1. Introduction
The North Equatorial Current (NEC) flows westward perennially, driven by the trade wind in the North Pacific Ocean. The NEC bifurcates into two branches as it encounters the east coast of the Philippines, becoming the southward-flowing Mindanao Current and the northward-flowing Kuroshio (Nitani 1972; Qiu and Lukas 1996; Qu and Lukas 2003; Nan et al. 2015). The Kuroshio is the western boundary current (WBC) of the North Pacific subtropical gyre; it flows northward persistently along the Philippine coast until it passes by the Luzon Strait (treated as a gap in this study). The Luzon Strait connects the South China Sea (SCS) with the Pacific. The path of the Kuroshio is either a leaping state or a penetrating state at the Luzon Strait due to the absence of coastal support (Caruso et al. 2006; Yuan et al. 2006). When the Kuroshio intrudes into the SCS, the main Kuroshio flows into the SCS through the Balintang Channel in the southern Luzon Strait and flows out of the SCS through the Bashi Channel in the northern Luzon Strait (Xue et al. 2004; Yuan et al. 2006; Nan et al. 2015; Mei et al. 2019). A similar gap-leaping system occurs as the Gulf Stream flowing from the Yucatan Peninsula to the Florida coast (National Academies of Sciences, Engineering, and Medicine 2018; Sheremet et al. 2021; Kuehl and Sheremet 2022; Pierini et al. 2022).
The SCS is the largest semienclosed marginal sea in the North Pacific. The large-scale circulation (LSC) in upper layer of the SCS is mainly controlled by the monsoon (Hu et al. 2000; Qu 2000; Su 2004; Wang et al. 2003; Xue et al. 2004; Wang et al. 2015) and significantly affected by the Kuroshio intrusion in the northeastern SCS (Li et al. 1998; Shu et al. 2011; Wang et al. 2013). The transition between the summer and winter monsoons results in spatial–temporal variation of the upper-layer circulation in the SCS (Wyrtki 1961; Shaw and Chao 1994; Chu et al. 1999; Liu et al. 2001, 2004). As a result, there is a basin-scale cyclonic gyre in winter; and the circulation splits into a cyclonic gyre and an anticyclonic gyre (with ∼12°N separating the two gyres) in summer, as shown in Figs. 1 and 2 (Liu et al. 2001; Fang et al. 2002; Wang et al. 2003, 2006; Liu et al. 2008; Chu et al. 2014; Gan et al. 2016; Wang et al. 2019; Shen et al. 2022). Along with the LSCs in winter and summer, the WBC appears in the SCS in different spatial patterns; however, the current of the LSC along the eastern boundary of the SCS near the Luzon Strait is always weak to compensate the WBC.
Altimeter sea surface height (cm; shading) and geostrophic currents (cm s−1; vectors) in the SCS and northwestern Pacific near the Luzon Strait showing an eddy-shedding event in 2011/12. A basinwide cyclonic circulation in the SCS driven by the winter monsoon is roughly outlined by red arrows. The Batanes Island Chain and Babuyan Island Chain in the Luzon Strait are marked by the red plus and red asterisk, respectively. Regions with water shallower than 100 m are whited out.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
As in Fig. 1, but showing the interaction of the Kuroshio with the SCS circulation driven by the summer monsoon in 2011. The northeastward current starting from the southeast of Vietnam near 12°N formed a cyclonic circulation and a weak anticyclonic circulation in the northern and southern parts of the basin, respectively.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
Existing studies paid more attention to the Kuroshio intrusion itself, and explored its influence on the variation of temperature, salinity, circulation, and eddy generation in the northeastern SCS (Qu et al. 2000, 2004; Caruso et al. 2006; Yuan et al. 2006; Xiu et al. 2010; Wu 2013; Nan et al. 2015), where the flow path of the Kuroshio is a key scientific interest. Several dynamic mechanisms were proposed to explain the Kuroshio intrusion into the SCS (Nan et al. 2015; Zhong et al. 2016; Zhang et al. 2017). In fact, potential vorticity balance is the intrinsic dynamic process that controls the flow pattern of the WBC at a gap, regardless of which external dynamic factor is considered, which may affect the WBC. Using a single-layer depth-averaged method, Sheremet (2001) first studied the hysteresis of the WBC flowing across a gap and gave the dimensionless parameter space of the gap width, which permits the existence of hysteresis, and his hysteresis result was confirmed by subsequent laboratory experiments (Sheremet and Kuehl 2007; Kuehl and Sheremet 2009, 2014; McMahon et al. 2021). No additional external factor was considered in his gap-leaping system, and the WBC flow pattern in the vicinity of the gap was only controlled by the WBC transport. More studies followed, by considering the influences of other external factors on bifurcation and hysteresis of the WBC, including wind forcing (Wang et al. 2010), mesoscale eddy (Yuan and Wang 2011), and placing an island in the gap (Mei et al. 2019). Recently, Mei et al. (2022) studied a hysteresis WBC perturbed by a mesoscale eddy and concluded that both cyclonic and anticyclonic eddies can induce regime shifts of the critical-state WBC from penetration to leap or from leap to penetration when an island is present in the gap. The parameter space of the critical eddy strength that is able to induce WBC transition was shown for variable island size in that study. In related studies, Wang and Yuan (2012, 2014) focused on two WBCs colliding at a gap to explain the dynamics of collision of the South Equatorial Current and Mindanao Current at the entrance of the Sulawesi Sea. Song et al. (2019) studied the effect of the mean throughflow on the hysteresis range of the WBC. The abovementioned studies all concerned the WBC flow pattern and transition in a gap-leaping system. Others (Song et al. 2018; Yuan et al. 2019) investigated interactions of mesoscale eddy with a WBC far away from the critical state, or with a critical-state WBC; these studies focused on the evolution of eddy rather than on the WBC transition.
