Cross-Slope Transport by a Mesoscale Anticyclone in the Northern South China Sea

Abstract

Cross-slope eddies play an important role in the exchange of water, salt, heat, nutrients, chlorophyll, phytoplankton and other biogeochemical elements between basin and shelf in the South China Sea. The cross-slope transport process by a mesoscale anticyclonic eddy is studied by ROMS model and satellite data. The 1000 m isobath was considered as a proxy for the slope. The anticyclone shows different features at different places on the slope: (a) the volume transport at the northeast of the slope was off-slope, while at the southwest was on-slope; (b) both on and off-slope transports were greatly enhanced during the cross-slope process, and gradually weakened after crossing the slope. The total cross-slope water transport was 5.97 Sv, which was higher than the along-slope component with −0.58 Sv. The Eulerian results also showed that enhanced cross-slope transport was related to the distance between the eddy and slope, the eddy radius, and the eccentricity of the eddy. The offline passive tracer experiment showed that particles were floating up during and after the crossing process, mainly due to the strong Ekman pumping.

1. Introduction

The Northern South China Sea (NSCS) is composed of a wide shelf, steep continental slope, and deep basin (Figure 1). Influenced by monsoon and Kuroshio, the area has always been an area with frequent occurrence of mesoscale eddies. The literature on mesoscale eddies in the South China Sea (SCS) has been focused on eddy statistical characteristics [1,2], eddy-induced transport of chlorophyll (CHL), heat, freshwater, salt, biogeochemical substances, and air–sea interaction and generation mechanisms [3,4,5,6,7,8,9]. Further, 21 years of satellite altimeter data found that the number of anticyclonic eddies was almost equal to cyclonic eddies every year and tended to occur during spring and summer, with more cyclonic eddies during autumn and winter [10]. Around 8.6 anticyclonic and 4.5 cyclonic eddies (with lifetimes of more than 28 days) occur in the NSCS area per year [11]. Due to the strong nonlinearity, eddies have a strong transport capacity of biogeochemical properties for heat, salt, water mass [5,6,7,8,9]. Recent studies have shown that mesoscale eddies play a vital role in the redistribution of surface chlorophyll in the SCS. Eddies can stir the ambient chlorophyll field and trap chlorophyll at the eddy center by advection and induce Ekman upwelling vertically, so in most boundary current regions, cyclonic eddies exhibit positive CHL anomalies and anticyclonic eddies contain negative CHL anomalies [12]. As calculated, the westward propagation of eddies also generates a basin-scale westward water transport of 1.4 Sverdrup, equivalent to about 30% of the annual-mean Luzon Strait transport [13].

The Dongsha current, the South China Sea Warm current, and their frontal eddies affect the shelf process outside the Pearl River Estuary [14]. In the southeast area of Dongsha Island, the mesoscale eddy at 2000 m or deeper is the most important process that transports a large amount of suspended sediment [15]. Because of the interaction with the complex local topography, the mesoscale eddies have greatly changed the bottom current. These eddies terrain interactions lead to a large amount of eddy energy dissipation and transfer to sub-mesoscale processes, which is the reason for the spatial heterogeneity of sediment and erosion patterns observed between different terrain features [16]. Net sediment transports of two anticyclones in the NSCS are estimated, reaching one million tons [15,17].

The monsoon is a major formation mechanism of the mesoscale eddies in the South China Sea [18,19]. The eddies caused by monsoon are mainly distributed in the NSCS, especially in the southwest of Luzon Island. The southwesterly wind prevails in summer and the northeasterly wind is dominant in winter. The wind stress curl generated by the monsoon promotes the generation of eddies and the eddies in winter is larger due to the stronger monsoon [20,21]. Along with the monsoon, Kuroshio also plays a significant role. The average annual number of warm eddies shed by Kuroshio is more than that of cold eddies [22,23,24,25]. The Kuroshio intrusion also affects the generation of eddies. In addition, local topography and front are also important eddy generation factors in the NSCS [15,26]. The fronts in the NSCS act as a barrier between coastal water and offshore water and are approximately aligned with the topography of shelf [27]. Due to the complex shelf dynamic processes, the occurrence of eddies can outcrop the front and advect coastal water. The cyclonic frontal eddy brings dense water from exterior of the front into the frontal area, while the anticyclonic frontal eddy brings light water out of the frontal area [14,28].

