1 INTRODUCTION

Submesoscale currents (SMCs) have spatial scales in O (0–10) km and temporal scales on the order of one day, which exist widely in upper ocean in the forms of surface fronts, elongated filaments, topographic wakes and submesoscale eddies (Mahadevan and Tandon, 2006; Capet et al., 2008a; McWilliams, 2016). Due to their small spatialtemporal scales, their vertical component of relative vorticity ζ_z is roughly equivalent to the planetary vorticity f; therefore, the Rossby number . R_o can be much greater than 1 where the SMC is strong (Qiu et al., 2014; Sasaki et al., 2014), indicating their highly ageostrophic behaviors. Breaking the constraint of geostrophic balance, SMCs can extract energy form mesoscale current and transfer it to microscale scales, acting as a bridge in the energy cascade between ocean multiscale dynamics (Gula et al., 2016; McWilliams, 2016). SMCs can lead to intensive horizontal convergences or divergences, resulting in strong vertical motions reaching O (100 m/day), which play an important role in exchanging tracers between upper and interior layer of ocean (Zhong et al., 2017). Besides, the secondary circulations caused by SMCs can restratify the well-mixed upper boundary layer, which influences the mixed layer depth, the air-sea exchanges and the transport between mixed layer and subsurface layer (Boccaletti et al., 2007; Thomas et al., 2013).

There are rare measurements about SMCs since they are too difficult to be detected. Using towed Seasoar equipped with thermometer, Pollard and Regier (1992) examined the potential vorticity and secondary circulation across the front. They found the maximum vertical velocity exceeded 40 m/day, and suggested submesoscale eddy plays a crucial role in the vertical transport of properties. Based on high resolution MODIS data of sea surface temperature and chlorophyll-a, Taylor and Ferrari (2011) indicated that submesoscale fronts, occurring in high latitude region of the Atlantic, weakened the mixing in the mixed layer by restratification and caused a phytoplankton explosive bloom.

In recent years, numerical simulations were gradually applied to investigate SMCs. With Regional Oceanic Modeling System (ROMS), Capet et al. (2008a, b, c) simulated the idealized California Current and analyzed the generation and evolution of SMCs in this area. Their results indicated that SMCs occur mainly in the upper ocean, where frontogenesis and mixed layer instabilities (MLI) are main driven factors. Moreover, they revealed a forward kinetic energy (KE) cascade in the submesoscale range, which suggests SMCs play an important role in ocean energy cascade. The SMCs' role of transporting mass and tracer in horizontal and vertical was also reported by Zhong and Bracco (2013) with ROMS. Using Oceanic General Circulation Model (OGCM) with a horizontal resolution of 1/30°, Qiu et al. (2014) and Sasaki et al (2014) revealed a clear seasonal variability of SMCs in North Pacific Subtropical Countercurrent.

It remains an issue that what dynamics could generate SMCs. Two mechanisms are frontogenesis (Roullet et al., 2012) and MLI (Boccaletti et al., 2007; Callies et al., 2016). Frontogenesis can be briefly expressed as follows. The preexistent mesoscale strain filed tends to intensify the lateral buoyancy gradient and break the geostrophic balance, which will cause a secondary circulation to tilt isopycnals horizontally and restore geostrophic balance. In ocean interior, the secondary circulation develops and erases the lateral buoyancy gradient. While at surface, the vertical velocity is blocked, and the strain field is unopposed to create submesoscale fronts (Capet et al., 2008b; Callies et al., 2016). As for MLI, it is a special kind of baroclinic instabilities being confined in the mixed layer. MLI energizes SMCs by releasing available potential energy to kinetic energy.

