Horizontal velocity can be reliably measured by SADCPs mounted on the hull of vessels during transits or research cruises. We use the historical transects around New Caledonia gathered into one dataset by in order to describe the regional circulation. This database consists of a collection of 109 cruises that have acquired measurements of longitudinal u∥ and transverse u⟂ velocities from 1990 to 2014 see Table 1 of for a full description. The SADCP data come from different institutes: IRD (73), JASADCP database from the University of Hawaii (11), CSIRO (23), JAMSTEC data centre (2). Most of the data are provided by 150 kHz SADCP instruments and cover an average range of 25 to 300 m depth, with an average vertical resolution of 8 m and an average temporal resolution of 5 min. Some SADCP instruments also provide measurements closer to the surface and down to 500 m depth. The available SADCP sections are shown in Fig. c. More details about data quality control and data filtering applied at this stage are given in .

The SADCP database has been edited to retain only data meeting certain requirements for computing structure functions. We have only considered high-frequency SADCP: ship tracks with minimal temporal sampling slower than 15 min were discarded from the analysis. The ship cruising speed must be faster than 4 m s-1 (around 8 knots); this condition aims at avoiding the subsampling of internal waves whose average phase velocity is around 1 m s-1 in the ocean. The segments were defined so that the ship travels almost in a straight line, with a 5∘ variation of the ship heading allowed. This condition is not necessary as we will use the assumption of isotropy in the following analyses, but it turned out to be efficient to avoid very long and winding trajectories. A maximum time break of 15 min between measurement is allowed within the same segment; longer time breaks result in the data split into different segments.

High-resolution near-surface temperature and salinity have been collected by the French Sea Surface Salinity Observation Service (SSS-SNO) from voluntary observing ships (mainly merchant ships) using TSG instruments . Tracers are measured near surface because seawater is pumped between 5 and 10 m depth on the side of the hull, depending on the ship configuration. Measurements are made every 15 s and are averaged every 5 min by taking the median. The average spatial resolution associated with this 5 min temporal resolution is around 2.5 km for a 20-knot cruise speed. The TSG data can be downloaded from the LEGOS Sea Surface Salinity database

http://www.legos.obs-mip.fr/observations/sss/ (last access: 20 July 2020)

The climatologies of temperature and salinity over the first 500 m of the water column are taken from the Roemmich–Gilson Argo climatology computed over the period 2004–2016

http://sio-argo.ucsd.edu/RG_Climatology.html (last access: 20 July 2020)

Based on large-scale considerations provided by the EKE and M2 climatology maps (Fig. a, b), as well as former studies around New Caledonia, we have selected four regions, delimited by red lines in Fig. , having different characteristics in terms of mesoscale activity and internal wave activity.

Region VAUB corresponds to the 100 km wide Vauban Channel between the New Caledonia main island and the Loyalty Islands . In this channel, a mean southeastward current, extending to at least 500 m depth, flows against the mean trade winds, overlying a deeper northwestward current. From Fig. , this small region has relatively small EKE and weak M2 internal tides. Yet, the interpolated altimetric product might underestimate EKE in this region because of the proximity of coastlines; this will also impact the mapping technique used to produce the M2 climatology. In situ observations have revealed that the Vauban current is strongly modulated at intraseasonal timescales by large ME eddies propagating westward . Velocity observations measured by SADCP in this region have shown substantial semi-diurnal currents, likely related to baroclinic tides .

Region ECAL is the large box situated east of New Caledonia, centred on the southern branch of the SEC. This region exhibits high ME EKE and substantial M2 internal tides. The internal tides in the SCAL region are likely to radiate from surrounding seamounts and islands. Region SCAL is situated south of New Caledonia and comprises high ME EKE as well as strong M2 internal tides, the latter arising partly from the generation site at the southern tip of New Caledonia. As mentioned in the introduction, those regions may involve substantial baroclinic instabilities that partly explains the large levels of EKE . Long-lived westward-travelling ME eddies also pass through those regions and contribute to EKE .

Region NCAL is situated north of New Caledonia and west of the Vanuatu islands. This region is less energetic than the southern ones in terms of ME activity but has substantial M2 tidal amplitude and is close to several generation sites induced by island topography. There is observational evidence that weak ME eddies may be generated in the lee of the Vanuatu islands . The NCAL region excludes the high-variability band at 16∘ S that is suggested to arise from barotropic instability between the North Vanuatu Jet and the surrounding countercurrents .

