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Xiaolong Huang, Zhiyou Jing, Ruixi Zheng, Haijin Cao. Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea[J]. Acta Oceanologica Sinica, 2020, 39(11): 1-12. doi: 10.1007/s13131-020-1671-4
Citation: Xiaolong Huang, Zhiyou Jing, Ruixi Zheng, Haijin Cao. Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea[J]. Acta Oceanologica Sinica, 2020, 39(11): 1-12. doi: 10.1007/s13131-020-1671-4

Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea

doi: 10.1007/s13131-020-1671-4
Funds:  This work is supported by the Chinese Academy of Sciences under contract Nos ZDBS-LY-DQC011, ZDRW-XH-2019-2 and ISEE2018PY05; the Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) under contract No. GML2019ZD0303; the National Natural Science Foundation of China under contract Nos 41776040 and 92058201; the Pilot National Laboratory for Marine Science and Technology (Qingdao) under contract No. OCFL-201804; the State Key Laboratory of Tropical Oceanography under contract No. LTO1907; the Guangzhou Science and Technology Project under contract No. 201904010420.
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  • Corresponding author: E-mail: jingzhiyou@scsio.ac.cn
  • Received Date: 2020-04-13
  • Accepted Date: 2020-07-08
  • Available Online: 2020-12-28
  • Publish Date: 2020-11-25
  • This study investigates the submesoscale fronts and their dynamic effects on the mean flow due to frontal instabilities in the wind-driven summer offshore jet of the western South China Sea (WSCS), using satellite observations, a 500 m-resolution numerical simulation, and diagnostic analysis. Both satellite measurements and simulation results show that the submesoscale fronts occupying a typical lateral scale of O(~10) km are characterized with one order of Rossby (Ro) and Richardson (Ri) numbers in the WSCS. This result implies that both geostrophic and ageostrophic motions feature in these submesoscale fronts. The diagnostic results indicate that a net cross-frontal Ekman transport driven by down-front wind forcing effectively advects cold water over warm water. By this way, the weakened local stratification and strong lateral buoyancy gradients are conducive to a negative Ertel potential vorticity (PV) and triggering frontal symmetric instability (SI) at the submesoscale density front. The cross-front ageostrophic secondary circulation caused by frontal instabilities is found to drive an enhanced vertical velocity reaching O(100) m/d. Additionally, the estimate of the down-front wind forcing the Ekman buoyancy flux (EBF) is found to be scaled with the geostrophic shear production (GSP) and buoyancy flux (BFLUX), which are the two primary energy sources for submesoscale turbulence. The large values of GSP and BFLUX at the fronts suggest an efficient downscale energy transfer from larger-scale geostrophic flows to the submesoscale turbulence owing to down-front wind forcing and frontal instabilities. In this content, submesoscale fronts and their instabilities substantially enhance the local vertical exchanges and geostrophic energy cascade towards smaller-scale. These active submesoscale processes associated density fronts and filaments likely provide new physical interpretations for the filamentary high chlorophyll concentration and frontal downscale energy transfer in the WSCS.
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Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea

doi: 10.1007/s13131-020-1671-4
Funds:  This work is supported by the Chinese Academy of Sciences under contract Nos ZDBS-LY-DQC011, ZDRW-XH-2019-2 and ISEE2018PY05; the Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) under contract No. GML2019ZD0303; the National Natural Science Foundation of China under contract Nos 41776040 and 92058201; the Pilot National Laboratory for Marine Science and Technology (Qingdao) under contract No. OCFL-201804; the State Key Laboratory of Tropical Oceanography under contract No. LTO1907; the Guangzhou Science and Technology Project under contract No. 201904010420.