Although almost all of the modeling studies paid attention to the influences of external factors from the eastern basin or from the gap on the WBC transition, few concerned influences from the western basin of the gap. Figures 1 and 2 show the interaction of the Kuroshio with the LSC in the SCS driven by the winter and summer monsoons, respectively, using the AVISO altimeter data (http://www.aviso.oceanobs.com/). In winter, the SCS circulation in the upper layer is characterized by a basinwide cyclonic circulation. In Fig. 1a, the Kuroshio first intruded into the SCS as a loop current. The Kuroshio Loop Current (KLC) gradually developed under the perturbation by the northeastern part of the SCS circulation (Figs. 1b,c). Finally, an anticyclonic eddy was shed from the KLC (Fig. 1d), namely, the transition of the Kuroshio flow pattern from the eddy-shedding path to the leaping path occurred. The Kuroshio path remained in the leaping state after the KLC eddy-shedding event was completed (Pichevin and Nof 1996, 1997). The duration of the Kuroshio shifting from the eddy-shedding path to the leaping path during its interaction with the SCS circulation was ∼46 days. Figure 2 shows a case in summer; a northeastward jet starting from the southeast of Vietnam near 12°N generated a cyclonic circulation in the northern part of the basin and a weak anticyclonic circulation in the southern part. Similarly, a KLC gradually formed from the Kuroshio. Then, an anticyclonic eddy was shed from the KLC under the impact of the SCS circulation; and the Kuroshio remained in the leaping state after the KLC eddy-shedding event finished (Fig. 2). It took ∼42 days for the Kuroshio to shift from the eddy-shedding path to the leaping path. One may suspect that the perturbation of the LSC driven by the monsoon in the SCS affects the Kuroshio flow pattern from the observations, although the LSC is weak in the northeastern SCS (Mei et al. 2019).
This current study extends the hysteresis results presented in Mei et al. (2019), concerning the WBC flowing across a gap with and without an island. We investigate the effect of LSC in the SCS on a critical-state WBC of regime shift using a nonlinear 1.5-layer ocean model. These idealized modeling results should improve our understanding of the dynamics of regional oceanography in the vicinity of the Luzon Strait. The model and method used are described in section 2. The interaction of the LSC in the SCS with the critical-state WBC and the dynamics of WBC transition are presented in section 3. The parameter space of the critical LSC, which can induce the regime shift of WBC far away from the critical state, is explored in section 4. Discussion and conclusions are given in sections 5 and 6, respectively.
2. Model and method
As in Mei et al. (2019, 2022), an idealized rectangular domain is adopted, which is separated by a thin barrier with a gap in the middle; so, there are two rectangular basins, resembling the SCS and the northwestern Pacific (Fig. 3). The western basin covers 100°–120°E, and the eastern basin covers 120°–150°E; both extend from 0° to 30°N. The thin meridional barrier is placed along 120°E, with a gap of ∼290 km in width from 13.7° to 16.3°N. An island of ∼56 km in width is inserted in the middle of the gap from 13.7° to 16.3°N along 120°E. In this study, the Munk boundary layer thickness is 24.7 km [LM = (Ah/β)1/3]. Then, the ratio of the half-width of the gap to the thickness of the Munk boundary layer is 5.87 [ω = Lg/(2LM)] in the no-island case; and it is 4.74 [ω′ = (Lg − Li)/(2LM)] in the island case. These ratios guarantee the existence of WBC hysteresis according to Sheremet (2001).
Sketch of the WBC flowing northward passing by a gap in the eastern basin, where the solid arrow is wind stress and the hollow arrow indicates the direction of the circulation. An LSC is added in the western basin when the WBC is in the critical state, where the solid and dashed arrows represent the winter and summer monsoons, respectively, and the hollow and dashed hollow arrows are the directions of the single- and double-gyre LSCs, respectively.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
Last, we solve the equations numerically by a finite difference method, namely, the Arakawa C scheme with the energy-conserving option. The model resolution is 0.1°. The nonslip boundary condition is applied at all boundaries, including the barrier and island. The minimum upper thermocline depth is set as 25 m in all experiments.
3. Interaction of WBC and LSC
We design a few numerical experiments to test whether an LSC in the western basin is able to induce the critical-state WBC transition or not, based on the hysteresis results in Mei et al. (2019). Then, we explore the critical strength of LSC and the dynamics of the WBC regime shift perturbed by the LSC.
a. Critical-state WBC
Mei et al. (2019) showed that the WBC experiences a regime shift from the eddy-shedding path to the leaping path at ReW–L,n = 65 (without island) and ReW–L,i = 74 (with island) in the wind stress increasing stage, and from the leaping path to the eddy-shedding path at ReW–P,n = 46 (without island) and ReW–P,i = 50 (with island) in the wind stress decreasing stage. In this study, the WBC critical from the eddy-shedding to the leaping regime (annotated as WBC-Ic) is defined by ReW,n = 64 (without island) and ReW,i = 73 (with island), and the WBC critical from the leaping to the eddy-shedding regime (annotated as WBC-Dc) is defined by ReW,n = 47 (without island) and ReW,i = 51 (with island), following Mei et al. (2019). The hysteresis curves of the WBC are not shown repeatedly in this study (see Fig. 2 in Mei et al. 2019). The abovementioned critical-state WBC is unchanged and is defined as the background flow. In this study, the model is first integrated long enough by adding a wind field of Eq. (4) or Eq. (5) alone, to obtain a steady LSC in the western basin without a gap in the meridional barrier; then, the LSC is added to the background flow by opening the gap in the middle of the barrier as the initial condition.
As the Munk layer is an important factor for improving the WBC to penetrate into the western basin; conversely, the inertial layer facilitates the WBC to leap across the gap. So, the inertial layer should be estimated to realize roughly the balance between relative vorticity advection and the β effect. Here, the inertial boundary layer thickness
b. WBC critical from penetration to leap
Let us investigate the influence of the LSC on the WBC critically from the eddy-shedding to the leaping regime (WBC-Ic). First, the steady state LSC is calculated for a large number of wind stress coefficients τx,L–W and τx,L–S in Eqs. (4) and (5). Then, we try to find a critical LSC that is able to induce the critical WBC transition from the eddy-shedding to the leaping regime.