In these regions around New Caledonia, the first mode of the M2 internal wave is dominant and accounts for over 30 %–50 % of the total M2 tidal energy conversion . The dissipation of M2 internal wave energy is also amongst the strongest in the world's oceans, with a substantial contribution coming from wave–wave interactions . The amplitude of coherent M2 mode 1 in terms of sea level variations ranges between 1 and 4 cm see Fig. ;; the amplitude of mode 2 is much weaker and estimated to be between 1 and 3 mm . In terms of wavelength, M2 mode 1 scales between 120 and 150 km, mode 2 scales between 60 and 70 km, and mode 3 scales between 40 and 50 km

These regions are well sampled by shipboard ADCPs and TSGs, as shown in Fig. c–d. All of these four regions will be crossed during the SWOT fast-sampling phase (black lines in Fig. a–b). They are identified as possible case studies to better understand the small-scale SSH signal, jointly with in situ datasets . The averaged hydrographic profiles (temperature, salinity, density and stratification) measured by ARGO floats are given for each region in Fig. .

Whilst most studies have used spectral techniques e.g. to characterise the scale-dependent distribution of horizontal velocities, measured by SADCP along ship tracks, we prefer using structure functions (SFs) as applied to atmospheric velocities measured during aircraft flights . The use of SFs is mainly motivated by the fact that SFs are more suited to study uneven observations in space. Less preprocessing is needed compared to Fourier methods, which often requires interpolation of velocity measurements on equidistant samples, detrending and windowing. However, SFs may only be applied on physical quantities whose scale-dependent variance decreases gently, that is for characterising spectra less steep than k-3 , where k is the horizontal wavenumber.

In addition to the Helmholtz decomposition, power laws estimated on SFs and spectra can be used to infer the dynamics at work. However, there are two limitations in predicting the turbulence regime using only the slopes of the KE spectra. On one hand, a typical value of a spectral slopes may correspond to different dynamical regimes. On the other hand, several dynamical regimes can combine or overlap at a certain range of scales, in our case, balanced motions and IGWs. In this section, we briefly review the different theories available to describe turbulent regimes occurring in the ocean by focusing on the corresponding spectra/SF scaling laws for KE and tracer variance as well as the ratio of divergent and rotational VSFs Rϕψ.

Second-order SFs are computed on longitudinal and transverse velocity components for the four regions of study on each ADCP ship track. The VSFs are averaged over different depth ranges: a surface layer at 0–100 m, a transition layer ranging from 100 to 200 m and an ocean interior layer ranging from 200 to 500 m. Figures  and show the SFs over these three layers for the four regions of study for the range of spatial scales of 3–100 km. The Helmholtz decomposition is eventually performed on every layer to separate the contribution of the rotational and divergent components. These operations are performed on each ADCP segments, then the median is computed. Confidence intervals at 5 % and 95 % are estimated using a bootstrap method by performing 10 000 realisations of randomly chosen ADCP segments.

In the VAUB region, the surface layer shows that the total VSF (green curve) has a slope close to 1 (1.01) consistent with surface-intensified dynamics (Fig. a). The total VSF slope tends to decrease with depth to get closer to the power law r2/3 in the ocean interior (slopes of 0.76 and 0.56, respectively, for the 100–200 and 200–500 m ranges shown in Fig. c–f). In the surface layer, the rotational VSF (red curve) contributes significantly to most of the total VSF over the 3–100 km range and clearly dominates the divergent SF (purple curve). Deeper in the water column (Fig. c–f), the rotational VSF still dominates in the 10–100 km range but its contribution to the total VSF drops in the 3–10 km range as the divergent SF contribution increases. The contribution of rotational and divergent motions become equivalent under 10 km in the 100–200 m layer and around 10 km in the 200–500 m layer, albeit with large uncertainties for the latter layer due to the quality of the data. In the 200–500 m layer, the shape of the total VSF more closely follows the shape of GM SF (black curve in Fig. e), while the average ratio Rϕψ is 0.6 (compared to 0.3 for the other layers).

