## Abstract

Observations suggest that a separation branch of the Kuroshio appears southwest of Kyushu, Japan. The observed density and surface current fields clearly show a separation branch in autumn. However, the separation branch disappears in winter and spring when the relatively homogeneous structure develops due to the intense surface cooling. A scenario generating a separation branch is examined using simple two-layer model. The northward Kuroshio along the shelf slope turns to the east abruptly, and leaves the shelf slope around Tokara Strait. A hump (local increase of the upper-layer thickness) is made by the lower-layer flow impinging on the bottom slope. This hump extends to the shallow shelf region due to the combined effect of advection and dissipation of the upper-layer thickness. Then the cross-isobath flow, that is, the separation branch, appears around the hump. When the thin upper layer obstructs the advection process in winter and spring, a separation branch disappears. Moreover, the separation branch disappears when a small damping coefficient is used.

## 1. Introduction

The northward Kuroshio current along the steep shelf edge in the East China Sea turns to the east at around 29°–30°N (see Fig. 1). Then it passes through Tokara Strait and flows along the south coast of Japan. Another stable ocean current has been observed as well, that is, the Tsushima Warm Current flowing northeastward in the Tsushima/Korea Strait. The volume transport of the Tsushima Warm Current is around 2–3 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) (Toba et al. 1982; Isobe 1994; Takikawa et al. 1999), roughly onetenth of that of the Kuroshio.

It has been believed that the Tsushima Warm Current appears as a separation branch at the location where the Kuroshio turns to the east (see A in Fig. 1; e.g., Uda 1934). However, we cannot find the northward separation branch southwest of Kyushu, Japan, in the climatological mean of the surface current field using historical GEK data (e.g., Qui and Imasato 1990). Lim (1971) and Sawara and Hanzawa (1979) also show that the water masses in the Tsushima Warm Current and the Kuroshio are fairly different. Thus the origin of the Tsushima Warm Current has remained an unresolved problem in the East China Sea.

As Lie and Cho (1994) pointed out, the GEK data in the shallow shelf region are usually contaminated by the tidal current. In order to overcome such uncertainty, Lie and Cho (1994) and Lie et al. (1998) performed satellite-traced drifter experiments west of Kyushu, and tried to find a separation branch of the Kuroshio there. They further estimated the distribution of the volume transport using the inverse method with their hydrographic data. It seems that part of their drifter trajectory shows the existence of a separation branch of the Kuroshio southwest of Kyushu. However, they released almost all drifters in the shallow shelf region, so it is difficult to conclude that a stable separation branch exists crossing the steep shelf edge.

On the other hand, Fang et al. (1991) analyzed Chinese current meter data in the East China Sea and found a continuity of the volume transport in the shelf region between Taiwan and Tsushima/Korea Straits. They concluded that the Tsushima Warm Current is not a separation branch of the Kuroshio southwest of Kyushu, but is a part of the so-called Taiwan–Tsushima Warm Current System (see B in Fig. 1). However, their result was obtained using only 138 datasets from one-day current meter moorings. Therefore more data are needed in order to confirm the existence of the Taiwan–Tsushima Warm Current System.

Recently, Isobe (1999) noted the seasonality on the origin of the Tsushima Warm Current. He used a diagnostic model with long-term observed hydrographic and wind data and found that the origin of the Tsushima Warm current is around Taiwan Strait except in autumn. However, a separation branch of the Kuroshio southwest of Kyushu was clearly identified in autumn in his model. Thus, Isobe (1999) considered that the origin of the Tsushima Warm Current changes seasonally.

In this study, we first show observational evidence on the seasonal variability of the branching of the Kuroshio southwest of Kyushu. In addition, a simple two-layer numerical model is constructed to identify the generation mechanism and seasonality of branching.

## 2. Observational evidence

### a. Hydrographic data

We first show the monthly mean of the horizontal distribution of density (*σ*_{t}) calculated using the historical temperature and salinity data within the box shown in Fig. 1. Data used here are the temperature and salinity profile dataset in CD-ROMs of the *World Ocean Atlas 1994* (Boyer and Levitus 1994). The climatological data at each ⅓° grid for each month were constructed by averaging the data at each standard depth using a Gaussian filter with an *e*-folding scale of 20 km in latitude and longitude. Tails of the weight function of the Gaussian filter lie within the area of 40 km in latitude and longitude. In order to eliminate the small-scale disturbance, grid data are smoothed by a combination of Laplacian and median filters.