When a single basinwide cyclonic gyre is inserted into the background flow (WBC-Ic), the critical transports of the LSC that can induce the WBC transition are calculated as QL–W,i = 0.28 × 104 m2 s−1 (with island) and QL–W,n = 0.19 × 104 m2 s−1 (without island), corresponding to ReL–W,i = 9.5 and ReL–W,n = 6.3, respectively. Figure 4 shows the interactive process of the critical-state WBC with the critical LSC in the western basin in the vicinity of the gap with (left) and without (right) an island. It can be seen that both WBCs can shift the regimes from the eddy-shedding path to the leaping path near day 200 under the perturbation of the single-gyre LSC from the west. Then, the WBC remains in the leaping path permanently. Finally, the WBC and LSC occupy mainly the eastern and western basins, respectively. Note that the speed of the LSC near the gap is northward; and this northward speed enhances the meridional speed of the main WBC so as to induce the WBC transition. The WBC transition under the perturbation of the single-gyre LSC is similar to the observed result shown in Fig. 1. The time for the WBC transiting from the eddy-shedding regime to the leaping regime is ∼200 days, which is about 4.3 times the observed time shown in Fig. 1, in accordance with the result of Mei et al. (2022). In this case, the critical-state WBC interacts with the steady LSC, ignoring the adjustment to the Sverdrup steady state of LSC driven by the winter monsoon, which takes the Rossby waves to propagate across the western basin. To estimate the effect of transient LSC on the WBC transition, we add a wind field in the western basin using Eq. (4) to the background flow (WBC-Ic) in the island case, which indicates that the LSC is continuously adjusted by the wind field over time. As a result, the critical LSC transport is 0.33 × 104 m2 s−1, which is slightly larger than that of the initial steady-state LSC. In addition, it takes about 20 more days for the WBC transition than that in Fig. 4 (left), due to the transient adjustment process to the steady Sverdrup circulation.
Time evolution of the WBC critical state from the eddy-shedding regime to the leaping regime perturbed by a critical single-gyre LSC from the west for WBC-Ic (left) with and (right) without an island in the gap. The thick curve indicates the ψ = QW/2 streamfunction of the WBC and shed eddy. Solid and dashed contours indicate positive and negative streamfunction values, respectively.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
Note that the steady LSC has weak currents near the eastern boundary of the western basin in this case. Why can the weak currents induce the WBC transition? We extract the mean transport of the LSC along 15°N from 119° to 120°E to estimate the strength of the eastern boundary current of the critical single-gyre LSC, and we find that the value of this critical LSC transport is 56 m2 s−1 for the island case. In fact, the WBC stays in the eddy-shedding regime near Re = 73.7 and in the leaping regime near Re = 74, according to Mei et al. (2019). To force the WBC transiting from the eddy-shedding to the leaping regime, the external perturbation needs to overcome the threshold of about ΔRe = 0.3, which corresponds to the transport ΔQ = 90 m2 s−1. We estimate the eastern boundary current of the LSC to be of the same order of magnitude as ΔQ. Therefore, the ability of the LSC in the western basin inducing the WBC regime shift is reasonable.
Next, we investigate the interaction of WBC and single-gyre LSC using the vorticity balance analysis. We extract each vorticity term for a particular point in the vicinity of XP from Eq. (6), where the value of XP represents the westmost distance of ψ = Q/2 streamline of the WBC into the western basin from the gap (Mei et al. 2019, 2022). Because of the particularity of XP, the inertia term is dominated by meridional advection. Note that XP is located to the west of the gap; then, the wind stress curl term in Eq. (6) is determined by τx,L–W or τx,L–S in Eq. (4) or Eq. (5), respectively. Figure 5 shows the time evolution of each vorticity balance term for the model with (top) and without (bottom) an island in the gap, corresponding to the WBC evolution shown in Fig. 4. At the early stage, all vorticity terms are oscillatory before the WBC transition occurs. Near day 200, as the LSC interacts fully with the WBC, the perturbation of the LSC’s northward current enhances the inflow of the WBC. As a result, the vorticity balance shows that the meridional advection term increases to balance the increased β and viscosity terms when the WBC shifts from the eddy-shedding regime to the leaping regime. Then, the WBC remains in the leaping path due to the nonlinear hysteresis. The WBC transition occurs no matter if there is an island in the gap or not, because the interaction of the WBC and LSC occurs at the west of the island. In fact, a positive potential vorticity flux (PVF) of WBC inflow enters the western basin through the southern gap, and a positive PVF of outflow exits the western basin through the northern gap. When the WBC is in the eddy-shedding regime, the incoming PVF is inadequate to promote the WBC to flow out of the western basin directly. In this case, the WBC needs to shed anticyclonic eddy (negative PVF) to enhance its positive PVF and ensure it flows out of the western basin. When the single basinwide cyclonic gyre (positive PVF) is inserted into the model, the positive PVF of the WBC is enhanced by the LSC. Then, the WBC does not need to shed eddy, and the WBC path shifts from the eddy-shedding path to the leaping path.
Vorticity balance terms near XP as a function of time for the WBC critical state from the eddy-shedding regime to the leaping regime, perturbed by a critical single-gyre LSC from the west for WBC-Ic (top) with and (bottom) without an island in the gap.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
As noted in section 2, we use a 1.5-layer ocean model for studying the gap-leaping system, neglecting the effect of lower-layer circulation in this study. To briefly illustrate the insignificance of the lower-layer circulation, its magnitude is estimated by adding an additional term of −[fhE/(2h)]ζ to the vorticity equation, where
When the WBC critical from the eddy-shedding regime to the leaping regime (WBC-Ic) is perturbed by the double-gyre circulation in the western basin driven by the summer monsoon, the critical transports of LSC inducing the WBC transition are QL–S,i = 0.21 × 104 m2 s−1 (with island) and QL–S,n = 0.13 × 104 m2 s−1 (without island), corresponding to ReL–S,i = 7.0 and ReL–S,n = 4.3, respectively. The interaction of the critical WBC with the double-gyre LSC is shown in Fig. 6, where the WBC with (left) or without (right) an island in the gap translates from the eddy-shedding path to the leaping path as time elapses. In this case, the northern circulation of the LSC is transported northward near the gap area, which enhances the northward current speed of the WBC. Last, an irreversible transition of the WBC flow pattern is induced by the perturbation of the LSC due to the nonlinear hysteresis. As the integration time of the model is long enough (e.g., 2000 days), both western and eastern basins are occupied entirely by the dipole structure of the double-gyre LSC and WBC, respectively. The WBC path variation affected by the double-gyre circulation in the model is similar to the observations, and the time (∼200 days) needed for the WBC transition from the leaping regime to the eddy-shedding regime is about 4.8 times the real-world event in Fig. 2. Moreover, similar to the single-gyre circulation case, we estimate the effect of the adjustment to the Sverdrup steady state driven by the summer monsoon on the WBC transition due to the critical-state WBC interacting with the transient double-gyre LSC by adding a wind field of Eq. (5) to the background flow (WBC-Ic) in the western basin. The critical LSC transport (0.40 × 104 m2 s−1) becomes larger than that of the initial steady-state LSC in the island case; and it also takes ∼20 more days for the WBC transition than that in Fig. 6 (left).