Thus, VSF analysis shows that the VAUB region is consistent with a surface-intensified regime, dominated by rotational dynamics over the ME to SM range, with a VSF slope consistent with frontogenesis and mixed layer dynamics. These surface dynamics contrast with the ocean interior as divergent dynamics become more substantial with depth and the slope of the total VSF tend to flatten towards r2/3. Although the VSFs get close to the shape of the GM SF, the divergent VSF never exceeds the rotational VSF in the interior as the ratio Rϕψ is smaller than unity. Stratified turbulence is then more likely to be at work than weak interactions between IGWs to yield such VSF shape. The interior layer (Fig. e) is, however, uncertain because less valid data are available at those depths, as shown by the large confidence intervals in Fig. e.

The VSF functions computed on SADCP data in the ECAL region (Fig. b, d, f) exhibit similar results than the VAUB region. The slope of the total VSF decreases with depth from 0.87 at surface (0–100 m) to 0.65 in the interior (200–500 m). The rotational motions (red curve) also dominate at surface but their relative contribution to the total VSF decreases with depth as divergent motions (purple curve) become more substantial. In the transition layer (Fig. c), divergent and rotational VSFs have a similar amplitude in the range of 3–10 km, whereas rotational motions still dominate the range of 10–100 km, yielding an average ratio Rϕψ of 0.49. VSFs computed in the interior layer (Fig. e) are less precise, with large confidence intervals, but they suggest that divergent motions have a substantial impact over the whole range of spatial scales (3–100 km) as Rϕψ gets slightly larger than unity (1.55). In this interior layer, the total VSF also resembles the GM structure function, suggesting, jointly with the previous value Rϕψ, that weak interactions between IGWs are possibly at work to generate the observed VSFs. As Rϕψ is close to unity, nonlinear interactions due to stratified turbulence could also be at work.

The NCAL region (Fig. a, c, e) differs from the ECAL and VAUB regions as the slope of the total VSF is already close to the r2/3 law at the surface (0.71) and consequently decreases with depth to a lesser extent (to a value of 0.49). At the surface, rotational and divergent VSFs have a similar magnitude over the range of 3–100 km with Rϕψ being equal to 1.07. Rotational and divergent motions have also a similar contribution in the intermediate layer (Rϕψ=0.95), albeit with weaker variance that also impacts on the slope of the total VSFs (green curve). Averaged results in the ocean interior (200–500 m) are not qualitatively different but SFs (grey curves) are noisier due to data of lesser quality at these depths. Unlike the ECAL and VAUB regions, surface dynamics in the NCAL region seem to be weak or potentially masked by more substantial unbalanced dynamics. The values of Rϕψ close to unity suggest that stratified turbulence might be at work but weak interactions between IGWs with frequencies close to f might also be responsible for the observed VSFs. The resemblance between the shape of the GM VSF and the total VSF, especially in the interior layers, also argues that observed VSFs could be consistent with IGW interactions.

In the SCAL region (Fig. b, d, f), the surface and intermediate layers show a total VSF with slopes close to 0.8, between the 1 and 2/3 power laws. Rotational motions (red curve) dominate over the whole range of scales (3–100 km), involving a substantial role of SM and ME processes, albeit the VSF slope is not fully consistent with frontogenesis and mixed layer dynamics. In the ocean interior (200–500 m; Fig. f), the slope of the total VSF slightly decreases to 0.76 as divergent motions becomes substantial in the 10–100 km range and equivalent to rotational motions in the 3–10 km range, yielding an average Rϕψ of 0.8 (compared to 0.4 for the other layers). In this layer, the regime at work is not clear because rotational motions have a slightly larger contribution to the total VSF than divergent motions. The equivalent contribution of rotational and divergent motions at smaller scales suggests, however, that stratified turbulence could be at work. In this region, the contribution of divergent motions to the total VSF might keep increasing with depth, as seen in the other regions.

Figures  and show that the total VSFs tend to flatten with depth in each of the four regions, albeit this decrease is less clear for the NCAL and SCAL regions. To illustrate this tendency, we compute averaged slopes for each total VSFs over 30 m bins of depth. Slopes less than 0.2 were discarded from the analysis because they are likely to be due to instrumental noise (i.e. a slope close to 0 characterises an uncorrelated signal). Results are plotted in Fig. a and clearly show a dependence with depth for the four regions. This depth dependence also supports our decomposition into a surface layer (0–100 m) where the VSF slope is relatively constant between 0.75 and 1, a transition layer where the VSF slope rapidly drops (100–200 m) and the interior layer where the VSF slope slightly decreases to reach values between 0.5 and 0.6. Note that the uncertainty on the VSF slopes at depth are stronger because less valid data are available. As previously noticed, Fig. a also shows that the transition with depth is less marked for the NCAL region.