Abstract: This study investigates the submesoscale fronts and their dynamic effects on the mean flow due to frontal instabilities in the wind-driven summer offshore jet of the western South China Sea (WSCS), using satellite observations, a 500 m-resolution numerical simulation, and diagnostic analysis. Both satellite measurements and simulation results show that the submesoscale fronts occupying a typical lateral scale of O(~10) km are characterized with one order of Rossby (Ro) and Richardson (Ri) numbers in the WSCS. This result implies that both geostrophic and ageostrophic motions feature in these submesoscale fronts. The diagnostic results indicate that a net cross-frontal Ekman transport driven by down-front wind forcing effectively advects cold water over warm water. By this way, the weakened local stratification and strong lateral buoyancy gradients are conducive to a negative Ertel potential vorticity (PV) and triggering frontal symmetric instability (SI) at the submesoscale density front. The cross-front ageostrophic secondary circulation caused by frontal instabilities is found to drive an enhanced vertical velocity reaching O(100) m/d. Additionally, the estimate of the down-front wind forcing the Ekman buoyancy flux (EBF) is found to be scaled with the geostrophic shear production (GSP) and buoyancy flux (BFLUX), which are the two primary energy sources for submesoscale turbulence. The large values of GSP and BFLUX at the fronts suggest an efficient downscale energy transfer from larger-scale geostrophic flows to the submesoscale turbulence owing to down-front wind forcing and frontal instabilities. In this content, submesoscale fronts and their instabilities substantially enhance the local vertical exchanges and geostrophic energy cascade towards smaller-scale. These active submesoscale processes associated density fronts and filaments likely provide new physical interpretations for the filamentary high chlorophyll concentration and frontal downscale energy transfer in the WSCS.

Xiaolong Huang, Zhiyou Jing, Ruixi Zheng, Haijin Cao. Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea[J]. Acta Oceanologica Sinica, 2020, 39(11): 1-12. doi: 10.1007/s13131-020-1671-4
Citation: Xiaolong Huang, Zhiyou Jing, Ruixi Zheng, Haijin Cao. Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea[J]. Acta Oceanologica Sinica, 2020, 39(11): 1-12. doi: 10.1007/s13131-020-1671-4
    • Upper ocean circulation, significantly influenced by atmospheric forcing consists of motions of a broad range of scales (Wunsch and Ferrari, 2004; Thomas and Taylor, 2010). The submesoscale fronts, which constitute an asymmetrical atmospheric forcing (e.g., down-front wind forcing and surface cooling), can be frequently detected from high-resolution satellite observations (Zheng et al., 2008; Liu et al., 2015; Liu and Levine, 2016). These elongated fronts are dynamically characterized by O(1) Rossby number (Ro) and Richardson number (Ri). In addition, they possess a typical lateral scale of O(1–10) km and a time scale of O(hour–day) (Thomas et al., 2008). For such space and time scales, the assumption of geostrophy is no longer valid (Gula et al., 2014; McWilliams, 2017, 2019). Thus, dynamic processes involved in submesoscale fronts or filaments include both geostrophic and ageostrophic motions. Furthermore, the ageostrophic processes associated with the submesoscale instabilities can produce significant divergent flows and stir up a large vertical velocity, thus substantially contributing to the enhanced vertical fluxes of heat, buoyancy, nutrient, and momentum in the upper oceans (Mahadevan and Tandon, 2006; Su et al., 2018; Zhang et al., 2019). The frontal instabilities at submesoscales have been detected to be able to extract kinetic energy (KE) from the larger-scale geostrophic flows, and cascade energy towards smaller scales (Mcwilliams et al., 2001; D’Asaro et al., 2011). These phenomena are widely viewed in the ocean and are interpreted as a bridge between the mesoscale and small-scale motions (Capet et al., 2008; McWilliams, 2016).

      The upper basin-scale circulation of the South China Sea (SCS) is mostly dominated by the east Asian monsoon system with a distinct seasonal cycle (Wyrtki, 1961). A three-dimensional ocean model with a high frequency atmospheric force is utilized to study the seasonal characteristics of flow and its associated dynamic analysis in SCS (Gan et al., 2006). Abundant mesoscale eddies are observed to be embedded in the seasonal circulation (Chu et al., 1998; Chen et al., 2011; Zhang et al., 2016; Xie and Zheng, 2017; Xie et al., 2018). The statistical properties of the mesoscale eddies and their spatio-temporal variability are widely studied using satellite altimeter data in the SCS (Wang et al., 2003; Chen et al., 2011; Zheng et al., 2017; He et al., 2018). A weeklong field campaign in the western South China Sea (WSCS) has revealed a three-dimensional structure and physical properties of a typical cold eddy, as well as its underlying forcing mechanism for the formation of the cyclonic cold eddy (Hu et al., 2011). These active eddies in the SCS are found to be effecting the biogeochemical cycles through upwelling and downwelling (Xiu and Chai, 2011), the dissipation of mesoscale eddies (Yang et al., 2019) and contributing energy transfer and vertical exchanges via multi-scale interactions (Chen et al., 2012). The southeast of Vietnam is an eddy active zone of the SCS with a high eddy kinetic energy (EKE) estimated from altimeter measurements (Fig. 1a). The unique orographic wind jet could be one of main reasons for the strong mesoscale variability in the WSCS (Wang et al., 2008).