As in Fig. 4, but for the interaction of the critical-state WBC with a critical double-gyre LSC from the west for WBC-Ic (left) with and (right) without an island in the gap.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
Similarly, we investigate the dynamics processes involved by carrying out vorticity balance analysis. Figure 7 shows the time evolution of each vorticity term in the vorticity equation for the double-gyre LSC-WBC interaction in the vicinity of the gap with (Fig. 7, top) and without (Fig. 7, bottom) an island. All vorticity balance terms are oscillatory at the early stage. Around day 200, as the LSC affects the main WBC near the gap, the WBC transition from periodic penetration to steady leap occurs, and all the vorticity curves become flat. At this time, the vorticity balance is mainly between the increased meridional advection with the increased β and viscosity terms. Then, the vorticity curves remain nearly invariable, which indicates the WBC is always in the leaping regime. As shown in Fig. 6, when the WBC sheds eddies into the western basin, the main loop current of the WBC bends northwestward due to nonlinearity. So, the WBC interacts mainly with the northern circulation of the double-gyre LSC, where the PVF is positive. Then, the positive PVF enhances the WBC’s PVF, and promotes the WBC to leap across the gap. This is why the WBC transition occurs in this case.
As in Fig. 5, but for the critical double-gyre LSC from the west (top) with and (bottom) without an island in the gap.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
c. WBC critical from leap to penetration
When the WBC critical from the leaping regime to the eddy-shedding regime is used as the background flow (WBC-Dc), it may also shift the regime perturbed by the LSC in the western basin. The LSC–WBC interaction and its underlying dynamics are investigated next.
First, a steady double-gyre circulation is added to the background flow (WBC-Dc), and the critical transport of the LSC that can induce the WBC transition is estimated as QL–S,i = 0.25 × 104 m2 s−1 (with island) or QL–S,n = 0.13 × 104 m2 s−1 (without island), corresponding to ReL–S,i = 8.3 and ReL–S,n = 4.3, respectively. Figure 8 shows the flow patterns of the interactive process of the WBC and LSC. In both cases, the WBC shifts from leaping across the gap to penetrating into the western basin. In these situations, the southern current of the LSC is transported southward, which reduces the meridional speed of the WBC inflow and induces the WBC transition. Then, the WBC stays in the penetration regime as time elapses. We calculate the critical LSC transport of the adjustment to the steady Sverdrup circulation inducing the WBC transition to be 0.29 × 104 m2 s−1 in the island case, which is slightly larger than that of the initial steady-state LSC. The time of the WBC transition is about 80 days longer than that in Fig. 8 (left).
Time evolution of the WBC critical state from the leaping regime to the eddy-shedding regime perturbed by a critical double-gyre LSC from the west for WBC-Dc (left) with and (right) without an island in the gap.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
The vorticity balance analysis illustrates that both the β and viscosity terms balance the meridional advection term as the WBC remains in the leaping regime before the transition occurs, as shown in Fig. 9. Then, the meridional advection term decreases dramatically during the interaction of the WBC and LSC around day 300. When the WBC translates from the leaping path to the penetrating path, each vorticity balance term shows periodic oscillation. The decreased meridional speed of the WBC inflow due to the southward current of the southern LSC reduces the meridional advection term in the transitional process of the WBC. Finally, the WBC remains in the eddy-shedding regime permanently. In this case, the main WBC is near the central part of the gap when the WBC is initially in the leaping regime (Fig. 8). So, the southern circulation of the double-gyre LSC can interact fully with the WBC. The negative PVF of the southern circulation reduces the positive PVF of the WBC inflow, which leads to the WBC enhancing its positive PVF to flow out of the gap by shedding eddies (negative PVF) into the western basin. This is why the double-gyre LSC can induce the WBC transition from the leaping regime to the eddy-shedding regime.
Vorticity balance terms near XP as a function of time for the WBC critical state from the leaping regime to the eddy-shedding regime, perturbed by a critical double-gyre LSC from the west for WBC-Dc (top) with and (bottom) without an island in the gap.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
We also examine the critical WBC perturbed by a single basinwide cyclonic gyre driven by the winter monsoon in the numerical experiments; however, no single cyclonic gyre can induce such WBC transition from leap to penetration. Why is the critical-state WBC not sensitive to the single-gyre LSC in winter? The current speed of the LSC near the gap is northward, and the northward speed further accelerates the main WBC, which leads to the WBC leaping across the gap more rapidly. The potential vorticity balance may also shed light on the dynamics of the case. When the WBC leaps across the gap, the positive PVF of the WBC inflow is adequate to ensure the WBC flows out of the gap directly. As a positive PVF of the single cyclonic gyre from the west of the gap is added to the WBC and interaction starts, the increased PVF in the WBC induced by the single-gyre LSC is more favorable for the WBC to leap across the gap. So, the WBC transition from leap to penetration is impossible in this case.
4. Parameter space of critical LSC and WBC
When the WBC is far away from the critical hysteresis state, the LSC in the western basin may also induce the WBC transition. In this section, we focus on the parameter space of critical strength of the LSC and WBC. Note that WBC-Ic and WBC-Dc are part of the background flow here. Then, for each LSC strength exceeding the critical value fixed in section 3, we seek the critical strength of the WBC of regime shift by changing τx,W based on the background field, which indicates the WBC is far away from the critical state.
First, the WBC critical from the eddy-shedding regime to the leaping regime, i.e., WBC-Ic, is used as the background flow. When a single basinwide cyclonic gyre with a strength exceeding the critical transport is added to the western basin of the model, we adjust the strength of τx,W to find a critical strength of the WBC, exceeding which the flow path of the WBC can be altered by the single-gyre LSC. Figure 10 shows the critical transport of the single-gyre LSC (defined as ReL–W,C) as a function of the critical WBC strength (defined as ReW,C) with and without an island in the gap. It can be seen that the critical strength of the single gyre increases as the critical transport of the WBC decreases. In other words, when the strength of the WBC is weakened, the LSC needs more energy to induce the WBC transition from penetration to leap. Of course, the transport of the WBC is not bigger than the critical value corresponding to ReW–L,n = 65 (corresponding to the WBC regime shift from the eddy-shedding path to the leaping path in the no-island case) or ReW–L,i = 74 (corresponding to the WBC regime shift from the eddy-shedding path to the leaping path in the island case); otherwise, the WBC would leap across the gap naturally due to the hysteresis and no matter there is a perturbation of the LSC or not. Furthermore, the single-gyre LSC cannot induce the WBC transition for ReW ≤ ReW–P,n (ReW–P,n = 46 representing the WBC regime shift from the leaping path to the eddy-shedding path in the no-island case) or ReW–P,i (ReW–P,i = 50 representing the WBC regime shift from the leaping path to the eddy-shedding path in the island case), because the WBC would stay in the eddy-shedding regime due to the hysteresis when its Reynolds number is lower than this critical value. Overall, the parameter range of the WBC that the single-gyre LSC can induce the WBC regime shift is in the hysteresis range, where the eddy-shedding and leaping paths of the WBC can coexist in view of the history of the WBC evolution.