In order to assess the scales at which the quasi-geostrophic balance is likely to hold, we infer the scale-dependent Rossby number from the total VSF as 9Ro(r)=DUUfr. The scale-dependent Rossby number is computed in each region and averaged over all depth. Figure b shows that Ro logically increases as the scale r decreases, with Ro being close to unity at the kilometric scale for all regions of study. At scales larger than 10 km, the Rossby number is large enough (>10) to consider that rotation effects dominate the dynamics and suggests that total VSFs with large rotational components are associated with quasi-geostrophic eddies at those scales. Below 10 km, a loss of geostrophic balance is likely to happen, and substantial ageostrophic motions would imprint on velocity divergence. This assessment is confirmed by a substantial contribution of the divergent VSFs (Figs.  and ) at scales smaller than 10 km for all the layers and regions.

In summary, the analysis of VSFs computed on SADCP measurements suggests that there is a surface-intensified regime at work in the VAUB and ECAL regions, and to a lesser extent in the SCAL region. Close to the surface (0–100 m), such a regime is in accordance with mixed layer dynamics and frontogenesis in the VAUB and ECAL regions, involving quasi-geostrophic vortices at scales >10 km with a predominant rotational component, whereas smaller scales are likely to undergo a loss of balance as the contribution of divergent motions increases. In the interior layer (200–500 m), divergent motions have generally equivalent amplitude as rotational motions, suggesting that stratified turbulence could be at work in the ocean interior. The hypothesis of a regime involving weak interactions between IGWs is also plausible as the shape of the total VSFs resembles that of the GM VSFs in some regions. Finally, the NCAL region does not show a surface-intensified regime, except for a slight transition of the slope of the total VSFs. The NCAL region seems to be rather impacted by IGWs in all the layers studied, in a similar way to the interior layer of the other regions.

The presence of substantial rotational motions in the ECAL and SCAL regions is consistent with substantial ME EKE estimated from altimetry and associated with baroclinic instabilities and westward-travelling ME eddies in those regions (see Sect. ). There is a discrepancy between the EKE map in the VAUB region and the importance of rotational motions in this region, perhaps due to an underestimate of sea level variance by mapping altimetric data close to the coast. The relative importance of divergent motions compared to rotational motions in region NCAL is also consistent with weak ME EKE and substantial coherent internal tides in this region.

To provide complementary insights into surface small-scale dynamics and analyse their seasonal variations, second-order SFs are now computed on each segment of surface tracers measured by shipboard TSGs in the NCAL, ECAL and SCAL regions. The TSG coverage over the VAUB region does not allow an accurate computation of surface tracer SFs, which are therefore not shown. Figure  shows the SFs computed on surface temperature (SST; Fig. a–c), salinity (SSS, red curves) and density (SSρ, green curves) from 3 up to 1000 km for each regions. The SFs of SST, SSS, SSρ have been, respectively, adimensionalised by α2 (thermal expansion coefficient), β2 (haline contraction coefficient) and 1/ρ0, ρ0=1025 kg m-3 being the reference density of seawater. The coefficients α and β were computed between consecutive TSG observations and averaged over each segment. This normalisation allows the comparison of the different tracer SFs on the same plot. The SFs of each segment are averaged over two different seasons of the year: one cool season (solid curves) from June to November and one warm season (dashed curves) from December to May. As for VSFs, confidence intervals at 5 % and 95 % are estimated using a similar bootstrap method.