      Figure 1.  Climatological EKE and sea surface temperature (SST) in the SCS. a. EKE based on 30–90 d band-pass filtered satellite altimeter SLA data from October 1992 to August 2016; and b. climatological SST distribution in the SCS during summer. The black box in a denotes the WSCS (9°–14°N, 108.5°–113°E); the black vectors and the green arrow marks in b indicate the geostrophic current (> 0.1 m/s) and the offshore jet, respectively.

      As shown in Fig. 1b, the SST and the surface current during the summer suggest that the summer offshore jet with surface cooling is a common phenomenon in the WSCS because of the southwest wind forcing (Kuo et al., 2000; Xie et al., 2003). The offshore jet and its associated flow variation are investigated by a high-resolution region ocean model and it is found that the coastal currents induced by the wind forcing and shelf topography contributed to the coastal jet separation (Gan and Qu, 2008). At the same time, the jet separation is also generated by a combination of wind stress, river discharge, and vorticity transport, which are originated from the coast off Vietnam and located around 12°N, between 110° and 113°E (Wang et al., 2006; Li et al., 2014). Owing to its underlying importance in the multi-scale interactions, enhanced air-sea communication, and regional ecosystem, the far-extended offshore jet has been widely investigated in the past decade, especially on its intra-seasonal, seasonal, inter-annual, and inter-decadal variations (Fang et al., 2002; Xie et al., 2007; Wang et al., 2010; Chen and Wang, 2014; Li et al., 2014). In summer, the upwelled cold water is advected offshore, as detected from the satellite images in the filament-shaped upwelled frontal zones (Metzger, 2003; Liu et al., 2015).

      The SCS is a region with active submesoscale processes (Zheng et al., 2020). In the WSCS, submesoscale structures with a length scale of 10 km are frequently detected in high-resolution ocean color images, which are generated on the frontal system of the cold jet (Liu et al., 2015). An active submesoscale vortex in the WSCS is also examined using ocean color observations and a high-resolution simulation (Yu et al., 2018). Although these submesoscale phenomena are viewed by high-resolution satellite observations, the dynamic characteristics of the submesoscale processes on the frontal system have not been well understood so far. In this study, we examine the dynamic features of the submesoscale density fronts and their potential effects on the vertical communication and energy cascade in the offshore jet of the WSCS, using a fine-resolution simulation and satellite measurements. The remainder of this paper is organized as follows. Section 2 describes the satellite data, fine-resolution simulations, and related dynamic parameters. Section 3 discusses the features of the submesoscale fronts under the influence of down-front wind forcing. Section 4 analyzes the forward energy transfer through submesoscale instabilities. Finally, Section 5 summarizes the results from this study.

    • The primary satellite datasets used in this study include high-resolution SST data, sea level anomaly (SLA) data, sea surface wind field data, and MEdium Resolution Imaging Spectrometer (MERIS) chlorophyll a data. The high resolution SST data are provided by the U.K. Meteorological Office and comprise 6 km×6 km daily products, distributed by the Group for High Resolution Sea Surface Temperature (GHRSST) project (http://data.nodc.noaa.gov/ghrsst/L4/GLOB/UKMO/OSTIA/), and merged with in situ, microwave, and infrared satellite data (Donlon et al., 2012). The daily SLA datasets are distributed by the French archiving, validation and interpretation of satellite oceanographic (AVSIO) setup and range from October 1992 to August 2016, with a spatial resolution of 0.25°×0.25°. This gridded SLA product is merged with TOPEX/Poseidon (T/P), Jason, ERS-1, ERS-2, and ENVISAT (ftp://ftp.aviso.oceanobs.com/global/). The daily surface winds are obtained from the NOAA National Climatic Data Center (NCDC) (ftp://eclipse.ncdc.noaa.gov/pub/seawinds/) at a 0.25° resolution (Zhang et al., 2006). The sea surface chlorophyll a concentration data are derived from the MERIS Level 2 Full Resolution Full Swath (FRS) dataset from May 17, 2002 to April 8, 2012 (ftp://merisfrs-ftp-ds.eo.esa.int). This dataset provides observations at high temporal, spatial (~300 m), and spectral resolution, and with a higher sensitivity than is provided by other satellite sensors, thus allowing us have new insights into the fine structure of the surface fronts and filaments.