The critical Re of the single-gyre LSC as a function of critical Re of the WBC transition induced by the perturbation of the LSC, where WBC-Ic is part of the background flow.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
Similarly, we add the double-gyre LSC driven by the summer monsoon to the background flow WBC-Ic, to identify the critical strength of the LSC (defined as ReL–S,C) that can induce the WBC transition. The solution is plotted as a function of the critical WBC strength (defined as ReW,C) in Fig. 11. The results show that the critical strength of the LSC increases as the critical transport of the WBC decreases in the no-island case. Moreover, the critical value increases as the critical WBC strength decreases at first and then, however, is proportional to the critical WBC strength for the model with an island in the gap. This is because the strength of the southern circulation of the LSC, where the current flows southward, is enhanced more than that of the northern circulation near the gap region due to strong nonlinearity (not shown). So, this southward current promotes the WBC to penetrate into the western basin, and the critical WBC transport needs to increase slightly to ensure the WBC leaps across the gap. In the no-island case, the WBC prefers to leap across the gap more easily when compared with that in the island case, as shown in Mei et al. (2019). Similar to the single-gyre case, the critical WBC strength is not larger than ReW–L,n = 65 (corresponding to the WBC regime shift from the eddy-shedding path to the leaping path in the no-island case) or ReW–L,i = 74 (corresponding to the WBC regime shift from the eddy-shedding path to the leaping path in the island case).
As in Fig. 10, but of the double-gyre LSC.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
We also examine the influence of the LSC on the critical WBC strength based on the background flow WBC-Dc. As discussed in section 3, the single-gyre circulation cannot induce the critical-state WBC shift from the leaping regime to the eddy-shedding regime. When the WBC was far away from the critical hysteresis state, numerical experiments also showed that no single-gyre circulation can induce such WBC transition. When the double-gyre circulation is added to WBC-Dc, the critical strength of the LSC (defined as ReL–S,C) as a function of the critical WBC strength (defined as ReW,C) is shown in Fig. 12. It can be seen that the critical strength of the LSC is proportional to the critical WBC strength. In this case, the transport of the WBC is not smaller than ReW–P,n = 46 (corresponding to the WBC regime shift from the leaping path to the eddy-shedding path in the no-island case) and ReW–P,i = 50 (corresponding to the WBC regime shift from the leaping path to the eddy-shedding path in the island case); otherwise, the WBC would penetrate into the western basin naturally due to the hysteresis.
As in Fig. 11, but where WBC-Dc is part of the background flow.
Citation: Journal of Physical Oceanography 53, 3; 10.1175/JPO-D-22-0194.1
5. Discussion
The numerical experiments presented in this paper help deepen our understanding, that is, the LCS in the western basin can affect the WBC flow pattern. Combining the present results with those of previous studies, we have a better understanding of the dynamics of Kuroshio intrusion and the explanation of observed facts in this regional ocean circulation. The ability of the LSC to induce WBC transition exhibits no difference between the cases with and without an island, except for the critical value of the LSC. Note that the perturbation of the LSC is from the west of the gap, and the main WBC is located at the west of the island; so, the WBC transition during the interaction of the LSC and WBC is not sensitive to having an island in the gap or not. In fact, a real topographic modeling study by Lu and Liu (2013) indicated that the western and eastern branches of the Kuroshio separated by the Batanes Islands carry 68% and 32% of the Kuroshio transport, respectively, as the WBC encounters the island, which explains why the main WBC is at the west of the island. On the other hand, the influence of the eastern perturbation, i.e., mesoscale eddy from the northwestern Pacific, exhibits obvious discrepancy in the two cases with and without an island, as presented in detail by Yuan and Wang (2011) and by Mei et al. (2022). This is because the island is located at the central section between the main WBC and the mesoscale eddy.
Observations showed that the time of the Kuroshio in the leaping regime was about twice of that in the penetrating regime in the real world, namely, a ratio of 2:1 (Yuan et al. 2006). The numerical experiments of Yuan and Wang (2011) and of Mei et al. (2022) suggested that the ratios of the chances of the WBC in the leaping regime to the penetrating regime affected by mesoscale eddy and island in the gap were 3:1 and 2:2, respectively, which clearly underestimate and overestimate the observation. The present study suggests that this ratio affected by the LSC in the SCS is 3:1, as the single-gyre circulation is not able to induce the WBC transition from the leaping regime to the eddy-shedding regime. Note that the numerical ratio is equal to 2:1 if we roughly consider the combined impact of mesoscale eddy, LSC, and island in the gap above. From the above discussion, it is reasonable to conclude that the LSC induced by the monsoon in the SCS indeed affects the Kuroshio intrusion in the Luzon Strait to some extent. Certainly, more external factors should be considered in this gap-leaping system, i.e., multiple islands and slope topography in an ocean model. These should be studied in future.
6. Conclusions
We investigate the influence of an LSC induced by the monsoon in the SCS on hysteresis WBC transition in a gap-leaping system numerically using a nonlinear 1.5-layer ocean model. Differing from previous studies, which considered the external impact factors from the gap or from the northwestern Pacific on the WBC transition, we examine the impact of a perturbation from the SCS on the WBC path in this study.
Our numerical experiments suggest that both single- and double-gyre circulations can induce critical-state WBC shift from the eddy-shedding regime to the leaping regime, while only the double-gyre circulation can induce the WBC transition from the leaping regime to the eddy-shedding regime. The vorticity balance analysis indicates that the meridional advection of the WBC enhanced by the perturbation of LSC is responsible for the WBC regime shift from penetration to leap and that the meridional advection of the WBC reduced by the perturbation of LSC is responsible for the WBC regime shift from leap to penetration. The adjustment to the Sverdrup steady state of the LSC enlarges the critical strength of the LSC inducing the WBC transition and delays the occurring time of WBC regime shift.
