Corresponding author: Q. Wang, State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academic of Sciences, Guangzhou, China. (firstname.lastname@example.org)
 Based on the in situ data and ADCP observation in fall, it is found that a northeastward current at inter-middle level flows on the Northern South China Sea (NSCS) continental shelf. This current flows almost along the isobaths, and it deflects from the isobaths veering toward deep water when flowing over the Dongsha Islands. Geographic currents derived from the climatologic hydrography data (WOA01) and absolute dynamic topography (ADT) data confirm the deflection of the northeastward current on NSCS continent. A fine resolution regional ocean model which can well reproduce the large scale circulation in the NSCS is used to analyze the dynamic about the deflection. The vorticity term balances shows that JEBAR (Joint Effect of Baroclinicity and Relief) drives the water column to depart from the isobaths. To the east of the Dongsha Islands, the isopycnal is almost orthogonal to the isobaths. The joint effect of the topographic and the baroclinic effect supplies negative vorticity and drives the water column to deflect from the isobaths and veer to deeper water. Momentum analysis along the stream line shows that, when the sea water flows around the Dongsha islands, the pressure gradient along the isobath pushes the sea water to accelerate, and then the Coriolis force orthogonal to the isobath increases and overcomes the corresponding pressure gradient, which drives the water deflected from the isobath toward the deep sea.
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 The South China Sea (SCS) is a semi-enclosed marginal sea in the western Pacific Ocean, with a broad shelf and slope in its northern part. The continental shelf in the northern SCS (NSCS) is in the northeast-southwest orientation and 150–250 km wide, with Dongsha Islands located about 200 km offshore on a plateau over the upper continental slope.
 The large-scale circulation in the SCS is driven mainly by Asian monsoons and the lateral influxes that intrude from the Luzon Strait and Taiwan Strait in the NSCS and from the Karimata Strait in the southwest SCS [e.g., Wyrtki, 1961; Dong et al., 2010; Wang et al., 2011; Shu et al., 2011]. Driven by the prevailing northeasterly (southwesterly) monsoon in winter (summer), the basin-scale cyclonic (anticyclonic) circulation is typically formed flowing around the continental margin in the SCS. An analysis using various observational data leads to the conclusion that JEBAR (Joint Effect of Baroclinicity and Relief) is an important impact factor on the SCS current, with the terrain effect superior to the β effect (i.e., planetary voriticity changes with latitudes ) [Wang et al., 2004, 2004; Liao et al., 2007, 2008; Yuan et al., 2008].
 In the NSCS, there are three adjacent band-like currents with alternative directions in winter, namely the leeward Guangdong coastal current, the SCS Warm Current (SCSWC), and the southwestward slop current [Guo et al., 1985]. The SCSWC consists of two distinct portions. The eastern portion exits at the east of the Dongsha Islands and flows steadily north-eastward; the western portion is at the west of the Dongsha Islands and the flow path, width, salinity, and flow velocity vary seasonally [Guan, 1985]. The eastern portion is stronger, wider, and deeper than the western one. In addition, the northeastward flow was observed in deeper waters east of the Dongsha Islands [Guo et al., 1985]. In view of the existence of the anticyclonic Kuroshio loop in this region, this deep current is probably some combination of the SCSWC and the return part of the anticyclonic loop [Hsueh and Zhong, 2004]. The north-east ward current discussed in this paper maybe have some relationships with the east portion SCSWC.
 The north-east ward inter-middle level current, behaving deflecting toward deep water, has been implied in some researches. Liao et al.  calculated the three-dimensional (3-D) structure of the winter circulation in the SCS using a 3-D diagnostic model. In their results, it can be found that the current at 500 m on the NSCS continental shelf flows eastward along the isobath, and then deflects isobath toward the deep sea direction, which happens around Dongsha Islands. This deflection current forms an eddy in the interior. The similar structure on the NSCS continental shelf also appears on their vertical integrated stream function distribution. Many researches based on the hydrographic data show that eddies occur near the Dongsha Island frequently [Liao et al., 2007, 2008; Yuan et al., 2007; Chow et al., 2008; Nan et al., 2011]. And the mechanisms are often connected with the shedding from the Kuroshio loop [Li et al., 1998; Jia and Liu, 2005; Jia et al., 2004] and locally wind stress curl [Metzger and Hurlburt, 2001; Wang et al., 2008]. Maybe the instability generated by the deflection is another local mechanism, while in this paper we focus on the dynamic of the deflection and discuss other related issues.