With the increase of in-situ data and the development of the oceanic models, more and more research is being carried out on eddies that cross the slope area (200 m–1000 m) [29,30]. Cross-slope eddies in the South China Sea are generated more frequently in winter and have smaller size and longer lifetimes than normal eddies [30]. They can induce about 10¹² W heat and 10¹⁴ kg·s⁻¹ salt due to eddies caused by the asymmetry of potential vorticity [31] and significantly alter bottom currents, as well as produce spatial heterogeneity in slope sedimentation and erosion [16]. There are more cross-slope anticyclonic eddies. They travel further and are mainly generated on the islands of Hainan and Dongsha, while Xisha and Dongsha islands are the main generation locations of cross-slope cyclonic eddies [29,30,32]. For a single eddy itself, the region of an eddy can be divided into four quadrants. It was identified that warm eddies which induce onshore flow are in the first and fourth quadrants, while offshore flow is present in the second and third quadrants. Meanwhile, the trend seems to be the opposite for cold eddies [6]. The asymmetry distribution of eddy and front near eddies are the main causes of cross-slope water and energy transport [26]. The asymmetry structure causes the horizontal distortion and vertical tilt, contributes to sub-mesoscales, and transfers energy to smaller scales [31]. The strong front between the eddy pair induces a northward deep flow, then interacts with the topography and increases a strong horizontal velocity shear, causing cross-slope transport [33].

With the development of high-resolution numerical models, significant progress has been made in the study of the three-dimensional structure of eddies, which helped accurately quantify the transport of water across the slope due to eddies. Three-dimensional statistics of various parameters of mesoscale and sub-mesoscale eddies conducted in the South China Sea defined three different types of three-dimensional eddy structures: bowl-shaped, lens-shaped, and cone-shaped. Among the three types of eddies, the number of bowl-shaped eddies was the highest [34]. However, there are few studies on the cross-slope eddies and their three-dimensional structure in the South China Sea. This study quantifies the cross-slope transport of a warm eddy generated in 2001, thus investigating the eddy-induced cross-slope exchange processes in the NSCS. The rest of the paper is organized as follows: Section 2 introduces the data and methods used to detect eddies, calculate the water transport, and the Ekman pumping velocity. Section 3 describes the cross-slope progress of the eddy, analyzes the variability of volume transport that cross slope and along the slope over time, and the movement of Lagrangian particles inside the warm eddy, also discussing the mechanism of the particles’ propagation. Conclusions are then presented in Section 4.

2. Data and Methods

2.1. Model Setup

Regional Ocean Modelling System (ROMS, Roms_Agrif_v2.1) was used in this study based on hydrostatic primitive equations in horizontal curvilinear coordinates and vertical sigma coordinate [35,36]. At the surface, the model was forced by surface fluxes and wind from daily NCEP/NCAR reanalysis 1 data. For the surface forcing, instead of directly prescribing the fluxes, we used the bulk formula COARE 3.0 to generate the air-sea turbulent fluxes from atmospheric variables during the model run [37,38]. The variables included air temperature and absolute humidity were recorded at a 2 m height, along with sea surface temperature (SST), shortwave and longwave radiation, and precipitation. The freshwater flux was derived from both precipitation and evaporation rate. The 10 m wind forcing was from two extracted datasets: NCEP/NCAR reanalysis 1 for the period of January 1958 to July 1999 (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.surfaceflux.html (accessed on 13 October 2021) ) and the daily blended sea winds from August 1999 to December 2008 (https://www.ncei.noaa.gov/products/blended-sea-winds (accessed on 13 October 2021)). The initial condition was from the SODA (http://apdrc.soest.hawaii.edu/datadoc/soda_2.2.4.php (accessed on 13 October 2021)) with a horizontal resolution of 0.5° which included temperature, salinity, current velocity, and sea surface height. We adopt the ETOPO2 dataset as the bottom topography. The ETOPO2 is a combination of satellite altimetry observations, shipboard echo-sounding measurements, data from the Digital Bathymetric Data Base Variable Resolution, and data from the GLOBE project which has a global digital elevation model (https://sos.noaa.gov/catalog/datasets/etopo2-topography-and-bathymetry-natural-colors/ (accessed on 13 October 2021)). In order to reduce the calculation error of pressure gradient force caused by steep terrain in sigma coordinate system, the Shapiro filter was used to smooth the terrain by taking the coefficient $\frac{h_{+1/2}-h_{-1/2}}{h_{+1/2}+h_{-1/2}}=0.2$. We chose the mixed boundary conditions as the open boundary condition because the outflow used the radiation condition and the inflow used the relaxation procedure. Monthly adjustment and preprocess were imposed at the lateral boundaries for volume conservation.

The regional grid configuration included the northwestern Pacific and the China Seas ranging from 99° E to 145°45′00″ E in longitude and 9° N to 41° N in latitude. The horizontal resolution was 1/12° and 32 sigma vertical levels, and a K-profile parameters (KPP) mixing scheme was used for the vertical mixing. We chose the northern South China Sea (14° N–24° N, 110° N–122° E) as the study area, as shown in the model domain in Figure 1. The model was run for 50 years (1958–2008) which allowed the first 10 years for spin-up. For a detailed description of the model configuration, please refer to Lin et al.’s study [39].