We also examine the parameter space of the critical LSC that can induce the WBC transition for the WBC far away from the critical state. When the WBC is in the eddy-shedding regime initially, the critical strength of the single-gyre LSC inducing the WBC transition increases as the critical transport of the WBC decreases in both no-island and island cases. The critical strength of the double-gyre LSC increases as the critical WBC transport decreases in the no-island case, while the critical value increases as the critical WBC transport decreases at first and then is proportional to the WBC transport in the island case. When the WBC is in the leaping regime initially, the critical strength of the double-gyre LSC is proportional to the WBC strength in both no-island and island cases. No single-gyre circulation is able to induce the WBC transition from leap to penetration. Overall, the WBC transport must be confined to the hysteresis range, over which the WBC would shift from one regime to another naturally due to the hysteresis.
Acknowledgments.
This research is supported by the National Natural Science Foundation of China (42076005 and 41706003) and the Natural Science Foundation of Jiangsu Province (BK20210885). The authors declare no conflict of interest. The authors thank the two anonymous reviewers for their constructive comments and suggestions.
Data availability statement.
Satellite altimeter data of sea surface height used in this study are openly available from the Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO http://www.aviso.oceanobs.com/).
REFERENCES
Caruso, M. J., G. G. Gawwarkiewicz, and R. C. Beardsley, 2006: Interannual variability of the Kuroshio intrusion in the South China Sea. J. Oceanogr., 62, 559–575, https://doi.org/10.1007/s10872-006-0076-0.
Cheng, X. H., J. P. McCreary, B. Qiu, Y. Q. Qi, and Y. Du, 2017: Intraseasonal-to-semiannual variability of sea-surface height in the eastern, equatorial Indian Ocean and southern Bay of Bengal. J. Geophys. Res. Oceans, 122, 4051–4067, https://doi.org/10.1002/2016JC012662.
Chu, P. C., N. L. Edmons, and C. W. Fan, 1999: Dynamical mechanisms for the South China Sea seasonal circulation and thermohaline variabilities. J. Phys. Oceanogr., 29, 2971–2989, https://doi.org/10.1175/1520-0485(1999)029<2971:DMFTSC>2.0.CO;2.
Chu, X. Q., H. J. Xue, Y. Q. Qi, G. X. Chen, Q. W. Mao, D. X. Wang, and F. Chai, 2014: An exceptional anticyclonic eddy in the South China Sea in 2010. J. Geophys. Res. Oceans, 119, 881–897, https://doi.org/10.1002/2013JC009314.
Cushiman-Roisin, B., and J.-M. Beckers, 2011: Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects. Academic Press, 875 pp.
Fang, W. D., G. H. Fang, P. Shi, Q. Z. Huang, and Q. Xie, 2002: Seasonal structures of upper layer circulation in the southern South China Sea from in situ observations. J. Geophys. Res., 107, 3202, https://doi.org/10.1029/2002JC001343.
Gan, J. P., Z. Q. Liu, and C. R. Hui, 2016: A three-layer alternating spinning circulation in the South China Sea. J. Phys. Oceanogr., 46, 2309–2315, https://doi.org/10.1175/JPO-D-16-0044.1.
He, Z. G., and D. Wang, 2009: Surface pattern of the South China Sea western boundary current in winter. Adv. Geosci., 12, 99–107, https://doi.org/10.1142/9789812836168_0008.
He, Z. G., and D. Sui, 2010: Remote sensing and validation of the South China Sea western boundary current in December 2003, 2004 and 2005. Proc. Second IITA Int. Conf. on Geoscience and Remote Sensing, Qingdao, China, Institute of Electrical and Electronics Engineers, 515–518, https://doi.org/10.1109/IITA-GRS.2010.5602670.
Hu, J. Y., K. Hiroshi, H. S. Hong, and Y. Q. Qi, 2000: A review on the currents in the South China Sea: Seasonal circulation, South China Sea warm current and Kuroshio intrusion. J. Oceanogr., 56, 607–624, https://doi.org/10.1023/A:1011117531252.
Kuehl, J., and V. A. Sheremet, 2009: Identification of a cusp catastrophe in a gap-leaping western boundary current. J. Mar. Res., 67, 25–42, https://doi.org/10.1357/002224009788597908.
Kuehl, J., and V. A. Sheremet, 2014: Two-layer gap-leaping oceanic boundary currents: Experimental investigation. J. Fluid Mech., 740, 97–113, https://doi.org/10.1017/jfm.2013.645.
Kuehl, J., and V. A. Sheremet, 2022: Effect of the coastline geometry on the boundary currents intruding through the gap. Fluids, 7, 71, https://doi.org/10.3390/fluids7020071.
Li, L., W. D. Nowlin Jr., and S. Jilan, 1998: Anticyclonic rings from the Kuroshio in the South China Sea. Deep-Sea Res. I, 45, 1469–1482, https://doi.org/10.1016/S0967-0637(98)00026-0.
Li, L., X. Guo, and R. Wu, 2018: The winter western boundary current of the South China Sea: Physical structure and volume transport in December 1998. Acta Oceanol. Sin., 37, 1–7, https://doi.org/10.1007/s13131-018-1195-3.
Liu, Q. Y., X. Jiang, S.-P. Xie, and W.-T. Liu, 2004: A gap in the Indo-Pacific warm pool over the South China Sea in boreal winter: Seasonal development and interannual variability. J. Geophys. Res., 109, C07012, https://doi.org/10.1029/2003JC002179.
Liu, Q. Y., A. Kaneko, and J. Su, 2008: Recent progress in studies of the South China Sea circulation. J. Oceanogr., 64, 753–762, https://doi.org/10.1007/s10872-008-0063-8.
Liu, Z. Y., H. J. Yang, and Q. Y. Liu, 2001: Regional dynamics of seasonal variability in the South China Sea. J. Phys. Oceanogr., 31, 272–284, https://doi.org/10.1175/1520-0485(2001)031<0272:RDOSVI>2.0.CO;2.