 The ocean current is expected to flow along the f/H contours (where f is the Coriolis parameter, and H is water depth) when the relative vorticity is much smaller than the planetary vorticity. Current deflection is a feature in which the current leaves the f/H contours that it is attached to and overshoots to form an eddy in the interior. The offshore deflection of the coastal jet from the coast of Vietnam is an example of current deflection [Haidvogel et al., 1992; Gan et al., 1997, 2004]. The deflection of the Gulf Stream from the continental slope near Cape Hatteras also has attracted much attention [Robinson and Niiler, 1967; Robinson et al., 1975; Luyten, 1977]. The mechanism for current deflection has been generally related to the formation of the adverse pressure gradient force, induced mainly by the intensified current (jet), wind forcing, coastal curvature, rotation, and other factors in the boundary layer [Gan and Qu, 2008]. Hsienwangou, Wilhelmus P.M. De Ruuter (1985) used a two-layer model to examine the deflection of an inertial boundary current from a curved coastline and found that the deflection occurs where the coastline has a large positive curvature (i.e., convex outward). Stern (1998) used an inviscid, steady, finite-amplitude longwave theory to study the deflection of a midlevel density current from the bottom of a continental slope and found that, when the cross-stream topographic slope increases gradually in the downstream direction, the midlevel current deflects off the bottom slope and onto the upper density interface.
 On the NSCS, the continental shelf is relatively straight, and the Dongsha Islands embedding in the east segment makes the continental shelf convex toward the deep sea side. The kuroshio intrusion affects the baroclinic temperature and the salinity field on the northeast continental shelf. The special terrain and baroclinic field complicate the NSCS oceanography background. The behavior of the northeastward midlevel current on the NSCS continental shelf must be related to the special terrain characters and the baroclinic background.
2 Observation of the NSCS Continental Shelf Current and the Deflection
2.1 NSCS Continental Shelf In Situ Observation
 In order to quantitatively give the current characteristics on the NSCS continental shelf, the pressure distribution on the continental shelf is calculated. The CTD data obtained between 5 and 23 September in 2005 from the SCS Open Cruise observation and the absolute dynamic topography (ADT) data are a merged product from TOPEX/Poseidon, ERS, and Jason-1 satellites. From the density and ADT data, the pressure distribution at 300 and 500 m are calculated using the hydrostatic equation.
 Pressure gradient is an important driving forcing in ocean and determines the geostrophic current directly. In Figure 1, each station's pressure has been calculated, and the comparison between two stations can give the geostrophic current. The observation sections are almost orthogonal to the isobath. From pressure distribution at the 300 and 500 m, it can be found that high pressure locates at the outer side of the continental shelf, and the pressure increases from the shallower water to the deep side. The pressure gradient forcing points to the shallower water side along all sections. Under the geostrophic constraint, the large-scale current direction of the current is northeast.
2.2 Ship-Mounted ADCP
 The ship-mounted ADCP data were obtained during the following three cruises: 5–23 September 2004, 11 August to 2 September 2008, and 5–25 September 2010. In order to remove the tides in the ship-mounted ADCP observation, a simple but useful method has been applied [Candela et al., 1992; Chen et al., 1994]. The fitted currents at 471.5 m are shown in Figure 2.
 It can be found that the current flows northeastward at the west of the Dongsha Islands, which is consistent with the pressure distribution, and almost along the isobath, while the current will deflect from the isobath and veer to the deep sea side, when flowing over the Dongsha islands. All the 3 year observations show the similar deflection character. The deflection occurs when the current flowing over the Dongsha Islands where the special convex topography may push the water to depart from the isobath (Hsienwangou, Wilhelmus P.M. De Ruuter, 1985). The detailed dynamic analysis will be shown later.
2.3 Mooring ADCP Observation
 The mooring station is located at (118°24.461′E, 20°34.851′N), east to the Dongsha Islands, and the water depth is 2474 m. At each level of 1500 and 2000 m, an Aanderaa current meter has been set, and sampling time is 30 min. The Aanderaa current meter at 1500 m level went wrong after it was placed. And the velocity data have been collected from 20 August 2000 to 17 March 2001. All the data have been processed with low-pass filter (7 days) and then averaged to daily mean. And the velocity vector has been turned an angle to fit the isobaths, i.e., the longitude velocity and latitude velocity have been replaced by cross-isobath velocity and along-isobath velocity.