      A fine-resolution nested Regional Oceanic Modeling System (ROMS) (Shchepetkin and McWilliams, 2005) is used to investigate the submesoscale processes in this study. The boundary and initial conditions of the model are derived from the monthly datasets of simple ocean data assimilation (SODA) (Carton and Giese, 2008). The simulations are forced by wind stress and atmospheric forcing. The wind forcing is from a daily mean climatology Quick Scatterometer (QuikSCAT) dataset (Risien and Chelton, 2008). The atmospheric forcing related to heat and freshwater fluxes are derived from the monthly climatology of the international Comprehensive Ocean-Atmosphere Data Set (ICOADS) (Woodruff et al., 2011). The bathymetry data for all the domains are obtained from the British Oceanographic Date Centre (BODC) (https://www.bodc.ac.uk/data/) based on the 30 arc-s dataset of General Bathymetric Chart of the Oceans (GEBCO).

    • The online nesting of the ROMS utilizes an approach of successive horizontal grid refinements from a parent grid (ROMS0) to two nested child grids (ROMS1 and ROMS2) (Penven et al., 2006; Gula et al., 2015). The model has 60 levels in terrain-following vertical S-coordinates with concentrated levels in the boundary layers (Lemarié et al., 2012). The vertical subgrid mixing of tracers and momentum is based on the K-profile parameterization (KPP) (Large et al., 1994).

      The ROMS0 with a grid resolution of approximately 7.5 km covers the entire western Pacific, which reaches an equilibrium state after a 20-year spin up, and then runs an additional two years to provide daily boundary information for the SCS (ROMS1, which has a grid resolution of approximately 1.5 km) and the WSCS (ROMS2, which has an approximate grid solution of 500 m) (Fig. 2). All of these nested models have a daily mean output in the 21st model year. In this study, the high-resolution results of ROMS2 are used to analyze the submesoscale fronts on the eastward jet of the WSCS.

      Figure 2.  Maps of Rossby number ($Ro \!= \! \zeta /f$) from ROMS0, ROMS1, and ROMS2 (black rectangle) simulation in the WSCS.

    • As an important dynamic tracer, the potential vorticity (PV) significantly affects the hydrostatic and geostrophic balance, and reflects the stability of the oceanic flow (Hoskins, 1974; Thomas, 2005; Thomas et al., 2013). Different types of instabilities develop when the Ertel PV takes the opposite sign of the Coriolis parameter f. The Ertel PV, denoted by q, is given by (Hoskins, 1974):

      where $ {\omega }_{{\rm{a}}}\!=\!f {{k}}\!+\!\nabla \!\times\! {{u}}$ is the absolute vorticity, in which k is local vertical unit vector; $b \!=\! - g\rho /{\rho _0}$ is the buoyancy (g is the gravitational acceleration, ρ is the potential density, and ρ0 is the reference density); and $\nabla b$ refers to the buoyancy gradient. $ (f\!+\!\zeta) $ and $ {\omega }_{\rm{h}}$ are the vertical and horizontal components of $ {\omega }_{\rm{a}}$, respectively. $\zeta \!=\! \!\partial v/\partial x \!-\!\! \partial u/\partial y$ is the relative vorticity; and ${N^2}\! \!=\!\! - \dfrac{g}{{{\rho _0}}}\dfrac{{\partial \rho }}{{\partial z}}$ is the buoyancy frequency. The last two terms of Eq. (1) are the horizontal component (Ertel PVh, i.e., EPVh) and vertical component (Ertel PVv, i.e., EPVv) of the Ertel PV, respectively.

      For a geostrophic flow, the Ertel PVh using the thermal wind relation can be approximately written as:

      The Ertel PVh is negative definite and plays a role in reducing the PV in the northern hemisphere. Moreover, the last term of Eq. (2) illuminates that the Ertel PVh is contributed by a sharp lateral buoyancy gradient forced by the geostrophic flow vertical shear (Boccaletti et al., 2007). The strength of the lateral buoyancy gradient can be expressed by the frontal sharpness (Gula et al., 2016),

      The wind-work is conducive to changing the buoyancy field in the upper ocean. The effect of the Ekman transport advecting buoyancy can be expressed in terms of the Ekman buoyancy flux (EBF) (Thomas, 2005):

      where Me is the Ekman transport and $\left({{\tau _x},{\tau _y}} \right)$ is the wind stress vector.