First, the dynamical regimes can be discussed in light of the tracer SF slopes, estimated over the range of 3–100 km and given in the legend of Fig. . The slopes of the temperature SFs are close to 1.2 for the two seasons in all the regions, except during the warm season in the NCAL region where it reaches 1.33. The temperature SFs are slightly steeper than those of salinity SFs, whose slopes are comprised between 0.93 and 1.07, close to the r1 law. The slopes of density SFs mostly reflect the slopes of temperature SFs and range from 1.09 to 1.21. Surface tracer SFs are therefore consistent with stirring induced by frontogenesis processes and submesoscale motions in the ECAL and NCAL regions, albeit the SST and density SFs are slightly steeper than theoretical prediction (i.e. r1 slope). Those tracer SF slopes are also consistent with those of the VSFs presented earlier principally in the ECAL region. The discrepancies between tracer and velocity SFs in the NCAL and the SCAL regions could be explained by the substantial IGWs occurring in these regions that possibly have a significant imprint on horizontal velocities near the surface but not on surface tracers. No substantial seasonal variation is noticed on the slope of the tracer VSFs, meaning that the rate of stirring by mesoscale and submesoscale structures is not seasonally dependent. Note that tracer SFs in the SCAL region are more uncertain, as shown by the large confidence intervals in Fig. c due to fewer TSG segments available.

The quality and the quantity of the TSG measurements allow the computation of tracer SFs up to scales as large as 1000 km, providing additional information in the range of 100–1000 km that was missing in the VSF analysis. For scales larger than 100 km, the tracer SF slopes seem to follow the same power law for the NCAL and SCAL regions (Fig. a, c), whereas the slopes tend to flatten in the ECAL regions (Fig. b) towards a zero slope. A r0 slope may indicate that the SF is uncorrelated at larger scales, perhaps because the assumption that turbulent statistics can be sampled with a moving vessel fails at those scales. However, a r0 slope is also compatible with nonlocal stirring of passive tracers by large-scale dominant eddies . The latter hypothesis is consistent with a similar flattening of tracer spectra (from k-2 to k-1) shown by in the subtropical North Atlantic using TSG data. Note that the ECAL region is particularly impacted by westward-propagating mesoscale structures, which are likely to follow quasi-geostrophic behaviour and explain large-scale stirring with r0 (k-1).

Although there is no significant seasonal variation of the tracer SF slopes, a striking feature of Fig.  is the seasonal variations of the amplitude of salinity and temperature SFs that are significative in the NCAL and ECAL regions, albeit with an opposite behaviour. Temperature SFs have larger amplitude during the cool season as opposed to the warm season, whereas salinity SFs have weaker amplitude during the cool season compared to the warm season. The seasonal variations of the density SFs are much weaker and cannot be properly disentangled because of the associated uncertainties; the median, however, suggests a similar seasonality as the temperature SFs. Because neither the temperature SFs nor the salinity SFs exceed the amplitude of the density SFs, no compensation between salinity and temperature is at work in those regions. On the contrary, there are constructive effects between salinity and temperature, whose intensity depends on the season; stronger constructive effects between temperature and salinity occur during the warm season. The tracer SFs in the SCAL region are noisier, with large confidence intervals that hamper the detection of a significant seasonality. The median tracer SFs, however, suggest similar seasonality to that noticed in the NCAL and ECAL regions.

To explore further the relative importance of temperature and salinity over spatial scales, the scale-dependent absolute density ratio |R(r)| may be inferred directly from the temperature and salinity SFs: 10Rρ(r)=αβDθθ(r)DSS(r). This ratio is shown in Fig. a for the three regions of study averaged during the cool and warm seasons. For all those cases, the density ratio |R(r)| is larger than unity over all scales, meaning that temperature effects dominate over salinity effects, except for the NCAL region during the cool season where both effects are equivalent (|R|∼1). The density ratio also tends to decrease with smaller scales, meaning that salinity effects on density become more important at small scales. At scales larger than 200 km, discrepancies between regions start to appear but less data are available at those scales; hence, there are more uncertainties. Figure a also exhibits a seasonality of the density ratio with larger |R| values during the cool season and smaller |R| values during the warm season. Thus, the relative contribution of temperature and salinity to density varies with seasons.