 Figure 3 shows the velocity vector. It can be seen that the velocity component orthogonal to the isobaths is dominant, and the direction toward deep sea is dominant. Except October and late February, the direction toward the deep sea almost did not change. From this observation, it can be seen that the deflection not only occurs in fall but also may occur in other seasons. We just focus on the fall in this paper.
2.4 Climate Large-Scale Current on the NSCS Continental Shelf
 In order to acquire the climate large-scale current on the NSCS continental shelf, the geostrophic current is calculated from the climatologic temperature and salinity data and ADT data. To avoid the error brought by the selection of the reference level, the geostrophic current is calculated from the sea surface, and the sea surface geostrophic current is derived from the ADT data [Ho et al., 2000; Li Li and Guo, 2000a, 2000b; Ge et al., 2012]. The temperature and salinity fields are from the World Ocean Atlas 2001 (WOA01; Boyer et al., 2005), with a space resolution of 0.25° × 0.25°, and ADT data are the same as above except that it is the seasonal mean.
 The velocity at 100, 300, and 500 m are shown in Figure 4. At the 100 m level, the southwest current dominates the NSCS continental shelf. At the 300 and 500 m levels especially the 500 m level, there is a regular northeast current on the continental shelf. The deflection happens when the current flows over the Dongsha Islands, which is consistent with the above discussion. The consistency confirms that the deflection is not just an occasional event, but a climate phenomenon.
3 Numerical Investigation of the Current Deflection
3.1 Model and Forcing Function
 In order to investigate the deflection around Dongsha Island, the Princeton Ocean Model (POM) [Blumberg and Mellor, 1987] which can well describe the topography has been utilized. The POM is a hydrostatic, free-surface, sigma-coordinate, primitive equation model and is propitious for studying nonlinear dynamics over a shallow, gently sloping continental shelf.
 The model domain includes the whole SCS, southern East China Sea, and part of the western Pacific Ocean, in order to achieve a better simulation of the Kuroshio intrusion through the Luzon Strait (Figure 5a). ETOPO2 [Marks and Smith, 2006] is used to prescribe the bathymetry in the model domain. The horizontal orthogonal curvilinear coordinates are utilized to improve the resolution of the currents on the NSCS for the coastline fitting and local refinement. The model grid has a spatial scale ranging from 10 to 30 km with an average of about 13 km. The vertical sigma-coordinate has 25 levels, which are logarithmically distributed with higher resolution near the surface and the bottom in order to better resolve the surface and bottom Ekman layers.
 The surface momentum flux is calculated from the monthly mean climatology based on 40 years of the ERA40 data set [Uppala et al., 2005]. The model is initialized by the January climatological hydrographic data (WOA01) with 0.25° resolution. The total surface heat flux is replaced by a relaxation scheme. Both the sea surface temperature and sea surface salinity are relaxed toward the monthly mean climatological data of WOA01, with a relaxation time scale of 30 days for both fields.
 The lateral forcing of the model is provided by the Simple Ocean Data Assimilation (SODA) reanalysis product [Carton and Giese, 2008] which have been interpolated into the model levels using a bilinear method, with the one-way radiative nesting scheme proposed by Flather  for the normal component of the external mode barotropic velocity. Non-gradient boundary condition is applied to the sea surface high (SSH). The internal mode velocity at each level is free to adjust geostrophically to the density field. Upstream scheme is adopted for the open boundary conditions of both temperature and salinity, which can best characterize the essence of the hyperbolic equations.
 The model is integrated from a state of rest. Under the January wind forcing, the model is integrated for 10 years, and the velocity, temperature, salinity, and SSH all adjust accordingly to reach a dynamic balance. After 10 years of integration, the results reach an equilibrium state, as indicated by the time series of the volume-averaged kinetic energy. After that, the model is forced by seasonal winds. Output from the 20th year is sampled daily and averaged over 30 days for the analysis.
3.2 Validation of Model Results
 Observational data for the velocity field in the SCS are very limited. First, the data from satellite remote sensing have been used for qualitative extraction of the large-scale circulation characteristics. The simulated sea surface height anomaly (SSHA) and satellite altimetry data are compared (Figure 6).
 Figure 6 shows that the simulated and observed SSHAs well resemble each other. They both show the negative/positive SSHA centers to the west of Philippines and to the east off Vietnam in the winter/summer, which denote the seasonal current transition characters. In fall, the negative SSHAs occupy the deep ocean and the high SSHA belt exists on the NSCS continental shelf in both fields. These consistencies suggest that the model is able to realistically capture the dynamic conditions in SCS.