Lu, J., and Q. Y. Liu, 2013: Gap-leaping Kuroshio and blocking westward-propagating Rossby wave and eddy in the Luzon Strait. J. Geophys. Res. Oceans, 118, 1170–1181, https://doi.org/10.1002/jgrc.20116.
McMahon, C. W., 2020: An investigation of oceanic gap-traversing boundary currents and shelf-slope dynamics through analytic and experimental models. Ph.D. thesis, University of Delaware, 178 pp., https://udspace.udel.edu/handle/19716/28697.
McMahon, C. W., J. Kuehl, and V. A. Sheremet, 2020: A viscous, two-layer western boundary current structure function. Fluids, 5, 63, https://doi.org/10.3390/fluids5020063.
McMahon, C. W., J. Kuehl, and V. A. Sheremet, 2021: Dynamics of gap-leaping western boundary currents with throughflow forcing. J. Phys. Oceanogr., 51, 2243–2256, https://doi.org/10.1175/JPO-D-20-0216.1.
Mei, H., Y. Q. Qi, B. Qiu, X. H. Cheng, and X. B. Wu, 2019: Influence of an island on hysteresis of a western boundary current flowing across a gap. J. Phys. Oceanogr., 49, 1353–1366, https://doi.org/10.1175/JPO-D-18-0116.1.
Mei, H., Y. Q. Qi, X. H. Cheng, X. B. Wu, and Q. Wang, 2022: Nonlinear dynamics of a hysteresis western boundary current perturbed by a mesoscale eddy at a gap with an island. J. Phys. Oceanogr., 52, 1993–2008, https://doi.org/10.1175/JPO-D-22-0016.1.
Nan, F., H. J. Xue, and F. Yu, 2015: Kuroshio intrusion into the South China Sea: A review. Prog. Oceanogr., 137, 314–333, https://doi.org/10.1016/j.pocean.2014.05.012.
National Academies of Sciences, Engineering, and Medicine, 2018: Understanding and Predicting the Gulf of Mexico Loop Current: Critical Gaps and Recommendations. National Academies Press, 116 pp., https://doi.org/10.17226/24823.
Nitani, H., 1972: Beginning of the Kuroshio. Kuroshio: Its Physical Aspects of the Japan Current, H. Stommel and K. Yashida, Eds., University of Tokyo Press, 129–163.
Pichevin, T., and D. Nof, 1996: The eddy cannon. Deep-Sea Res. I, 43, 1475–1507, https://doi.org/10.1016/S0967-0637(96)00064-7.
Pichevin, T., and D. Nof, 1997: The momentum imbalance paradox. Tellus, 49A, 298–319, https://doi.org/10.3402/tellusa.v49i2.14484.
Pierini, S., and Coauthors, 2022: Laboratory experiments reveal intrinsic self-sustained oscillations in ocean relevant rotating fluid flows. Sci. Rep., 12, 1375, https://doi.org/10.1038/s41598-022-05094-1.
Qiu, B., and R. Lukas, 1996: Seasonal and interannual variability of the North Equatorial Current, the Mindanao Current, and the Kuroshio along the Pacific western boundary. J. Geophys. Res., 101, 12 315–12 330, https://doi.org/10.1029/95JC03204.
Qiu, B., and S. Chen, 2012: Multidecadal sea level and gyre circulation variability in the northwestern tropical Pacific Ocean. J. Phys. Oceanogr., 42, 193–206, https://doi.org/10.1175/JPO-D-11-061.1.
Qu, T. D., 2000: Upper-layer circulation in the South China Sea. J. Phys. Oceanogr., 30, 1450–1460, https://doi.org/10.1175/1520-0485(2000)030<1450:ULCITS>2.0.CO;2.
Qu, T. D., and R. Lukas, 2003: The bifurcation of the north equatorial current in the Pacific. J. Phys. Oceanogr., 33, 5–18, https://doi.org/10.1175/1520-0485(2003)033<0005:TBOTNE>2.0.CO;2.
Qu, T. D., H. Mitsudera, and T. Yamagata, 2000: Intrusion of the North Pacific waters into the South China Sea. J. Geophys. Res., 105, 6415–6424, https://doi.org/10.1029/1999JC900323.
Qu, T. D., Y. Y. Kim, M. Yaremchuk, T. Tozuka, A. Ishida, and T. Yamagata, 2004: Can Luzon Strait transport play a role in conveying the impact of ENSO to the South China Sea? J. Climate, 17, 3644–3657, https://doi.org/10.1175/1520-0442(2004)017<3644:CLSTPA>2.0.CO;2.
Shaw, P. T., and S. Y. Chao, 1994: Surface circulation in the South China Sea. Deep-Sea Res. I, 41, 1663–1683, https://doi.org/10.1016/0967-0637(94)90067-1.
Shen, J. Q., W. D. Fang, L. Li, Y. Qiu, Z. Xiao, J. P. Zhang, and X. G. Guo, 2022: Slope undercurrent in the northwestern South China Sea beneath the winter western boundary current. Front. Mar. Sci., 9, 918077, https://doi.org/10.3389/fmars.2022.918077.
Sheremet, V. A., 2001: Hysteresis of a western boundary current leaping across a gap. J. Phys. Oceanogr., 31, 1247–1259, https://doi.org/10.1175/1520-0485(2001)031<1247:HOAWBC>2.0.CO;2.
Sheremet, V. A., and J. Kuehl, 2007: Gap-leaping western boundary current in a circular tank model. J. Phys. Oceanogr., 37, 1488–1495, https://doi.org/10.1175/JPO3069.1.
Sheremet, V.A., A. A. Khan, and J. Kuehl, 2021: Multiple equilibrium states of the Loop Current in the Gulf of Mexico. arXiv, 2111.13810, https://doi.org/10.48550/arXiv.2111.13810.
Shu, Y. Q., D. X. Wang, J. Zhu, and S. Q. Peng, 2011: The 4-D structure of upwelling and Pearl River plume in the northern South China Sea during summer 2008 revealed by a data assimilation model. Ocean Modell., 36, 228–241, https://doi.org/10.1016/j.ocemod.2011.01.002.
Song, X. X., D. Yuan, R. X. Li, and Z. Wang, 2018: Migration of mesoscale eddies across a leaping or penetrating western boundary current in the vicinity of a gap. J. Oceanol. Limnol., 36, 2098–2109, https://doi.org/10.1007/s00343-019-7296-9.