      A negative PV is a key parameter to diagnose the frontal instabilities (e.g., symmetric instability (SI)). SI is a type of shear instability at submesoscale, which can draw KE from the background geostrophic flow (Taylor and Ferrari, 2009; Thomas, 2012). The rate at which the shear instabilities extract geostrophic KE can be represented by the geostrophic shear production (GSP) (Thomas and Taylor, 2010):

      where the overbars and primes denote spatial averaged and perturbations from the average, respectively; ug refers to the geostrophic velocity; and w is the vertical velocity from the simulations. Similarly, the buoyancy flux (BFLUX) can be used to estimate the rate of releasing the available potential energy (APE) stored in the front (Fox-Kemper et al., 2008):

      where b′ denotes the abnormal buoyancy after subtracting the spatial average.

    • In Fig. 3a, a conspicuous feature is that the upwelled cold water (<27.5°C) is pumped from the subsurface water in the coastal region and is advected to the east. The offshore cold jet from the coast also causes an offshore transport of the coastal upwelled nutrition (>1 mg/m3) (the tongue-shaped ocean color image with a high chlorophyll a concentration on a lateral scale of approximately 30 km in Fig. 3b). Furthermore, active fine structures can be observed in the periphery of high chlorophyll a, which is also an active thermal front zone. These structures are roughly within the submesoscale range.

      Figure 3.  Spatial distribution of SST of the Moderate Resolution Imaging Spectroradiometer (MODIS) in the WSCS (black box shown in Fig. 1) (a); and maps of chlorophyll a concentration (mg/m3, shading) base 10 log and wind vectors on July 26, 2009 (b).

      Although snapshots of ocean color image provide observational evidence for the submesoscale structures near the eastward jet (Liu et al., 2015), they cannot support a dynamic interpretation for the submesoscale motions, as they are fast evolving. To further analyze submesoscale dynamical processes associated with wind forcing in the WSCS upwelling zone. A representative and clean filamentary case with strong lateral buoyancy gradients is selected from the ROMS2 results. Figure 4 shows their snapshots of spatial characteristics and zoomed structures on August 4. These simulation results have been evaluated against the limited historical observations and reanalysis data. The comparisons to measurements show that the simulations are reliable to characterize the upwelling and front conditions.

      Figure 4.  Snapshot of the SST (shading) and eastward jet (bold black line) in the WSCS from ROMS2 simulation at 13:00 on August 4, 21 model years (a) (the gray contours denote the SLA, unit: m); the SST zoomed into the rectangles of Fig. 4a (b); and probability density function (PDF) of Ro within a dashed rectangle in Fig. 4b (c), refers to the frontal zone of jet (11.8°–12.1°N, 110.57°–111°E) at depths of 5 m and 100 m, respectively.

      The diagnostic parameters are estimated for the sub-region (Fig. 4b, 11.8°–12.1°N, 110.57°–111°E) as explained below to show the fine dynamic features of the submesoscale fronts in the summer offshore cold jet. Here we define the zero vorticity contour as the jet axis according to Chen and Wang (2014). In this frontal zone, the probability density function (PDF) of Ro$\left({\zeta /f} \right)$ tends to be asymmetric with a positive skewness at the surface layer (5 m) compared to that at 100 m (Fig. 4c). It exhibits a feature that O(1) Ro widely exists in the upper ocean of the frontal zone of jet. This implies a departure from the balanced geostrophic prediction (Dong and Zhong, 2018). As a result, this frontal zone with enhanced lateral buoyance gradients has a favorable situation for the occurrence of submesoscale processes. Owing to the presence of the wind forcing and offshore cold jet, the enhanced frontal sharpness normalized by f 3 can be clearly detected along the elongated front (Fig. 5a). The frontal sharpness has a peak within a width of approximately 5 km between the outcropping isopycnals of 21.4 and 21.8 near the surface eastward jet. The across-front section (magenta solid line in Fig. 5a) is mapped to show its vertical profile (Fig. 5b). The submesoscale density front is mostly active in the upper mixed layer with a strong frontal sharpness. Furthermore, some scattered strong frontal sharpness can be seen at the base of the mixed layer (MLD) owing to the mixed layer instability.

      Figure 5.  Frontal sharpness (M4, shading) normalized by f 3: horizontal distribution of the frontal sharpness (a); vertical profiles of the frontal sharpness (b). The MLD is shown as black lines. The gray contours refer to isopycnals with a spacing of 0.1 kg/m3.