2.2. Wind Data for Calculating the Ekman Pumping Velocity

Since the horizontal resolution of NCEP wind dataset is coarse and the quickscat wind data has been available since 2003, surface wind data were obtained from J-OFURO3 to calculate the Ekman pumping velocity. This is a third-generation dataset developed by the Japanese Ocean Flux Data Sets with Use of Remote-Sensing Observations (J-OFURO) research project, representing a significant improvement from older data sets as the result of research and development conducted from several perspectives (https://j-ofuro.isee.nagoya-u.ac.jp, accessed on 13 October 2021). J-OFURO3 uses multi-satellite data for the estimation of various parameters and provides a dataset on surface flux over the oceans except for sea ice areas, along with relevant physical parameters including sea surface temperature, surface wind speed, and surface air specific humidity with daily mean values of 0.25-degree grids from 1988 to 2013. J-OFURO3 data have been proven to be of good quality and they can be used to understand ocean–atmosphere features, such as ocean fronts, mesoscale eddies, and geographic features [40,41].

The model output had been previously validated [39,42]. A similar seasonal flow pattern was found in AVISO, and the SST and Eddy Kinetic Energy (EKE) also matched well with the remote sensing data. The eddy number and radius also had good agreement between the model and satellite altimeter results as well. Therefore, the model output was used for studying of three-dimensional eddies and abnormal anticyclonic cold-core eddies and cyclonic warm-core eddies in the South China Sea and northwestern Pacific Ocean [39,42,43]. Despite model bias, strong similarity between the model and remote sensing data suggested that the model can be used to investigate cross-slope eddy processes in the northern South China Sea.

An offline Lagrangian experiment was taken to qualify the fate of particles during eddy lifetime. The third-order upstream horizontal advection and fourth-order centered vertical advection were used as tracer advection schemes to reduce fake diapycnal mixing. Then, 2000 particles were released into the warm eddy on 16 August 2001 representing its maturity stage. The exchange rate and particle travel distance were calculated to reveal the influence of slope on eddy-induced transport [44].

2.3. Eddy Detection and Tracking Algorithm

2.3.1. Eddy-Detection Algorithm Based on Vector Geometry

The vector geometry method [45] was used to detect two-dimensional eddy. The method set four constraints to determine the eddy center and the eddy boundary was defined as the outermost closed contour of the stream functions around the center point. The average distance from the boundary to the eddy center was considered as the eddy radius. Eddy trajectory was identified by comparing the position of the eddy at successive moments: if the eddy with the same polarity and closest distance to the eddy center at moment t + 1 in a searching area was found, it was determined as the next moment of the eddy until the eddy cannot be found. This method was applied to the study of eddies in different areas of the world [42,43]. The method was also used to extend 2D eddy detection to 3D eddy identification in the Southern California Bight and compare the different generation mechanisms in Kuroshio and Subtropic Countercurrent [34,42].

2.3.2. Three-Dimensional Eddy Detection

The detection method based on the velocity vector method was applied to a 21-layer velocity field with depths of 10 m, 50 m, 100 m, 150 m, 200 m, 250 m, 300 m, 350 m, 400 m, 450 m, 500 m, 550 m, 600 m, 650 m, 700 m, 750 m, 800 m, 850 m, 900 m, 950 m, and 1000 m from the first to the last layer, respectively, where eddy detection was used to obtain information on the location, polarity, radius, energy, generation, and extinction times of each layer of eddies. Moreover, the vertical direction was used to determine if the eddies were the same between the layers, where the following basic assumption was made: the center of an eddy does not drift more than 0.25 times of the eddy radius. Starting with the eddy detected in the surface layer, we searched downwards to find if there was an eddy of the same polarity within 0.25 times of the eddy radius. If so, the search continued to the next layer, until reaching 1000 m. If no eddy signal was found in the next layer, the depth of the current layer was taken as the maximum depth of the eddy. Using this algorithm, we ended up with a discrete 3D eddy dataset that included the type of eddy, generation time, depth, drift distance, radius, and location.

2.4. Cross-Slope Volume Transport Induced by the Warm Eddy

The slope in the northern South China Sea region is changeable: following previous experience, the region with depths between the 200–1000 m isobath is generally regarded as the slope region [29,30,32]. Here, the 1000-m isobath was considered as the outmost edge of the slope for cross-slope transport calculations. Since the 1000 m isobath is southwest-northeast oriented, we defined the most southwest-oriented point and the most northwest-oriented point where the outermost closed contour of the eddy intersects the slope during its lifetime as points a and e. The intersection of the track of the eddy center with the slope is defined as point c, with points b and d being two intermediate points to fit the slope (Figure 2). Hence, the area is divided into 4 regions and the cross-slope volume transport in each region is calculated. The specific calculation method is as follows:

Step 1: Use the three-dimensional eddy detection method to determine the depth (h) that the eddy can reach in each day during its lifetime.