 In order to further validate model results, we compare the modeled and observed vertical structures of currents at a mooring station (marked in Figure 5b by solid pentacle) east to the Dongsha Islands. The observed data are then averaged to monthly mean (Figure 7). From the comparison, it can be seen that the model results to a little underestimate of the current amplitude, while the direction is similar.
 Deflection is anther criterion of the model result validation. The mean flow in fall at 500 m is shown in Figure 8. The current on the NSCS continent west to the Dongsha Islands almost flows along the isobath and deflects from the isobath veering to the deeper sea side when flowing over the Dongsha Islands. The current deflection characters are well reproduced.
 Based on the agreement, the model results are used to investigate the possible dynamic mechanism for the current deflection when flowing over the Dongsha Islands.
3.3 Dynamical Analyses
 The ocean currents are expected to flow along the f/H contours when the relative vorticity is much smaller than the planetary vorticity. The north-south scale of the deflection feature around the Dongsha Islands is very small, about 100 km, which means that the variability of the Coriolis parameter is very small, so the f-plane can be used. Then, the isobath is equivalent to the f/H contour in some extent. From the earlier discussion, we saw that the current around the Dongsha Islands does not follow the f/H contour, but deflects from the f/H contour and veers toward the deep water after flowing over the Dongsha Islands. Then, the velocity appears to be perpendicular to the isobath and the joint effect of bottom slope and density field arises. In order to clarify the dynamic mechanism of the deflection, the vorticity balance and momentum balance are investigated in the following sections.
3.3.1 Vorticity Balance
 Cross-differentiate the vertically integrated momentum equation will result in the vertically integrated vorticity equation [Wang et al., 2010]
where (, ) represents the vertically integrated velocity, is the JEBAR term, is the potential energy, ρ is the density, η is the surface elevation, D = H + η is the water column depth, (τx,τy,)a and (τx,τy,)b are the surface and bottom stresses, respectively, and and are the vertically integrated horizontal diffusion term and the nonlinear advection term, respectively. The left-hand side of equation ((3.1)) includes (a) the tendency term. The right-hand side of equation ((3.1)) includes (b) advection of the planet potential vorticity f/D (APV) term, (c) the JEBAR term, (d) the diffusion term, (e) the advection term, (f) surface stress torque, and (g) bottom stress torque. All the terms are diagnosed using the model results. In the quasi-steady state, the tendency term should approximately be zero.
 The APV term denotes the cross-isobath transport of the planetary potential vorticity. If the APV term is positive, the transport is in the offshore direction and the current tends to veer toward the deep ocean [Sakamoto and Yamagata, 1996; Guo et al., 2003].
 Figure 9 displays the spatial distribution of each term in equation ((3.1)) in fall, limited to the deflection domain. The JEBAR and APV terms are dominant, and the advection term is secondary. Comparing between the JEBAR distribution and current deflection, it can be seen that the deflection occurs at the negative JEBAR region. Negative JEBAR supplies negative vorticity, and the current has to anticyclone bend under the negative JEBAR.
3.3.2 JEBAR Effect on the Deflection
Sakamoto and Yamagata  first explicitly applied the dynamic (i.e., time-dependent) aspects of JEBAR to the seasonal variation of a wind-driven gyre. Generally, JEBAR represents the torque exerted on the fluid column by the joint action of density and topographic gradients to drive it from following the f/H contour [e.g., Sarkisyan and Ivanov, 1971; Holland, 1973; Mellor et al., 1982; Myers et al., 1996; Isobe, 2000; Guo et al., 2003]. Two sections along the isobath (marketed in Figure 6b) have been selected to clarify the relationship between the JEBAR and the deflection.
 The regions bounded between 900 and 1000 m and between 1400 and 1500 m are selected for the analyses of the vertical deflection structure. The vertical profile of the across-shelf flow together with the vorticity terms is shown in Figure 10. The velocity profile and the vorticity terms are all averaged in the across-shelf direction in the two selected ranges. Negative value denotes the current flowing toward the deep sea, and the positive value is the opposite. It can be seen that the vertical structure (except the surface and the bottom) presents the same character that the direction is almost consistent for both ranges. Each offshore (onshore) flow corresponds to the negative (positive) JEBAR. The JEBAR term is the dominant one of such deflection in this area based on the term-by-term analyses in Figure 9. The JEBAR term supplies the negative vorticity, so there must be positive vorticity transport in order to maintain the vorticity balance (i.e., offshore flow). On the west of the Dongsha Islands, the water column on the shallower field which contains larger planet potential vorticity (f/D) has to flow across the isobaths toward the deeper water where the smaller planet potential vorticity exists and induces the positive planet potential vorticity advection to balance the JEBAR term. And then, the deflection occurs.