      Figure 6 presents the divergence ($\text{δ} \!=\! {u_x} \!+\! {v_y}$) and vertical velocity to illustrate the ageostrophic effect at the frontal zone. The instantaneous vertical velocity is characterized with a positive-negative pattern, similar to the horizontal divergence. It means that the convergence appears in the frontal jet, where the downwelling can reach 100 m/d and is one order of magnitude larger than the typical mesoscale effects (Mahadevan and Tandon, 2006), which substantially enhances the local vertical exchanges.

      Figure 6.  Maps at 10 m of divergence normalized by f (shading) (a) and vertical velocity (shading) (b). The gray contours represent isopycnals with a spacing of 0.1 kg/m3.

      The temperature and along-front perturbation velocity in the vertical section show a typical ageostrophic secondary circulation across the submesoscale front (Fig. 7). The secondary circulations have a double-cell structure with dowelling on the dense side of the front and upwelling on the light side away from the front, which acts to restratify the MLD, and release the frontal APE. As a result, on the cold side of the recirculation cell, the maximum downwelling can reach approximately 100 m/d (Fig. 7b). The intensified ageostrophic vertical velocities can penetrate into the ocean interior, and substantially enhance the vertical communication of momentum and tracers between the surface and the oceanic interior.

      Figure 7.  Cross-front slices of temperature (shading) (a) and streamlines (vectors) (b) with along-front velocity anomaly (shading). The gray contours represent isopycnals with a spacing of 0.1 kg/m3.

      Some theoretical studies have found that the strong secondary circulation in the submesoscale front is closely related to the frontal instabilities (Mahadevan and Tandon, 2006; McWilliams, 2016). The negative PV in the flow is a sufficient criterion for the SI (Thomas et al., 2013). In a typical front considered in this study, the Ertel PVh is non-negligible in comparison to the Ertel PVv because of the strong lateral buoyancy gradient, enhanced vertical shear, and decreased local stratification in the upper ocean of the offshore jet (Figs 8a and b). The angle $ {\phi }_{Ri_{\rm{g}}}{\rm{= tan}}^{-1}(-1/{{Ri}}_{\rm{g}}) $, ${{Ri}}_{\rm{g}}={{N}^{2}}/{{\left({{\rm{d}}{u}_{g}}/{{\rm{d}}z}\right)}^{2}}, $ is another criterion for the frontal instability at submesoscale (Thomas et al., 2013). The estimates of $ {\phi }_{Ri_{\rm{g}}}$ in this front fall in between –90° and –45°, which is consistent with the pattern of negative Ertel PV in the elongated frontal zone (Fig. 8c), and also indicative of the favorable conditions for the SI. The cross-front vertical distribution of the Ertel PV and its decomposed terms show that a negative Ertel PV is injected into the oceanic interior along the outcropping isopycnals by the strong downwelling at the density front (Figs 8d and e). To quantify the possibility of SI, we also calculated the cumulative distribution function (CDF). The value of CDF is approximately 70% (Fig. 8f), which implies that SI is the most probable instability at this front case, similar to the fontal analysis results in the Antarctic Circumpolar Current (Barkan et al., 2015).

      Figure 8.  Horizontal distribution of Ertel PVh (a), Ertel PVv (b), and Ertel PV (c) averaged over the MLD normalized by f2 (shading), respectively; instantaneous cross-front profiles (magenta line in Fig. 8c) of Ertel PVh, Ertel PVv, and Ertel PV (d); vertical profiles of Ertel PV (shading) (e); and cumulative distribution function (CDF) of SI (the condition for SI is Ertel PV<0) (f). The gray contours in a–c and e represent isopycnals with a spacing of 0.1 kg/m3. The green line in c denotes an angle of –45° for $ {\phi }_{Ri_{\rm{g}}}$. The shaded region in d is the frontal zone and the gray dashed line denotes the MLD.

      Although the PV tends to be conservative in the oceanic interior, it can be removed by atmospheric forcing and enhanced baroclinicity in density fronts (Thomas, 2005). As shown in Fig. 9, the wind direction is along the geostrophic current near the offshore jet, that is, the down-front wind has a significant impact on the frontal jet by driving a nonlinear Ekman transport and advecting cold water over warm water. The down-front wind forced Ekman transport can reduce the frontal stratification at the submesoscales (Thomas and Lee, 2005; D’Asaro et al., 2011). These conditions amplify the EBF to the order of O(10–5) m2/s3 and increase the convective mixing of the buoyancy at the frontal jet. By this process, the destratification caused by the wind forcing contributes a negative PV injection and exacerbates the frontal instabilities.