Figure 2 shows the density fields at 75-m depth in January (winter), April (spring), July (summer), and October (autumn). The density is neglected in areas with depth less than 100 m since the observed data are sparse. It is found that the Kuroshio Front lies along the shelf edge (200-m isobath in Fig. 2). It turns to the east at around 30°N, and reaches Tokara Strait. In January and April, the northern edge of the Kuroshio Front southwest of Kyushu extends toward the shallow shelf region, making a hump as shown by an arrow in each panel. In July, such a hump extends farther to the north compared to those of January and April. We can see the hump extending to Tsushima/Korea Strait in October. In October, it is suggested that a separation branch of the Kuroshio crossing the shelf edge exists along the northern edge of the hump southwest of Kyushu. Thus a separation branch is considered to develop, especially in autumn as Isobe (1999) suggested. Although a separation branch can be seen in layers below 75 m, it is difficult to identify clearly in the upper layer (not shown). The frontal structure is weakened in the uppermost layer since heat flux through the sea surface makes the uppermost layer homogeneous.

### b. Surface current

Next, we show the monthly mean field of the surface current in order to examine the existence of a separation branch and its seasonality. Data used here are the historical GEK, ship drift, and acoustic Doppler current profiler (ADCP) data assembled by Japan Oceanographic Data Center (JODC). The GEK, ship drift, and ADCP data had been obtained during 1953–92, 1900–74, and 1985–92, respectively. About 38000 data are available within the box area shown in Fig. 1. Climatological data at each ⅓° grid for each month were constructed averaging the data using a Gaussian filter with an *e*-folding scale of 20 km in latitude and longitude. Tails of the weight function of the Gaussian filter lie within the area of 40 km in latitude and longitude. A three standard deviation check was performed in each grid. In order to remove contamination of the tidal current, we have averaged the data as many times as possible within each grid. The average current is estimated in each grid for each month when the available number of data in a grid exceeds 10. The averaged current is neglected in areas with depths less than 100 m since the currents are somewhat noisy due to limited number of observations there.

We emphasize the currents within a box surrounded by the broken line in Fig. 3, where the hump and branching pattern can be seen in the density fields. In January and April, current vectors in the box are heading eastward or northeastward, which suggest geostrophy associated with the Kuroshio front lying east–west as shown in Fig. 2. In July, the current direction in the box is northeastward. However, the current direction changes to the east in the northern part of the box. This is also consistent with the direction of the Kuroshio Front in July. In October, the northward or northeastward current can be seen in the box, connecting to the northeastward current in the Tsushima/Korea Strait. Such a current field is consistent with the distribution pattern of the Kuroshio Front in October. Thus, both the density and surface current fields show that a separation branch of the Kuroshio develops especially in autumn.

### c. The process in phase with the branching

Why does a separation branch develop southwest of Kyushu in autumn? Before answering this question, processes in conjunction with the development of a separation branch are noted below.

The northeast monsoon begins to cover the East China Sea in autumn. Then the wind-induced circulation develops in this area. The northeast wind is, however, more intense in winter, when a separation branch southwest of Kyushu disappears (January in Figs. 2 and 3). In addition, we can regard the density and surface current fields in July as a transient state that leads to a separation branch, when the southeast monsoon existed. Therefore it is concluded that a separation branch southwest of Kyushu is not a part of the wind-induced circulation in the East China Sea.

Figure 4 shows the vertical sections of the monthly mean density along A–A′ line in January, April, July, and October. To depict these figures, the dataset in *World Ocean Atlas 1994* is used as in Fig. 2. In January and April, the Kuroshio Front can be seen in the right-hand side of each panel. The density in the shallow shelf region is vertically homogeneous due to the intense surface cooling, so that the Kuroshio Front outcrops around the shelf edge. In July, the seasonal pycnocline develops in the shelf region, which connects to the Kuroshio Front offshore. The seasonal pycnocline deepens to 50 m in October because of the onset of surface cooling. Namely, the thickness of the upper layer increases from spring to autumn and then vanishes again in the following winter. As shown in Fig. 2, a hump southwest of Kyushu develops from spring to autumn, and a separation branch appears in autumn. Then it vanishes in the following winter. Therefore it is anticipated that the thickness of the upper layer is a critical factor in the separation southwest of Kyushu.