3.3.3 Factors Influencing JEBAR Effect
 The magnitude and sign of the JEBAR term are determined by both the topographic gradient and horizontal density gradient. Figure 11 is the horizontal distribution of the density from WOA01 and simulated results integrated in the upper 500 m. Both present the same character that the density isoline is almost orthogonal to the isobaths at the east of the Dongsha Islands. This special structure is the important factor that determines the JEBAR distribution. The along-isobath density gradient interacts with the topography and generates large negative JEBAR distribution which makes the current direction turn to the deep side.
3.3.4 Momentum Balance
 Here, we present the momentum balance to identify the dynamic cause of the deflection. In order to analyze the current deflection dynamic characteristics, the coordinate has been transformed to the isobath coordinate and the momentum balance is based on the Euler equations (see Appendix A). We selected a stream line at 500 m level around the Dongsha Island (see Figure 8) to analyze the momentum balance (Figure 12).
 In both directions, the geostrophic balance dominates the continental shelf current. The along-isobath acceleration is positive during the deflection, and the ageostrophic term is the main contribution, which demonstrates the along-isobath pressure gradient is the active force that pushes the current to accelerate. From the above discussion, it can be found that the vertical integrated density gradient along the isobath at the Dongsha Island is westward, and then the along-isobath pressure gradient forcing is positive. The positive pressure gradient forcing is stronger than the Coriolis forcing and pushes the current to accelerate.
 In the cross-isobath direction, the pressure gradient forcing is positive which is consistent with the observation (Figure 1). The high pressure at the continental shelf outer maintains the eastward current. The acceleration of the current is negative, and the ageostrophic term is also dominant, in which the Coriolis forcing is the active driver.The deflection process can be described as that the along-isobath pressure gradient pushes the current to accelerate and the Coriolis forcing vertical to the isobath increases gradually, and then becomes larger than the cross-isobath pressure gradient forcing. So, the cross-isobath acceleration is negative, and then the current is pushed to deflect from the isobath toward the deep sea side, after enough time to accelerate.
3.4 Numerical Experiments
 From the above analysis, it can be seen that the topography of the Dongsha Islands plays an important role in the current deflection. In order to investigate the contribution of the Dongsha Islands topography, a simple numerical experiment has been designed.
 The forcing function is the same as the control run, but the topography around the Dongsha Islands has been changed. The changed domain has been shown in Figure 13. In order to remove the convex topography, five-point smooth has been utilized.
 The numerical experiment currents have been shown in Figure 14. It can be found that the northeastward midlevel current still exists, while the deflection disappears. This current flows along the isobath and combines with the intrusion of the Kuroshio at the southwest of Taiwan. This numerical experiment explores the important role of the topography in the deflection.
 In the NSCS, the current on the continental shelf flows along the isobath west to the Dongsha Islands, and then veers toward the deep water when flowing over the islands, deflecting from the isobath. Dynamic analysis shows that the JEBAR term is an important balance term that derives the current's departure from the isobath toward the deep water when flowing over the Dongsha Islands. We want to obtain a clear picture about the JEBAR term's contribution to the current's departure from the isobath. The linear vertical integrated vorticity equation can be written as
where is the vertical integrated velocity, and on the right-hand side the WSR is the wind stress curl and BSR term is bottom stress curl. The variation of the potential vorticity is mainly determined by the change of the water depth. For the relative vorticity is much smaller than the planetary vorticity, the variation of ξ/H is much smaller than the f/H and the relative vorticity has been omitted. Equation ((4.1)) can be rewritten as follows, after the Boussinesq approximation has been used:
 Following the discussion in section 'Dynamical Analyses', it has been found that the JEBAR is the dominant term, and then the linear vertical integrated vorticity equation can been simplified to
where is the planet potential vorticity.