      Figure 9.  Spatial distribution of EBF (shading) at the same time as Fig. 4b from ROMS2 in the frontal zone of the jet. The geostrophic velocity (wind stress) is shown in black (gray) arrows. The thin gray contours represent isopycnals with a spacing of 0.1 kg/m3.

      As a result of the frontal submesoscale instabilities, the ageostrophic secondary circulations crossing the fronts develop, and provide a pathway for enhancing the vertical exchange of heat, momentum, and tracers between the surface and oceanic interior. Furthermore, the secondary circulation can effectively redistribute the buoyancy in the mixed layer and tend to restore the frontal flows to geostrophic balance (Boccaletti et al., 2007; Taylor and Ferrari, 2009; Gula et al., 2014). As the schematic in Fig. 10 shows, the submesoscale processes associated down-front wind forcing and frontal instabilities likely provide a new physical understanding for the enhanced nutrient supply for phytoplankton bloom at the fronts and filaments detected from satellite images in the WSCS (Fig. 3). This dynamical process can contribute the total tracers supply in the similar frontal zone according to the result of Omand et al. (2015).

      Figure 10.  Schematic diagram of the submesoscale front (similar with D’Asaro et al., 2011) associated with wind forcing and the cross-front ageostrophic secondary circulation. The Ekman transport cross-front transports cold water to the warm side of the front under the effect of down-front wind forcing, thus reducing the stratification and PV. The negative Ertel PV is conducive to submesoscale instability. The submesoscale instability effectively extracts energy from frontal jet and drives a cross-front ageostrophic secondary current to enhance vertical communication and restore geostrophic balance. $ {\rho }^{+}({\rho }^{-})$ denotes the positive (negative) anomaly of density.

    • Theoretical arguments show that submesoscale instabilities not only contribute to enhanced vertical exchanges, but also play an important role in the forward energy cascade of the geostrophic energy (Molemaker et al., 2010; Capet et al., 2008). At the submesoscale density front of the WSCS, the Ertel PV is negative and the ratio of the convective layer depth (h) to MLD (H) is $h/H \!\approx\! 0.3 \!<\! 1$. This result means that the wind-forced shear dominates over the convection (Thomas et al., 2013) and the shear production is the major contributor to the downscale geostrophic KE in this region (Thomas et al., 2016). With the weakening of the fronts by the ageostrophic secondary circulation, the submesoscale instabilities drive a destabilizing momentum flux to restore the geostrophic balance (Fig. 10). The geostrophic shear KE is drawn at the rate of GSP from larger-scale frontal flows (Thomas and Taylor, 2010). A subsequent slumping of the isopycnals arising from the geostrophic adjustment is expected to lead to a release of the APE stored in the fronts at the rate of BFLUX.

      As shown in Fig. 11, both the energy conversion rates, namely GSP and BFLUX, which are the two primary energy sources for the submesoscale turbulence, are particularly large along the density front. The large positive GSP and BFLUX are mostly located in the frontal zone of the offshore jet with a magnitude of the order of O(10–6) m2/s3, which is comparable to the scaling mixing caused by wind and surface buoyancy flux (Nagai et al., 2012), even though these parameters are decaying quickly out of the front. The large positive GSP and BFLUX are found in the frontal jet of the WSCS, indicating an effective forward energy cascade.

      Figure 11.  Horizontal distribution of mean energy conversion terms in MLD (shading): GSP (a) and BFLUX (b). The gray contours represent isopycnals with a spacing of 0.1 kg/m3.

      The vertical distributions of GSP and BFLUX are similar to those of the Ertel PV. The large values are primarily located in the central part of the frontal jet and they rapidly decrease away from the jet (Fig. 12). A negative $\overline{u^{\prime} w^{\prime}}$ is a result of the vertical exchange of momentum associated with the frontal instability and the ageostrophic secondary circulations owing to the strong negative vertical velocity. Therefore, the positive GSP arises in the upper ocean. The other important energy conversion term, BFLUX, is positive over much of the MLD, especially near the frontal jet, where it has a strong vertical velocity and abnormal buoyancy, which is consistent with the previous results (Thomas and Taylor, 2010). These diagnostic results suggest that the frontal submesoscale instabilities can effectively facilitate the energy conversion from the background geostrophic flows and feed the submesoscale turbulence in the upper ocean.

      Figure 12.  Section of the energy conversion terms (shading): GSP (a) and BFLUX (b). The gray contours represent isopycnals with a spacing of 0.1 kg/m3.