The South China Sea (SCS) is the largest marginal sea of the Pacific, where predominant topographic features and dynamics with different spatial-temporal scales, such as general circulations (Zhou et al., 2014), mesoscale eddies (Wang et al., 2003; Zhang et al., 2016), internal waves (Xie et al., 2009; Ramp et al., 2010) and turbulent mixing (Liu and Lozovatsky, 2012; Yang et al., 2016; Shang et al., 2017), are all connected to the SMCs. The energy cascade routes between these processes are still unclear, and it remains an open question that how the mesoscale eddy transfers its energy to dissipation scales. Although it is expected that the mostly possible candidate is SMCs, the studies of SMCs based on either observations or numerical simulations are rather limited in the SCS. Based on numerical simulation, Luo et al. (2016) indicated that symmetry instabilities around submesoscale eddies could draw energy from geostrophic shear and then cascade it to turbulent mixing, which was as high as 4×10^-7 W/kg. Ji et al. (2017) observed SMCs in the periphery of mesoscale eddies, where the energy of SMCs is significantly elevated when compared with those in the central area. Based on three-cruise measurements, Yang et al. (2017) found elevated mixing near the periphery of mesoscale eddies, which is related to the active SMCs, indicating a direct contribution of SMCs to turbulent mixing.

These studies have undoubtedly improved our understanding of SMCs in the SCS, however, they failed to provide a regional picture of SMCs in the SCS. Therefore, it is the intent of this study, in which, the spatial distribution and temporal variabilities of SMCs and their associated mechanisms are explored in detail based on ROMS with a high horizontal resolution of 1 km. This paper is organized as follows. Section 2 gives the basic model setups and the method used. Section 3 presents the vertical and horizontal distribution of SMCs in the northeastern SCS and their mechanisms. Section 4 gives the seasonal variability of SMCs and its driven factors. Section 5 examines the parameterization proposed by Fox-Kemper et al. (2008, hereafter FFH parameterization). A summary is followed at last.

2 MATERIAL AND METHOD 2.1 Model setup

The model used here is hydrostatic Regional Ocean Modeling System (ROMS; Shchepetkin and McWilliams, 2005). Although some SMCs are nonhydrostatic, their aspect ratio still meets within the mixed layer, which indicates an applicability of hydrostatic approximation. For example, Mahadevan (2006) simulated SMCs by nonhydrostatic model with a horizontal resolution of 500 m, and find the output is hydrostatic.

One-way offline nesting procedure (Mason et al., 2010) is setup to reduce errors during simulating the SMCs. The large zone, named as R5, is located in 110°–126°E, 15°–25°N, with a horizontal resolution of 5 km. And the small zone, named as R1, is located in 114.5°–121°E, 18°–23°N, with a horizontal resolution of 1 km (Fig. 1). This model simulates the whole depth of the ocean using ETOPO2 bathymetry data, and SMCs are diagnosed from the output of the upper 200 m in 31 layers. The turbulence closure scheme used here is Generic Length Scale (GLS) model (Umlauf and Burchard, 2003), and the boundary condition is radioactive boundary condition (Orlanski, 1976).

For R5 zone, the forcing field is 0.125° monthly data from European Centre for Medium-Range Weather Forecasts (ECMWF), and the boundary condition is from HYCOM dataset. The model is firstly run for 25 years to be statistically stable using climatological data of ECMWF and HYCOM products. Then the simulation is performed for another 13 months using monthly averaged state of forcing and boundary condition from Dec. 2012 to Dec. 2013. For R1 zone, its boundary condition is replaced with the output of R5 simulation. The temporal resolution of the model is 90 s, and the output is saved daily. The velocity (u, v, w), sea surface height (h), salinity (s), and sea surface temperature (t) are all available in the output.

2.2 Velocity decomposition

The total velocity field, take u as an example, can be divided into components of submesoscale u_s, mesoscale u_m and the large scale u_l. Based on the spatial scale developed from baroclinic instabilities L_i=NH_i/f, where buoyancy frequency N≈10^-2/s, the mean depth of SCS H₁≈10³ m or the mean mixed layer depth (MLD) of SCS H₂≈10² m, and the Coriolis parameter f≈5×10^-5/s, we determine L₁≈200 km and L₂≈20 km as the threshold that distinguish large scale, mesoscale and submesoscale dynamics in the SCS. Highpass, bandpass and lowpass filters are applied to the total velocity field, then u_s, u_m and u_l are obtained. Decomposition of velocity magnitude shows that the submesoscale component appeared as elongated filaments are weak when compared with large or mesoscale components, which correspond to the background flow and mesoscale eddies (Fig. 2).