Can we link the seasonal variations of tracer SFs and those of the vertical hydrographic profiles? In the NCAL and ECAL regions, Fig.  shows that the upper 100 m of the ocean also undergo seasonal variations. During the cool season, salinity close to the upper 50 m tends to increase in relation to the seasonality of the South Pacific Convergence Zone e.g., leading to a reduction of the salinity stratification in the upper 100 m. This surface saltening during the cool season is associated with weaker salinity variance at small scales, as shown by the smaller amplitude of salinity SFs (red curves in Fig. ). In the SCAL region, the weak seasonal variation in the salinity profile is associated with weak seasonality in salinity SFs during this season. The opposite effect happens for upper ocean temperature. While temperature and its associated stratification are reduced in the upper 100 m during the cool season, in relation to the seasonal variations of the solar input and the mixed layer, small-scale temperature variance increases as shown by the larger amplitude of temperature SFs during this season (blue curves in Fig. ). Although the upper ocean density tends to decrease during the warm season as stratification increases (bottom row in Fig. ), the density SFs do not seem to be influenced by this seasonal variation, contrary to temperature and salinity. Thus, no clear dynamical link between seasonal variations of the hydrographic profiles and tracer SFs seems to emerge from this analysis.

Although the seasonality of EKE cannot be inferred from the VSFs because of the lack of data, the seasonality of the EKE counterpart that is the available potential energy (APE) can be inferred from the density SFs and the vertical profile of N. The corresponding SF for the APE near the surface is estimated as 11DAPE(r)=g2N2Dρρ(r)ρ02, where g is the gravitational acceleration. As TSG measures temperature and salinity between 5 and 10 m depth, N is taken averaged in this depth range from the Argo climatological mean profiles for each region. The APE represents the reservoir of energy that can be converted into EKE by oceanic instabilities. The APE SFs are shown in Fig. b for the three regions and for the two seasons. First of all, there are substantial seasonal variations with more APE during the cool season (solid curves) than during the warm season (dashed curves). The finding of seasonal variation of the APE in the ECAL and SCAL regions is consistent with the seasonal modulation of the EKE in the South Pacific STCC shown by using altimetric data: EKE increases during the cool season (June–November) to peak in November/December, whereas EKE decreases during the warm season (December–May) to its minimum in June. The same authors also show that the cool season is more favourable to baroclinic instability, which is a necessary condition to release energy from a larger APE reservoir during the cool season. Since we have seen earlier that the seasonality of the surface density SFs is weak, most of this APE seasonality is due to seasonal changes in the stratification (see Fig. ). The APE is also smaller in the NCAL region compared to the ECAL and SCAL regions, consistent with larger EKE in the latter regions as shown in Fig. b. The seasonal and spatial variations noticed on large mesoscale EKE captured by altimeters may also be valid for smaller scales as the APE follow similar seasonal and spatial variations in the range of 3–100 km.

In summary, the SFs applied on surface tracers are in accordance with submesoscale dynamics (e.g. mixed layer dynamics, frontogenesis) as slopes are close to r1 over the range of 3–100 km. In the ECAL region, the slopes of tracer SFs are also consistent with those of VSFs for the surface layer. Differences are noticed for scales larger than 100 km that are either due to a lack of quality data (NCAL and SCAL) or to a different dynamical regime (ECAL). Temperature and salinity SFs exhibit seasonal variations in phase opposition and are associated with seasonal modulation of constructive effects yielding to a weak seasonality in the density SFs. No clear dynamical link is established between the seasonal variations of temperature and salinity SFs and those of hydrographic profiles. Contrary to the density SFs, the APE SFs show seasonal variation mainly due to the seasonality of the stratification that could yield seasonal variation in surface EKE and VSFs. Spatial and seasonal variations of APE in the range of 3–100 km are consistent with larger-scale variation of EKE observed by altimetry.

First, we found that different dynamical regimes are likely to be at work between the surface and the ocean interior in the regions south (SCAL) and east (ECAL) of New Caledonia as well as in the Vauban (VAUB) channel. Our results in those regions suggest the existence of a surface-intensified regime consistent with submesoscale dynamics involving frontogenesis and mixed layer instabilities. This hypothesis is supported by total velocity and tracer SFs having slopes close to r1 (k-2) near the surface, with motions involving a dominant rotational component. However, the importance of rotational motions weakens with depth at the same time as the total VSF slopes flatten out to get closer to the r2/3 (k-5/3) law. Because the average ratio of divergent and rotational components Rϕψ is close to unity at these depths, we concluded that stratified turbulence could be a regime at work in the interior layer (200–500 m). However, the shape of the total VSF at these depths is also close to the GM SF, which suggests together with Rϕψ that the turbulent regime could consist in weak nonlinear interactions between IGWs.