      Additionally, the intensity of GSP is scaled with EBF; however, the contribution of BFLUX is only 1/3 of the GSP (Fig. 13a). These results agree with the conclusion that the EBF scales with the strength of GSP and BFLUX if the atmospheric forced surface buoyancy loss is not taken into account in a large eddy simulation (LES) (Thomas, 2005; Thomas and Taylor, 2010). It suggests that the GSP is likely the dominant energy source for the submesoscale turbulent KE in the fronts of the WSCS. The submesoscale processes associated with the down-front wind forcing can partly contribute to the enhanced air-sea interactions in the WSCS (Xie et al., 2003). Moreover, as detected from the vertical profiles, the GSP and BFLUX quickly grow with depth in the Ekman layer (Fig. 13b). The maximum GSP appears at approximately 15 m, while the BFLUX reaches a maximum at approximately 18 m owing to the strong vertical velocity. Then, both the GSP and BFLUX rapidly reduce with depth. These results indicate that the submesoscale fronts and their instabilities can enhance the dissipation of geostrophic KE and transport energy towards a smaller scale but above the scale of Kolmogorov dissipation (Su et al., 2016).

      Figure 13.  Profiles of the instantaneous local energy conversion terms, GSP, BFLUX, and EBF averaged over the boundary layer (a); and the same quantities horizontally averaged on the section (b). The shading in a indicates the frontal zone. The black dashed line in a and b denotes a value of 0.

    • The surface density fronts are ubiquitous in the SCS and their underlying dynamic effects at submesoscale are examined using a fine-resolution nested simulation in the frontal jet of the WSCS during the summer. Both the fine-resolution satellite images and the model results show active submesoscale fronts on the offshore jet system. Unlike in the geostrophic theory (Charney, 1971), here, these submesoscale fronts are characterized with unbalanced three-dimensional motions with a typical time scale of O(hour–day), a lateral scale of O(1–10) km, and an order of one of Ro and Ri.

      The summer offshore jet with surface cooling is a common phenomenon in the WSCS owing to the southwest wind forcing. The high-resolution simulation and diagnostic results indicate that the cross-front Ekman transport, driven by the down-front wind forcing advects cold water to the warm water, effectively enhancing the vertical shear and reducing the frontal stratification. The enhanced vertical shear and the lateral buoyancy gradients intensify the frontal baroclinicity, thus contributing a negative Ertel PV in conjunction with the surface atmospheric forcing at approximately 5 km submesoscale front. More importantly, the conditions (e.g., negative Ertel PV, $ {\phi }_{Ri_{\rm{g}}}$ mostly varying within a range of –90° to –45°, and the CDF of SI being up to 70%) are conducive to the submesoscale SI. Owing to the frontal instabilities, the ageostrophic secondary circulation can develop, crossing the active submesoscale fronts. Such an ageostrophic process can redistribute the buoyancy for restoring the geostrophic balance by the submesoscale instabilities. Meanwhile, the submesoscale frontal vertical velocity is obviously increased to approximately 100 m/d, which is one order greater than that of the mesoscale. Enhanced vertical velocity contributes to the vertical exchanges and provides a new physical explanation for the frontal phytoplankton blooms in the WSCS.

      The frontal instabilities at the submesoscale also provide an effective downscale energy pathway for the frontal geostrophic flows in the presence of a negative PV. The shear production caused by the ageostrophic secondary circulation can effectively extract the geostrophic KE at the rate of GSP, and the APE stored at the front is released at the rate of BFLUX. Both the diagnostic energy conversion rates, GSP and BFLUX, are particularly large in the frontal zone of the WSCS. The order of magnitude of GSP is scaled with EBF, while BFLUX contributes only 1/3 of the GSP, suggesting that the GSP in the density front of the WSCS plays a leading role in the mesoscale energy dissipation. Both the maxima of GSP and BFLUX are located in the submesoscale front, suggesting an effective downscale energy transfer. These results imply that down-front wind forced submesoscale processes likely provide downscale energy pathway in the WSCS from the larger-scale geostrophic flows to the submesoscale turbulence.

    • We thank GHRSST-PP (http://ghrsst-pp.metoffice.com), AVISO+ (http://www.aviso.altimetry.fr), NODC/NOAA (http://data.nodc.noaa.gov), and ESA (ftp://merisfrs-ftp-ds.eo.esa.int) for providing a suite of high-resolution satellite data and reanalysis products.

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