Step 2: Decompose velocity into cross-slope and along-slope components (Figure 3). u_c is the velocity component perpendicular to the isobath of the slope representing the cross-slope velocity: u_c = vcosθ − usinθ. Here, u and v are the zonal and meridional components of velocity and θ is the angle between slope and the horizontal direction. Meanwhile, u_a = vsinθ + ucosθ is the along-slope velocity component.

Step 3: Calculate the cross-slope volume transport. Due to the length of each section being different, the volume transport is divided by section length. The equation is as follows [46]:

$$CS{T}_{\left(i,t\right)}=\left({{\displaystyle \int }}_{l_S\left(i\right)}^{l_E\left(i\right)} {{\displaystyle \int }}_{h_{\left(i\right)}}^0{u}_{a}dhdl\right)/l_i\ast l_a$$

(1)

where CST stands for cross slope transport, i.e., transportation across the slope. i represents the section number, t is the date during the eddy life, l_S(i) and l_E(i) denote the start and end point of each section, l_i is the length of the section, and l_a is the unit length (1 km) chosen to compare the magnitude of transport in each section. Positive values represent on-slope transport while negative values mean off-slope transport. To investigate the overall effect of the eddy on the cross-slope volume transport, the time series of net transport was obtained by adding the space-averaged transport of each section during the whole eddy lifetime, herein expressed as:

$$NCS{T}_{\left(l\right)}={\displaystyle \sum }_{i=1}^{n}CS{T}_{\left(i\right)}$$

(2)

where l represents the section ab, bc, cd, de or ae, n is the number of the slope section. Additionally, the sum of the total volume transport was also calculated for each section.

2.5. Ekman Pumping/Suction Velocity

Ekman pumping velocity (EPV) is an important indicator to represent ocean upwelling and reflects the influence of the inhomogeneity of the ocean surface wind system on the vertical upwelling/downwelling flow and the horizontal mass transport in the upper surface layer. Positive EPV indicates upwelling flow (Ekman suction), while negative EPV indicates downwelling flow (Ekman pumping). The relationship between Ekman pumping/suction velocity and wind stress is expressed as follows:

$$w_e=\frac{\partial }{{\partial }_x}\left(\frac{{\tau }_y}{\rho f}\right)-\frac{\partial }{{\partial }_y}\left(\frac{{\tau }_x}{\rho f}\right)$$

(3)

where f denotes the Coriolis parameter and ρ is the density of seawater; τ_x and τ_y are the zonal and meridional wind stresses, respectively, was calculated using the bulk formula, which is an empirical formula obtained in the laboratory from experimental studies and field observations. Wind stress was obtained mainly by parameterizing the wind field at 10 m above the sea surface. The expression formula is expressed as follows:

$${\tau }_x={\rho }_a{c}_d{w}_{10}{u}_{10}$$

(4)

$${\tau }_y={\rho }_a{c}_d{w}_{10}{v}_{10}$$

(5)

$$c_d\ast {10}^3=\{\begin{array}{c}1.2, 0<w_{10}<11 \mathrm{m}/\mathrm{s} \\ 0.49+0.065w_{10}, 11<w_{10}<19 \mathrm{m}/\mathrm{s}\\ 1.364+0.0234w_{10}-0.00023158w_{10}^2, 19<w_{10}<100 \mathrm{m}/\mathrm{s}\end{array}$$

(6)

where c_d is the drag coefficient at the sea surface, w₁₀ is the magnitude of the wind speed at 10 m above sea surface level, and ρ_a is the air density at sea surface where it takes the value ρ_a = 1.293 ${\mathrm{kg}\ast \mathrm{m}}^{-3}$. u₁₀ and v₁₀ denote the meridional and zonal velocity components of the wind speed at 10 m above the sea surface, respectively.

2.6. Vorticity and Deformation Index

To investigate the asymmetry of mesoscale eddies, vorticity and deformation index (VDI) is used to analyze variations in eddy morphology [31,47]. The VDI is calculated as follows [48]:

$$VDI=\frac{1}{\frac{1}{F}+\frac{1}{\left|\omega \right|}}=\frac{F·\left|\omega \right|}{F+\left|\omega \right|}$$

(7)

$$F=\sqrt{S_n^2+S_s^2}$$

(8)

of which

$$S_n=\frac{\partial u}{\partial x}-\frac{\partial v}{\partial y}$$

(9)

$$S_s=\frac{\partial v}{\partial x}+\frac{\partial u}{\partial y}$$

(10)

$$\omega =\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y}$$

(11)

where ω is the relative vorticity; S_n and S_s are the normal and shear components of strain, respectively, and (u, v) represent the horizontal velocity, with positive values indicating the east and northward directions, respectively.