As noticed by in some regions of the North Pacific, we found that the turbulent regime is depth dependent with rotational motions decreasing in the ocean interior. What controls the depth dependence of the turbulent regime we found is unclear, but there are reasons to think that the depth of the mean currents might have an impact. Our study has not addressed the processes at work in the generation of submesoscale structures that could explain this surface-intensified regime, including mixed layer instabilities, strain-induced frontogenesis and the turbulent thermal wind balance . Those instabilities extract their energy from the mesoscale gradients of buoyancy, which are substantial south and east of New Caledonia. In addition to observational datasets, a modelling approach to simulate submesoscale dynamics and IGWs around New Caledonia would be valuable to characterise in detail the submesoscale processes at work and investigate this depth dependence.

Secondly, our analysis exhibited regional discrepancies between the SCAL and ECAL regions, which include the surface-intensified STCC current flowing eastward associated with substantial levels of EKE, and the NCAL region, which has weaker EKE but substantial internal tides. In particular, we did not find a clear surface-intensified regime in the NCAL region. Instead, we found that IGWs might already dominate near the surface with similar contributions of rotational and divergent motions across the submesoscale-to-mesoscale range as well as a slope close to r2/3 (k-5/3). We also found that the NCAL region has lower APE in this range of scales, consistent with a weaker EKE and weaker submesoscale motions associated with a large rotational component. In the interior layer (200–500 m), we also found that rotational motions still predominate at scales larger than 10 km in the VAUB region contrary to the others. At scales larger than 100 km, the tracer SFs in the ECAL region flatten out and depart from the other regions, suggesting a regime closer to interior quasi-geostrophic turbulence, whose stirring is nonlocally generated by large-scale eddies.

The location of hotspots of ME EKE and coherent internal tides shown in Fig.  seems to be linked with the dynamical regimes occurring in the range of 3–100 km and supports the decomposition of the SF analyses into different regions. This regional link partly exists because coherent internal tides are associated with substantial non-coherent smaller IGWs and ME EKE provides APE for submesoscale structures. In some regions around New Caledonia, we also expect that some submesoscale structures can be generated in the lee of islands due to horizontal shear instabilities of the mean currents : found a substantial amount of eddies in the wake of the Vanuatu islands and north of New Caledonia where the lagoon ends using an eddy-tracking algorithm on altimetric sea level maps.

Because of those regional peculiarities, the turbulent regimes around New Caledonia characterised by SFs within the range of 3–100 km are substantially different from those occurring at midlatitude eddy-active regions e.g.. We did not find spectra transitioning from k-3 to k-2 near the surface, characterising a transition between balanced and unbalanced flows. Instead, we found slopes close to k-2 in three regions (ECAL, SCAL, VAUB), as in regions of weaker EKE such the North Equatorial Current region and the southern California Current system .

With the region north of New Caledonia (NCAL), we also provide the first observational evidence that the KE spectrum may already be close to k-5/3 (r-2/3 for VSFs) in the range of 3–100 km, with a substantial contribution of divergent motions. In the Gulf of Mexico, VSFs were shown to have an inertial range of r-2/3 but at scales smaller than 1 km, and a slope close to r1 in the range of 1–100 km . Thus, the NCAL region is likely to exhibit a turbulent regime involving IGWs at larger scales that would normally occur at smaller scales in other regions. This finding is consistent with the transition scale between balanced motions and waves found to be larger than 150–200 km by in the NCAL region.

Thirdly, we highlighted seasonal variations of the surface oceanic fine scales around New Caledonia. In the submesoscale-to-mesoscale range, temperature variance tends to increase during the cool season (June to November) compared to the warm season (December to May), whereas salinity variance decreases. However, only a weak seasonality is observed on the density variance, suggesting that constructive effects between temperature and salinity also seasonally vary, with the relative importance of temperature diminishing during the warm season. We did not find any links with the seasonal variations of the upper temperature and salinity profiles. Even if the density variance undergoes only weak seasonal variations, we found substantial variations of the APE at the surface with a larger reservoir during the cool season, mainly due to a less stratified water column during this season. Unfortunately, our dataset does not allow a separation of VSFs into different seasons, and we are unable to determine if the seasonality found on APE implies a seasonality on EKE and VSFs.

