in the hot spots of internal-tide generation and dissipation south of New Caledonia. Successfully recovered in November 2023, these moorings provide a unique dataset to better understand the internal-tide life cycle, while assessing our numerical model output. Furthermore, this region is located beneath the two swaths of SWOT's fast sampling phase (1 d repeat orbit). The moorings and the numerical simulation output will play an essential role in the dynamical interpretation of SWOT SSH by allocating the different dynamics such as balanced and unbalanced motions. Emphasis will be given to the SSH signature of the incoherent internal tide, which represents a major challenge for SWOT SSH observability.