 Equation ((4.3)) is a simple but useful expression of the linear vertical integrated vorticity equation to explain the JEBAR effect on the current. It is known that the current without any forcing is expected to flow along the isoline of , where ζ is the relative vorticity [Pedlosky, 1996]. In most cases, ζ is very small compared to the planet vorticity, so is a good approximation. That is to say all the terms on the right-hand side of equation ((4.2)) equal to zero, which gives the potential vorticity conservation. However, when the JEBAR terms are involved in equation ((4.2)), the current departs from the isoline of . JEBAR term can be interpreted as the bottom torque, which is simply the curl of the horizontal force exerted by the bottom on the fluid to change the stretching of the vortex tube, and also analogous as a transport-generating term in that it is a baroclinic effect of flow across contours of f/H [Mertz and Wright, 1992]. As in equation ((4.2)), JEBAR is analogous to the curl of the surface and bottom torque, and may play the same role of PV input and dissipation like the wind stress and bottom friction which are in the form of curl(τ)/H (where τ stands for the wind stress and bottom friction). So, when the wind stress and bottom friction are omitted, the JEBAR/H term serves as the PV input or dissipation term.
 The relative vorticity calculated from the model output around the Dongsha Islands is smaller than the planet vorticity by one order at least (Figure 16a, which is calculated along the streamline marked in Figure 15), and the nonlinear influence is also smaller than the geostrophic terms (Figures 10 and 11). In order to diagnose the relationship between the JEBAR/H and the variability of the planetary potential vorticity, we give Figure 16b which is also calculated along the streamline marked in Figure 15. It can be found that the equation ((4.3)) is a good approximate. Based on the above discussion that the JEBAR is the dominant term, equation ((4.3)) is a good simplified model to explain the deflection east of the Dongsha Islands. Near the Dongsha Islands, the f-plane is a good approximation for the scale of the domain is so small, and then the variation of topography is the dominant factor that controls the planet potential vorticity.
 From the distribution of the JEBAR (Figures 10 and 11), it can be found that there is negative JEBAR at the east of the Dongsha Islands; in responding to the negative JEBAR, the current must flow toward to the field where smaller occurs, under the constraint of the potential vorticity balance of equation ((4.3)). A schematic of the Dongsha Islands inter-middle current deflection mechanism has been given (Figure 17).
 From the observation in fall, it is found that the northeastward midlevel current on the NSCS continental shelf deflected from the isobath veering to the deep sea side when flowing over the Dongsha Islands. In order to investigate the dynamic mechanism, a fine resolution regional ocean model has been used. Some conclusions can be summarized as follows.
 The vorticity balance analysis based on the ocean model shows that the JEBAR term is the dominant balance term that makes the current depart from the isobaths around the Dongsha Islands. The along-isobath gradient of the density field interacts with the topography that supplies negative potential vorticity and drives the column-integrated flow away from the isobaths, veering toward the deep water.
 The momentum balance shows that the along-isobath pressure gradient forcing accelerates the current when flowing over the Dongsha Islands, and then the cross-isobath Coriolis forcing is increased (the sign is negative and the absolute value is increased). The cross-isobath Coriolis forcing becomes larger than the cross-isobath pressure gradient forcing, and then pushes the current deflected from the isobath and turned to the deep sea side.
 The along isobath density gradient at the east to the Dongsha Islands is the mainly active factor that makes the current deflect from the isobath toward the deep sea side. However, the reason how the density gradient occurs is not investigated in this paper, and maybe related to the Kuroshio intrusion. The generation of the background density fields needs further investigation.
 In order to reveal the relationship between the isobath and the velocity, the momentum equations are rewritten in the isobath-coordinate (Figure A1). The x and y directions denote the eastward and the northward directions, respectively. θ is the angle that the isobath deflects from the eastward. In the x-y coordinate, the momentum equations can be written as
where (u, v) denote the longitude and latitude velocity, and the (Fx,Fy) denote the forcing terms. The forcing terms can be written as [Wang et al., 2010]
where (a) horizontal diffusion (difh), (b) Coriolis (cor), (c) pressure gradient (pre), and (d) vertical diffusion (difv).
 In isobath-coordinate, the momentum equations can be rewritten as
 The velocity in the isobath-coordinate can also been given as
where ug is the velocity that along the isobath and vg is vertical to the isobath. To simplify the momentum equations, it can been given as
 The second term on the right side of equation ((A5)) is the joint effect of the velocity and the terrain, in this paper, it is called terrain term.
 This work is supported by National Basic Research Program of China (Grant No. 2011CB403504), Natural Science Foundation of China (Grant No. 91228202), Knowledge Innovation Project for Distinguished Young Scholar of the Chinese Academy of Sciences (Grant No. KZCX2-EW-QN203) and National Natural Science Foundation of China (Grant No. 40776009). We would like to thank two anonymous reviewers for comments that helped to improve the manuscript.