3. Results

3.1. Cross-slope Process of the Warm Eddy

As shown in Figure 1, the cross-slope anticyclonic eddies are common in the northern South China sea. Based on the AVISO dataset from 1993 to 2019, there are 56 cross-slope anticyclonic eddies in total (red lines). It is found that the area of 116° E–118° E, 20° N–22° N is a high frequency area with 26 eddies crossing the slope, almost one eddy per year on average. Based on ROMS output (2000–2008), there are 13 eddies crossing the slope (yellow lines) and 8 eddies locate in the high frequency area. For the annual generation number and spatial distribution of cross-slope eddies, the result of ROMS model output matches well with the AVISO dataset, so we use ROMS data to investigate cross-slope transport process of eddies in the high frequency area.

The cross-slope transport and along-slope transport of the entire year 2001 are calculated (Figure S1) and it can be found that the total transport changes significantly over time and affected by the passing eddies near the 1000 m isobath (Figure S2). For instance, there is a large anticyclonic eddy located in the east of the slope on 16 November and the cross-slope transport on that day almost reaches the highest value in this year. Moreover, the water transport in section bc (yellow lines) reaches the highest value in the entire year and it is obvious that the flow near the slope is perpendicular to the 1000 m isobath, in which case the flow velocity contributes to the cross-slope movement and the along-slope transport is lower relatively. In addition, the along-slope on 16 November was also higher than that of most other times of the year. Similarly, the change of the along-slope transport is also drastic. On 6 March, the total along-slope transport reaches the highest value in 2001 with an eddy near the 1000 m isobath and the transport in section bc and cd reaches the highest value on that day. Additionally, the transport on 25 June reaches the lowest value in this year.

Among these eddies passing near the 1000 m isobath, the eddy generated on 5 August is chosen to investigate further with most apparent cross-slope process. Two vertical black dotted lines represent the generation and dissipation dates of this eddy (Figure 2). As shown in Figure 2, the warm eddy was generated at 119°22′48″ E, 19°43′48″ N (Red star) on 5 August 2001 and moved westward to the slope on 2 September. Finally, it dissipated to the northeast of Dongsha Island (117°45′00″ E, 21°12′36″ N, blue triangle) on 14 September. The average radius of the eddy was 92.9 km. The cross-slope evolution of the warm eddy is shown in Figure 4.

When the warm eddy is near the 1000 m isobath on 18 August (Figure 4a), the eddy shape is a regular circle and the radius is 92.9 km. The flows in the southwest periphery of the eddy are much stronger than other regions near the eddy and consistently on-slope. Similarly, the vorticity also has high value at the southwest edge of the eddy and in the eddy center. As the eddy just approaches the 1000 m isobath on 23 August with its sharper shape at northwest edge (Figure 4b), it has similar magnitude of flows and vorticity with its previous days. Then, the eddy continues to move towards the slope with a slightly reduced radius of 77.3 km. On 28 August, a small part of the eddy crossed the slope area (Figure 4c), but the warm eddy center is still located at deeper than 1000 m and the radius increases to 118.2 km with the increased flow velocity and vorticity southwest of the eddy. When the eddy continues to move across the continental slope (Figure 4d,e), the magnitude of eddy velocity and vorticity similarly strengthen in its southwest, influenced by the cyclonic eddy in the same direction. The eddy has noticeable shape on 12 September due to its interaction with the slope, where it becomes an ellipse with long axis in east-west direction and a slightly smaller radius of 102.5 km. During the life cycle of the warm eddy, there is always a cyclone accompany in its southwest, induces a strong horizontal shear velocity between the eddy pair, which may be the main reason for the cross-slope process.

3.2. Quantitative Analysis of Cross-Slope Volume Transport

Following Figure 2, during the eddy’s youth and matured stage, it moves perpendicular to the 1000 m isobath along the northwest. After climbing up the slope and approaching Dongsha Island, it almost turns at 90 degrees and travels to the northeast. The movement and evolution of this warm eddy are affected by the interaction with the cyclonic eddy at its southwest. To quantitatively analysis cross-slope process, the cross-slope volume transport of four sections was calculated and compared with the along-slope process.

Figure 5a shows the timeseries of net cross-slope transport at each section. Section ab (red dark line in Figure 5a), which at the southwestern rim of the selected slope has significant cross-slope activity, varies during the cross-slope period. On 1 September, it reached the peak at 0.14 Sv and an average daily transport growth rate of 193.2% (

Table 1. Daily average transport of each section in different timeseries, growth rate during cross-slope and reduction rate after cross-slope of each section and all of them.