3 RESULT 3.1 Vertical distribution of SMCs in the northeastern SCS

Take the case on Dec. 22, 2012 as an example, an energetic warm eddy exists near 118°E, 21°N, within which sea level anomaly (SLA) is up to 36 cm (Fig. 3a) and Rossby number R_o is negative with the absolute value smaller than 1 (Fig. 3b). Near the eddy periphery, submesoscale filaments are very clear, and R_o values were elevated being larger than 1, indicating Coriolis effect is no longer dominant, and the geostrophic balance is broken. Besides, submesoscale filaments and eddies spread widely in regions with predominant topography features, such as continental slopes and west of Taiwan Island.

A vertical variability of SMCs is implied by maps of R_o at 20 m, 45 m and 110 m on Jan. 20, 2013 (Fig. 4a, b, c). At 20 m, there exist abundant submesoscale filaments and eddies, mostly north of 20°N, and the maximum R_o value reaches 10.3, with a probability of R_o≥1 being 0.05. At 45 m, approximately the bottom of mixed layer, although SMCs become slightly weak, there exist clear filaments with large R_o values reaching 9.9, and probability of R_o≥1 is 0.04, indicating active SMCs. However, beneath the mixed layer and deepening to 110 m, the probability of R_o≥1 decrease to 0.01, the SMCs only occur near shore and around islands. The submesoscale filaments almost disappeared, suggesting SMCs turn weak dramatically out of the mixed layer.

Due to the ageostrophic feature, there are strong vertical motions where SMCs are active (Fig. 4d). At 20 m depth, although the background vertical velocity field is generally weak, there are distinct filaments with elevated vertical velocity O (100 m/day), which matched well with the SMCs locations. These filaments with strong vertical motions may play key roles in exchanging material, chemical and biological tracers between ocean surface and interior (Thomas et al., 2008; Zhong and Bracco, 2013).

According to the quasi-geostrophic theory, the slope of horizontal wavenumber spectra showed a power law of k^-3 when quasi-geostrophic currents are dominant (Charney, 1971). However, if there are active SMCs, both the observations and simulations show the spectra slope becomes flatter and obeys a power law of k^-2 (Capet et al., 2008a; Callies and Ferrari, 2013; Callies et al., 2015). The kinetic energy spectra of horizontal velocity u, v in SA region (indicated by box in Fig. 3) is examined (Fig. 5). The spectra in surface layer show a power law of k^-2 in submesoscale ranges (with a wavelength smaller than 20 km), which indicates submesoscale motions being dominant there. However, the spectra slope at 190 m steepens and shows a power law of k^-3, suggesting SMCs become weak compared with surface layer.

To be more representative, we calculated the probabilities of R_o≥1 at different depths in Jan. 2013 (Fig. 6). The probabilities are biggest at surface, the mean value of which is 0.03, and the maximum reaches 0.05. Though the probability profiles are different for each day, they decrease wholly with depth. At 200 m, the mean probability decrease to a minimum value 0.01, 1/3 of that in the surface layer, consistent with R_o map at different depths, suggesting SMCs are notably active in the mixed layer.

The vertical variation of SMCs is essentially controlled by their generation mechanisms: frontogenesis and MLI. Frontogenesis is obviously active at ocean surface. MLI can be estimated by the baroclinic energy conversion rate w_sb_s (BCR, Callies et al., 2016; Uchida et al., 2017), where w_s and b_s are vertical velocity and buoyancy in submesoscale range obtained by high-pass filter. Zonal averaged BCR section during winter of 2012 (Fig. 7) shows the vertical variation of MLI. Within the mixed layer, whose depth is about 50 m averagely, the BCR is highly large, which elevated to ~10^-9 m²/s³ in upper 30 m, about an order of magnitude larger than that in interior being ~10^-10 m²/s³. The vertical pattern of BCR indicates that MLI is also active within the mixed layer, revealing the mechanism of the vertical distribution of SMCs.

3.2 Horizontal distribution of SMCs in the northeastern SCS

Seen from sea surface temperature (SST) on Dec. 22, 2012 (Fig. 8), there are two anti-cyclonic eddies that are close to each other. SST varies sharply between the edge of two eddies, and the horizontal gradient reaches as high as 0.56℃/km, which is a typically strong thermal front compared with that of 1.2℃ change across ~5 km near Kuroshio (D'Asaro et al., 2011). As the velocity field shown, the cold frontal tongue is mainly formed the nearshore cold water carried by the strong rotation of the warm eddy. The consistence of this strong front and active submesoscale filaments (Fig. 3b) indicates the eddy periphery is a favorable site for SMCs generation.