Song, X. X., D. Yuan, and Z. Wang, 2019: Hysteresis of a periodic or leaking western boundary current flowing by a gap. Acta Oceanol. Sin., 38, 90–96, https://doi.org/10.1007/s13131-018-1251-z.
Su, J. L., 2004: Overview of the South China Sea circulation and its influence on the coastal physical oceanography outside the Pearl River Estuary. Cont. Shelf Res., 24, 1745–1760, https://doi.org/10.1016/j.csr.2004.06.005.
Wang, D. X., Q. Wang, W. Zhou, S. Cai, L. Li, and B. Hong, 2013: An analysis of the current deflection around Dongsha Islands in the northern South China Sea. J. Geophys. Res. Oceans, 118, 490–501, https://doi.org/10.1029/2012JC008429.
Wang, D. X., and Coauthors, 2019: Advances in research of the mid-deep South China Sea circulation. Sci. China Earth Sci., 62, 1992–2004, https://doi.org/10.1007/s11430-019-9546-3.
Wang, G. H., J. L. Su, and P. C. Chu, 2003: Mesoscale eddies in the South China Sea observed with altimeter data. Geophys. Res. Lett., 30, 2121, https://doi.org/10.1029/2003GL018532.
Wang, G. H., D. K. Chen, and J. L. Su, 2006: Generation and life cycle of the dipole in the South China Sea summer circulation. J. Geophys. Res., 111, C06002, https://doi.org/10.1029/2005JC003314.
Wang, G. H., S.-P. Xie, T. D. Qu, and R. X. Huang, 2011: Deep South China Sea circulation. Geophys. Res. Lett., 38, L05601, https://doi.org/10.1029/2010GL046626.
Wang, Q., L. Zeng, W. Zhou, Q. Xie, S. Cai, J. Yao, and D. Wang, 2015: Mesoscale eddies cases study at Xisha waters in the South China Sea in 2009/2010. J. Geophys. Res. Oceans, 120, 517–532, https://doi.org/10.1002/2014JC009814.
Wang, Z., and D. Yuan, 2012: Nonlinear dynamics of two western boundary currents colliding at a gap. J. Phys. Oceanogr., 42, 2030–2040, https://doi.org/10.1175/JPO-D-12-05.1.
Wang, Z., and D. Yuan, 2014: Multiple equilibria and hysteresis of two unequal-transport western boundary currents colliding at a gap. J. Phys. Oceanogr., 44, 1873–1885, https://doi.org/10.1175/JPO-D-13-0234.1.
Wang, Z., D. Yuan, and Y. Hou, 2010: Effect of meridional wind on gap-leaping western boundary current. Chin. J. Oceanol. Limnol., 28, 354–358, https://doi.org/10.1007/s00343-010-9281-1.
Wu, C.-R., 2013: Interannual modulation of the Pacific Decadal Oscillation (PDO) on the low-latitude western North Pacific. Prog. Oceanogr., 110, 49–58, https://doi.org/10.1016/j.pocean.2012.12.001.
Wyrtki, K., 1961: Physical oceanography of the Southeast Asia waters. Scripps Institution of Oceanography Naga Rep. Vol. 2, 195 pp., https://escholarship.org/uc/item/49n9x3t4.
Xiu, P., F. Chai, L. Shi, H. J. Xue, and Y. Chao, 2010: A census of eddy activities in the South China Sea during 1993–2007. J. Geophys. Res., 115, C03012, https://doi.org/10.1029/2009JC005657.
Xue, H. J., F. Chai, N. Pettigrew, D. Y. Xu, M. C. Shi, and J. P. Xu, 2004: Kuroshio intrusion and the circulation in the South China Sea. J. Geophys. Res., 109, C02017, https://doi.org/10.1029/2002JC001724.
Yuan, D. L., and Z. Wang, 2011: Hysteresis and dynamics of a western boundary current flowing by a gap forced by impingement of mesoscale eddies. J. Phys. Oceanogr., 41, 878–888, https://doi.org/10.1175/2010JPO4489.1.
Yuan, D. L., W. Han, and D. Hu, 2006: Surface Kuroshio path in the Luzon Strait area derived from satellite remote sensing data. J. Geophys. Res., 111, C11007, https://doi.org/10.1029/2005JC003412.
Yuan, D. L., X. X. Song, Y. Yang, and W. K. Dewar, 2019: Dynamics of mesoscale eddies interacting with a western boundary current flowing by a gap. J. Geophys. Res. Oceans, 124, 4117–4132, https://doi.org/10.1029/2019JC014949.
Zavala Sansón, L., and G. J. F. Van Heijst, 2002: Ekman effects in a rotating flow over bottom topography. J. Fluid Mech., 471, 239–255, https://doi.org/10.1017/S0022112002002239.
Zhang, Z. W., W. Zhao, B. Qiu, and J. W. Tian, 2017: Anticyclonic eddy shedding from Kuroshio Loop and the accompanying cyclonic eddy in the northeastern South China Sea. J. Phys. Oceanogr., 47, 1243–1259, https://doi.org/10.1175/JPO-D-16-0185.1.
Zheng, H., C. Zhang, R. Zhao, X. Zhu, Z. Zhu, Z. Liu, and M. Wang, 2021: Structure and variability of abyssal current in northern South China Sea based on CPIES observations. J. Geophys. Res. Oceans, 126, e2020JC016780, https://doi.org/10.1029/2020JC016780.
Zhong, L. H., L. Hua, and D. Luo, 2016: The eddy-mean flow interaction and the intrusion of western boundary current into the South China Sea-type basin in an idealized model. J. Phys. Oceanogr., 46, 2493–2527, https://doi.org/10.1175/JPO-D-15-0220.1.
Zhou, C., W. Zhao, J. Tian, X. Zhao, Y. Zhu, Q. Yang, and T. Qu, 2017: Deep western boundary current in the South China Sea. Sci. Rep., 7, 9303, https://doi.org/10.1038/s41598-017-09436-2.
Zhu, X., R. Zhao, X. Guo, Y. Long, Y. Ma, and X. Fan, 2015: A long-term volume transport time series estimated by combining in situ observation and satellite altimeter data in the northern South China Sea. J. Oceanogr., 71, 663–673, https://doi.org/10.1007/s10872-015-0305-5.
Zhu, Y., and Coauthors, 2022: Decadal weakening of abyssal South China Sea circulation. Geophys. Res. Lett., 49, e2022GL100582, https://doi.org/10.1029/2022GL100582.