Section	Transport before Cross-Slope	Transport during Cross-Slope	Transport after Cross-Slope	Growth Rate during Cross-Slope	Reduction Rate after Cross-Slope
ab	0.04	0.12	0.03	193.2%	−71.1%
bc	0.09	0.11	0.05	24.3%	−53.2%
cd	0.05	0.02	0.08	−56.6%	277.9%
de	−0.03	−0.08	−0.05	203.3%	−44.3%
all	0.15	0.16	0.11	11.4%	−30.3%

) and decreases rapidly after the eddy weakens, with a decrease rate of 71.1%. A consistent and intense on-slope transport trend is revealed in section bc as the yellow line shown in Figure 5, with an increase of 24.4% (Table 1) during the cross-slope period along with a decrease of 53.3% afterwards. Because section bc covers most lifetime of the warm eddy, its maximum transportation value is 0.15 Sv. However, the peak value of section bc occurs earlier than in section ab, peaking on 27 August and lagging 5 days. This is mainly due to the movement of the eddy, section bc being closer to the eddy and is affected by it earlier, while section ab is relatively farther from it.

As the warm eddy travels northwest, the cross-slope variability reduces in section cd (blue line) at the northeast edge of eddies, which is notably the most unusual. It is positive just before the arrival of the eddy and decreases until the eddy reaches the slope, and then starts to increase after crossing slope. This is also caused by the track of eddy. As the eddy slowly approaches the slope area, the flow caused by the west side of the eddy is on-slope transport when the edge of the eddy just touches this section. Then, as the eddy moves westward, the center of the eddy keeps approaching point c and the eddy-induced transport gradually decreases to near zero. The volume transport in section de (green line) shows the opposite trends to that in sections ab and bc with predominant off-slope flows. The sum of the volume transport in the four sections shows on-slope movement and its variation pattern is roughly the same as in section bc. It increases continuously during the approach of the eddy to the slope and decreases rapidly after the eddy crossed the slope.

Compared with the cross-slope transport, the total transport volume of the eddy along the slope is much lower but has a more significant change over time (Figure 5b). Generally, the transportation is along the continental slope to the northeast before 22 August and then turns to the southwest. On the different sections on the slope, the southwestward transport of section ab is the highest (red line) which is because the eddy is significantly affected by the cyclone at the southwest of the warm eddy and section ab is located at the intersection of the two eddies. In this case, the section ab is the factor that most affects the total water transport along the slope. The sign of section ab is always negative, which means the direction of the along-slope flow is northwestward. The other three sections of transport fluctuate with time and are relatively low. Section bc (yellow line) is the lowest part in four sections and the direction of along-slope flow has since change during the eddy life. Before cross-slope process, it is positive (northeast-ward) at first and then becomes negative (southwest-ward). During the process of cross-slope, the variation is similar to the change before cross-slope but is lower than that after. After crossing the slope, the along-slope transport is negative and the value is growing. The transport in section cd is positive (northeast-ward) before the cross-slope and has an obvious decrease during, which finally turns into negative (southwest-ward). Section de is the highest part that brings positive transport along the slope and is always positive (northeast-ward). The maximum of the net along-slope transport occurred on 14 August, which is the turning point of the eddy from moving northward to moving westward. The direction of the along-slope flow changes when the eddy crosses the slope.

The total of transport in each section is also different (as shown in Figure 6). Section ab and section bc are most significantly affected by the eddy, and the water transport generated during the eddy life is on-slope transport. Section bc is even higher than section ab and has the highest water transport among the four sections, with a total transport of 3.61 Sv. Section cd is also an on-slope transport, mainly because of the eddy’s trajectory. The transport caused by its edge is mainly influenced by the current west of the eddy, which is clockwise and the current west of the eddy is roughly to the north, resulting in an on-slope transport.

Unlike sections ab and bc, section de produces off-slope transport. For the total transport along the slope (Figure 6b), the magnitude of ab is the highest, reaching 4.37 Sv, and the direction of transport of sections ab and bc are southwest, whereas section cd and de are northeast. This contrasts with cross-slope transport where sections ab, bc, and cd are on-slope. From eddy shapes in Figure 4, it is evident that the eddy velocity has obvious asymmetry, and the southwest part is stronger than the northeast one. Hence, the transportation is mainly due to the asymmetry of eddy velocities, which produce stronger on-slope flow than off-slope flow, i.e., the velocity is higher on the south-west orientation and lower on the northeast orientation [6]. Based on the net water transport, it is clear that the anticyclonic eddy causes a higher on-slope water transport, effectively bringing basin seawater to the slope area, which plays a role in water renewal in the slope area.