A parameter of frontal tendency (F) was used to examine the fronts evolution,

where Q is the straining deformation caused by the horizontal velocity. Frontal tendency reveals the lateral density gradient variance caused by the straining of horizontal velocity field (Hoskins, 1982; Brannigan et al., 2015; Uchida et al., 2017). If F>0, the horizontal density gradient would become stronger, which means a front generation process. Otherwise, the density gradient goes weaker, leading to a frontal elimination. From the snapshot of F on Dec. 22, 2012 (Fig. 9), frontogeneses (indicated by positive values) are ubiquitous in this area, especially at the edge of mesoscale eddies and nearshore regions, which are more than twice of frontal eliminations. Generally, the submesoscale filaments shown in Fig. 3b and positive F values share a highly similar spatial pattern, which indicates frontogenesis is a dominant generation mechanism of SMCs in the northeastern SCS. Over continental shelves, such as Dongsha Island and Taiwan Island, the sharply varied topography also contributes to the SMCs generation (Zheng et al., 2008).

To further examine the horizontal distribution of SMCs, we choose January and February of 2013 as a study period, and count the number of days when R_o≥1 (Fig. 10). The result suggests that SMCs are much more active north of 20°N than those south of 20°N, both in area and duration. Specifically, in west of Dongsha Island and southwest of Taiwan Island, the SMCs are extremely vigorous and last for a long time reaching more than 50 days.

This spatial variability is caused by the regional difference of eddies features. In the northern region, the eddies have a ~200-km diameter in average, with a high SLA of 50 cm; while in the south part, the eddy diameter is only about 100 km with a SLA of 30 cm. Moreover, eddies in the northern region are mostly cyclonic, which deepen the mixed layer and make SMCs develop sufficiently. In contrast, the eddies in the southern part are mostly anticyclonic. Significantly active SMCs in the patchy area around the Dongsha and Taiwan Island are likely related to topographic wakes.

3.3 Seasonal variability of SMCs in the northeastern SCS

Map of R_o on Dec. 22, 2012 (winter, Fig. 11a) is compared with that on Aug. 25, 2013 (summer, Fig. 11b). In summer, R_o values are only elevated near Luzon Strait, suggesting active topography induced SMCs there (Zheng et al., 2008). But away from the shore, the R_o values are wholly small, being 0.4 or even smaller, and there are no clear submesoscale filaments with large R_o reaching 10 occurred in winter, which indicates SMCs are generally more active in winter than summer.

To examine the seasonal variability statistically, we calculate the probabilities of R_o≥1 at 5 m from Dec. 2012 to Dec. 2013 (Fig. 12a). The results show a clear seasonal variability that being large in winter and small in summer. In winter, the probabilities are 0.04 on average and the maximum value reaches 0.06. In summer, the probabilities decreased to the minimum of the whole year, with a mean value of only 0.02. In addition, variability of submesoscale kinetic energy (KE_s) was also examined (Fig. 12b), which lies in a mean level of O (10⁸ m²/s²) and shares Maps of R_o at 5 m on Dec. 22, 2012 (a) and Aug. 25, 2013 (b) a similar seasonal variability with that of probabilities of R_o≥1, validating that SMCs are strong in winter and weak in summer. To explore the reason responsible for this seasonal variability, mesoscale KE (KE_m), Strain Rate , frontal tendency F and baroclinic energy conversion rate BCR are investigated (Fig. 12c, d, e, f). Both KE_m and SR are significantly enhanced in winter and drop to a minimum in summer, the correlation coefficients between them and KE_s are 0.68 and 0.83, respectively. The frontal tendency and BCR are elevated in winter and turn weak in summer, implying the seasonalities of frontogenesis and MLI. These suggest that the seasonalities of frontogenesis and MLI are the essential causes leading to the similar seasonal pattern of SMCs.