However, the seasonality of IGWs and SM motions has been shown to be out of phase near the surface, with SM motions being the most energetic in late winter/early spring, while IGWs are amplified during summer . Our estimate of the surface APE is maximum during the cool season, consistent with SM motions energised in late winter by mixed layer instabilities. demonstrate that the amplification/dampening of IGWs at the surface compared to the interior is captured by a linear IGW model. Based on this model, they estimate global maps of the horizontal KE ratio between the surface and the interior: the ratio of mode 1 shows weak seasonality around New Caledonia, but higher modes (2, 3 and 4) have a higher ratio (i.e. amplification) during February. We would then expect that surface VSFs would exhibit seasonal variations due to a change in SM KE fed by a larger reservoir of APE during the cool season, as well as an amplification of IGW at the surface during the warm season. In the interior, however, showed that balanced motions are not likely to undergo substantial seasonal cycles around New Caledonia, whereas unbalanced motions will be more important in the winter/spring period. We would then expect that interior VSFs around New Caledonia would exhibit seasonal variations in amplitude but would still exhibit similar slopes and divergent contributions, characteristics of dynamics driven by IGWs.

Finally, we showed different scale dependence in the submesoscale-to-mesoscale range. Using the scale-dependent Rossby number, we found that 10 km is a cutoff scale under which the loss of balance is likely to occur. The Helmholtz decomposition performed on VSFs globally show that ageostrophic motions are non negligible at scales smaller than 10 km as motions start to have an important divergent component. The scale-dependent density ratio also showed that the dominant effect of temperature on density slightly tends to diminish at smaller scales.

The SF analysis performed here only characterised a continuum of scales without capturing the particular scales at which the coherent internal tides vibrate. Those have well-defined propagation and wavenumber, so that they can be captured by along-track altimetry over a long record. Around New Caledonia, the first baroclinic mode associated with the M2 internal tide is the most energetic and has a wavelength between 120 and 150 km . Our SFs should not be impacted by the dominant wave (i.e. M2 mode 1) around New Caledonia. Because SFs are averaged isotropically over bins of distance in our study, the signature of coherent internal tides is also likely to be weak. However, the exact impacts of coherent internal tides on structure functions have not been studied in the literature and should be quantified by performing sensitivity analyses with idealised models including turbulence and waves. Such sensitivity studies are beyond the scope of the current work and are left for future work.

Overall, our results suggest that the structure function analysis is a powerful tool that provides physically consistent results. Amongst the benefits of the SF analysis, the capacity to be directly computed on uneven samples is clearly an advantage compared to Fourier techniques. In order to provide more insights into the turbulent regimes at work, we tried to investigate the direction of the KE cascade using third-order structure functions as done in , but our dataset revealed to be too insufficient to compute accurate higher order statistics. We believe that more ADCP observations would solve this problem and provide better statistics in order to infer the direction of the energy cascades from SFs. A larger SADCP database would also allow disentangling seasonal and local variations in order to provide information on the seasonality of SFs and turbulent regimes.

The confidence levels of the divergent components can be substantial in Figs.  and , especially for the lower bound. Those confidence levels may be the result of the combination of data of heterogeneous quality coming from different devices and ships. The confidence intervals could be reduced by increasing the number of observations in the database. Another possibility is that one or more assumptions – isotropy, homogeneity, stationarity – used to compute the divergent and rotational components may fail. Checking the validity of those assumptions is not possible from unidimensional ADCP transects only and we will need to use outputs from a high-resolution ocean model including tides and submesoscale features as done by .

Because of the substantial imprint of IGWs around New Caledonia, small-scale sea level features, that will be captured by the next generation of altimeters, will require additional work to disentangle wave signatures and geostrophic velocities. With the forthcoming SWOT satellite, an unprecedented opportunity exists to combine small-scale sea level measurements from space and in situ observing systems to better understand the small-scale ocean dynamics in regions of substantial KE and IGW activity, such as the New Caledonia region. We also believe in the support of high-resolution modelling to select a judicious deployment of in situ observations around New Caledonia and to provide valuable information about the link between sea level dynamics and the water column at fine scales. High-resolution modelling around New Caledonia is to be performed in the near future and will also help to assess the working hypothesis for the use of structure functions.