3.3. Lagrangian Particle Experiments

The Lagrangian particle tracking experiment was conducted to track the water particles participating the cross-slope exchange. Thus, 2000 particles were released into the interior of the warm eddy at an initial depth of 10 m after the eddy had been stable on 16 August 2001. Then, the movement and variation of the particles are illustrated in three stages of eddies: near the slope, cross the slope, and away from the slope which lasted 41 days.

The timeseries of trajectory of all particles in the warm eddy is shown in Figure 7. On 16 August, the particles are released in the warm eddy and they are carried along by the current. Five days later, the particles at the boundary of the eddy start to go away from the eddy and most of particles are located in the center of the eddy, with few particles the outside of the eddy. On 28 August, the particles are thrown away from the eddy and present as a striation. On 7 September, there is a clear straight line, indicating that the particles are away from the eddy boundary. On 12 September, the particles move further. Based on the position of the particles, the particles are divided into two types: inside and outside the eddy. If a particle is located inside the eddy on the first day and moves out of the eddy or vice versa, the particle will be considered as an exchange particle. Before the process of the cross-slope, 3.6% of the particles move outwards. Meanwhile, during the cross-slope process, 15.0% of the particles interact with surrounding field and 33.0% of the particles exchange after cross-slope. Due to the conservation of the eddy, 55.8% of the particles are always kept inside it.

To better understand the effect of the cross-slope process on the particles in the eddy, the vertical distribution of particles is studied, to better shown the trajectories of particles, we chosen 13 particles that always moving within the eddy and the vertical velocities of them are shown in Figure 8. The particles inside the eddy changed with depth from 16 August to 21 August as the particles first sank (blue dots) then floated upward from 21 August to 7 September (red dots) in a clockwise rotation. On 2 September, when the eddy crossed the slope, all types of particles showed an upward trend. Finally, 51.65% remained inside the eddy and 48.35% were dissipated near the eddy. This ratio is slightly different from that in Figure 7, because the three-dimensional structure of eddy is used as boundary here, while Figure 7 uses the surface boundary of the eddy.

To investigate the upward trend of all the particles in the warm eddy, we analyzed the vertical distribution characteristics of all particles (Figure 9). Statistics show that the particles can be divided into three types: those who floated after sinking, fluctuated, and floated up. Hence, 37.30% of the particles floated after sinking, 50.95% of particles fluctuated, and only 11.75% of particles floated up during whole lifetime. The gradient of depth changes about three types of particles at each stage was also calculated. At the first stage, the eddy is near the slope, 37.3% of particles in eddy sank dramatically to 15 m, the slope of the fitted blue line is −1.17. While 11.75% of particles floated up to 7 m with a slope of 0.49, about half of particles fluctuated near 10 m with little change. The three types of particles were all floating up at the second stage when eddy crossed the slope. The sank particles floated up with a slope of 0.33, while other two types is smaller with slopes of 0.22 (fluctuate), 0.17 (float up), respectively. After most part of eddy crossed the slope, all of the particles were fluctuating and the gradients of the three types were quite small, the slopes are 0.05 (float up after sank), 0.03 (fluctuate), 0.01 (float up). All the particles show an upward trend during the eddy crossing the slope process.

4. Discussion

The eddy generates at the southwest of Taiwan, usually because of the path of the Kuroshio intrusion (Figure 2). The Kuroshio intrusion was divided into three types: the looping path, the leaping path, and the leaking path [48]. According to the location of the warm eddy, the eddy is affected by the Kuroshio path because the warm eddies are frequently shed from the looping path. As shown in Figure 9, the particles exhibit an upwelling trend during the eddy crossing the slope after 21 August (inflection point). The vertical velocity distribution of 22 August is presented in Figure 10. Evidently, the vertical velocity inside the warm eddy is positive from the surface to 700 m. Generally, the upwelling at the centers of anticyclonic eddies is mainly due to eddy–wind interactions [49], ageostrophic circulation near eddy periphery [50], and submesoscale processes [51]. By calculating the Ekman pumping velocity due to the wind stress curl (Figure 11), the magnitude of the Ekman pumping velocity is of the same order of magnitude as the vertical velocity, causing the surface water to dissipate and the upward flow which matches the vertical velocity. Hence, Ekman pumping caused by the wind stress curl is the main cause of particles upward movement. The VDI distribution is shown in Figure 12, from Formula 7, the value of VDI is increased when the strain of velocity or the relative vorticity of eddy is larger, that means the interaction between the eddy and background current is significant. The value inside the eddy is higher than that in the surrounding area, especially near the eddy center. Before the cross-slope process, on 16 and 21 August, the VDI is uneven at the edge of the eddy and is higher in the northwest than in other regions. Then, the VDI becomes higher in the eddy when the eddy crosses the slope. The cross-slope transport is also growing at the same time. On 7 and 12 September, the shape of eddy is turning into an ellipse and the eddy center is biased to the northeast of the eddy, close to Dongsha Island. Depending on the conservation of potential vorticity, as the depth of water decreases rapidly with the eddy center near Dongsha Island, the vorticity becomes lower and the VDI becomes higher, which means that the asymmetry of eddy is reinforced. This leads to the change of eddy track: moving from northwest to northeast and quickly terminating [31,47].