MLI plays an important role in modulating SMCs seasonality. SMCs are confined in mixed layer, and they are closely related to the depth and stability of mixed layer (Fig. 13). In winter, the thermal loss from ocean surface and the strong wind forcing induce enhanced turbulent mixing, which make the mixed layer as thick as about 70 m, and the stratification N² as weak as 10^-5/s². Moreover, there are sharp lateral gradients of density in mixed layer, which reaches 0.31 kg/(m³∙km). These lateral gradients of buoyancy develop the MLI, resulting in vigorous SMCs. In contrary, the situation is inverse in summer.

3.4 FFH parameterization

The ocean surface layer is biologically active but nutrient-depleted, some vertical motions play important roles in transporting nutrients from thermocline to surface for phytoplankton production (Thomas et al., 2008). Some studies (e.g. McGillicuddy et al., 1998) believe mesoscale eddies are helpful for the vertical transport, but Oschlies (2008) estimated the eddy-pumping fluxes and found that they are insufficient to supply the required nutrients. Because of the ubiquity of SMCs in the ocean and their associated strong vertical motions, submesoscale vertical fluxes of nutrients may play critical roles in maintain the ocean primary productivity (Thomas et al., 2008).

One important mechanism of SMCs generation is MLIs, whose spatial-temporal scales are as small as 200 m ~20 km and 1 day (Boccaletti et al., 2007). MLIs only exist in surface mixed layer and are formed by extracting energy from fronts. Submesoscale eddies would be excited in the mixed layer when MLIs dominate there. Associated with these eddies, a prominent vertical motion was induced. Fox-Kemper et al. (2008) developed a parameterization to estimate the magnitude of this vertical velocity in terms of stream function as

where H denotes MLD, b^z is the buoyancy averaged within the mixed layer, f is the Coriolis parameter, C_e is an efficiency factor that assigned as 0.07 here and μ(z) is a vertical structure function in the form of

based on this parameterization, vertical velocity caused by the submesoscale eddies can be obtained as .

A snapshot of w_p field at 5 m is given in Fig. 14b, which shows that w_p has a downwelling-upwelling coupled structure, generally shares a similar pattern with numerical simulated one w_s (Fig. 14a). The magnitude of the well-parameterized w_p lies in the order of O (100 m/day), in the same level as the numerical simulation. Besides, we investigated the energy spectra of the parameterized and simulated vertical velocity (Fig. 14c) to see if they are statically comparable. The spectra have similar pattern, which stay in high energy level over small wavenumber range and drop rapidly over large wavenumbers, indicating this parameterization is capable of deducing submesoscale vertical velocity to some extent. However, there are specific quantitive discrepancies between the profiles of them in the mixed layer, such as at 118.46°E, 20.23°N (Fig. 14d). w_p decreases with depth, from 27.3 m/day at 1 m to 0 m/day at 40 m, which is due to the relation between μ(z) and depth z. w_s is wholly larger than wp, ranging from 30 to 80 m/day. The vertical trend of w_s is also different with that of w_p, with smaller values in both two bound of the mixed layer. The discrepancy implies that the FFH parameterization does not work well where other mechanisms, such as frontogenesis (here F=1.3×10^-14kg²/(m⁸∙s)), are responsible for generation of SMCs.

4 CONCLUSION

Spatial-temporal variabilities of SMCs in the northeastern SCS are examined based on a numerical simulation with ROMS model, along with the reasons responsible for those variability. The results suggest that SMCs are active at ocean surface, especially near eddy periphery and around predominant topographic features. In vertical, SMCs are intensified in mixed layer and turn weak when going deeper. Strong vertical motions are associated with SMCs due to their ageostrophic feature, with magnitude on the order of 100 m/day. In horizontal, SMCs north of 20°N are generally strong than those south of 20°N, both in occurring area and strength. A clear seasonal variability that being vigorous in winter and weak in summer is revealed, which is likely due to the high strain rate and deep mixed layer depth in winter. FFH parameterization is tested, and the result indicates that this parameterization could reproduce a reasonable vertical motion where the MLIs dominate, but perform bad in areas where other mechanisms are responsible for SMCs generation. This study could improve our understanding of SMCs in the SCS.

5 DATA AVAILABILITY STATEMENT

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.