5. Conclusions

Based on the model detection results, a warm eddy generated on 5 August 2001 and dissipated on 14 September was chosen to study the cross-slope transport. The results of water transport induced by cross-slope anticyclonic eddy and the particle experiments are as follows.

According to the time variation of eddy transport across the slope in each section, the transport in sections ab, bc, and de all greatly increased during the period when the eddy crosses the slope, with growth rates of 193.2%, 24.4%, and 203.1%, respectively (Table 1). Meanwhile, the transport notably decreases after the eddy crosses the slope with reduced rates of 71.1%, 53.2%, and 44.1%, respectively. Each section has been reduced by more than 40% [52]. The dates of maximum water transport (absolute value) in sections ab, bc, and de were on 27 August, 1 September, and 6 September with water transport values of 0.14, 0.15, and −0.09 Sv, respectively. Moreover, the date of minimum water transport in section cd was on September 1 with less than 0.01 Sv. The change of cd section is relatively special, which decreases during the crossing of the slope and increases afterwards, which is mainly due to the influence of the trajectory of the eddy.

The relative position of the eddy on the slope makes the variation of section cd different from the other three sections. The total cross-slope transport in sections ab, bc, and cd were positive, and the de section was negative. The total cross-slope transport in four sections were at 2.51, 3.61, 1.77, and −1.93 Sv, respectively and the accumulation of four sections was 5.97 Sv. The total water transport across the slope in section bc is the highest at 3.61 Sv. The total water transport in the four sections is positive, indicating that the eddy brings a large amount of open sea water to the slope area.

According to the variations of transport along the slope over time, the ab section is the one with the more pronounced variation mainly due to the presence of a cold eddy near the southwest of the warm eddy. Section ab is located at the intersection of the two eddies and thus has the largest flow along the slope, showing a westward transport. The other three sections of transport fluctuate with time and are relatively low. Ultimately, the total cross-slope water transport was at 5.97 Sv, which was higher than the along-slope component with −0.58 Sv and showing that the eddy brought massive water into slope area instead of carrying water moving along the isobaths. The magnitude of cross-slope water transport was related to the distance between the eddy and slope, the radius, and the eccentricity of the eddy. The transport was higher when the eddy was closer to the slope, the radius of the eddy was higher, and the shape of the eddy was more rounded. Additionally, the asymmetry of mesoscale eddies is the most important factor that allows the cross-slope water transport.

With observation of the trajectory of the particles through the particle experiments, it is found that particles initially moved downwards and then rotated clockwise and upwards, and they were supposed to sink. To compare the features of this warm eddy on the slope, we divided the lifespan of the warm eddy into three stages: before, during, and after the eddy crossing the slope. Before reaching the slope (5–21 August), the eddy was propagating northward and westward. Then, it moved to the northwest during cross-slope stage (22 August–7 September), and eventually travelled northeastward and died out after the crossing process (8–14 September). Based on the change in particle depth, we classified the particles into three categories: floated after sinking, fluctuated, and floated up. Only 11.75% of the particles were floating up, 37.3% of the particles were sinking and then floating, and 50.95% of the particles were floating up and down. All of the particles were floating during the cross-slope. According to the temperature distribution in vertical direction, before 2 September, the distance between the eddy and the slope was far, and the temperature contour was more concave. On 2 September, the eddy center was just coincident with the 1000 m isobath. Afterwards, the temperature contour became flat, so the topography change near Dongsha Island is an important factor in lifting the particles. The divergence distribution calculated from the velocity field also matches well with the vertical velocity distribution. Moreover, based on the Ekman pumping velocity caused by the wind stress curl, a very strong divergence in the sea surface wind field on the turning point of the particle depth variation of the “float after sink” type particles were found on 22 August. Ultimately, the propagation of particles was mainly influenced by the topography, Ekman pumping, and characteristics of eddy itself.

Since resolution of the numerical model determines the refinement of some mesoscale and sub-mesoscale dynamical process simulations and the horizontal resolution of the model in this paper is 1/12° and 32 layers in the vertical direction, it may cause bias to the results on the transport of water. Nonetheless, it is evident that the influence of eddies on volume transport is important.