A simple two-layer model is constructed in order to find a mechanism generating the separation branch of the Kuroshio southwest of Kyushu. Also we examine the importance of the upper-layer thickness on the branching and its seasonality.

## 3. Model descriptions

Figure 5 shows the rectangular model ocean (600 km in *x* direction, 300 km in *y* direction) of the study and the bottom topography. The depth only varies along the *y* direction. The shelf slope is located in the lower portion of the figure. In this region, the depth changes from 500 m to 200 m. The shelf region is at the center of the domain with depth varying from 200 m to 100 m. In the upper portion of the figure, the region is flat at 100-m depths. The model ocean is divided into two active layers. In this model, the Kuroshio enters the basin from segment I–H in Fig. 5. It exits from G–F (Tokara Strait) and C–D (Tsushima/Korea Strait) segments. Inflow and outflow are permitted in both layers.

We use the same model as Salmon (1992) except that the model is on a *f* plane since our application is different in scale. The branching proceeds gradually in a year as shown previously. In such a process, we can assume that the barotropic adjustment occurs instantaneously as in the model of Sakamoto and Yamagata (1996). Thus the time derivative term is neglected in the momentum equations in order to obtain a steady-state vorticity equation of the vertically averaged flow (shown later). The time derivative term remains in the continuity equations in order to investigate the timescale to form the branching. In addition, considering the spatial scale of this problem (>100 km), small internal deformation radius (*R* < 10 km in the shelf region of the East China Sea) implies less importance of relative vorticity on the branching. This justifies that the advection of the momentum is also negligible in our two-layer model. As shown previously, the wind stress is considered to be less important on the branching. Hence, we omit it for simplicity. Furthermore, we impose hydrostatic, rigid-lid and Boussinesq approximations. The momentum and continuity equations in the upper and the lower layers are as follows:

where subscripts 1 and 2 mean the upper and lower layers, respectively; *u* and *υ* are the velocities in *x* and *y* directions; *ϕ*_{s} is the surface pressure divided by the mean density; *r* (*r* ≪ *f*) the damping coefficient in Rayleigh-type friction; and *h* is the layer thickness: otherwise the notation is standard. Parameter values used in this study are listed in Table 1.

Using the momentum equations (1), (2), (4), and (5), the velocities in the upper and lower layers can be obtained:

where *D* is the depth, *ψ* the (volume transport) streamfunction. Substituting (7) into the continuity equation (3) we obtain the advective–diffusive equation of the upper-layer thickness (*h*_{1}),

where *R*^{2} is the squared deformation radius (=*g*′*h*_{1}*h*_{2}/*Df*^{2}). Equation (8) means that three processes determine the distribution pattern of *h*_{1} in the steady state. The first is the advection due to the depth-averaged flow expressed by the second and third terms in the left-hand side of Eq. (8). The second is the dissipation process represented by the first term in the right-hand side. The third is the upwelling or downwelling represented by the last term in the right-hand side, which occurs when the flow impinges on the bottom slope. The last term of the right-hand side in Eq. (8) can be rewritten as

Note that the upwelling or downwelling occurs when the flow, the lower layer flow without its viscous part, impinges on the bottom slope.

After vertically averaging the momentum equations (1), (2), (4), and (5), we cross-differentiate them to obtain a vorticity equation in the steady state:

The first term in the left-hand side is the topographic *β* term, which expresses the vortex-tube stretching when the depth-averaged flow crosses isobaths. The second term in the left-hand side is the so-called JEBAR term, which is a correction term of the topographic *β* term to account for the fact that the lower-layer flow, not the depth-averaged flow, produces topographic vortex-tube stretching (Mertz and Wright 1992; Cane et al. 1998). In fact, the left-hand side of Eq. (10) can be rewritten as

Thus, the sum of the left-hand side of Eq. (10) represents the topographic stretching due to the lower-layer flow without its viscous part. The right-hand side of Eq. (10) is the dissipation term. This term is usually small outside the boundary layer near the wall. Therefore, the topographic *β* term should be small outside the boundary layer if Eq. (10) does not include the JEBAR term (i.e., one-layer model). In such a case, the streamfunction would be nearly along-isobath. However, the cross-isobath transport is permitted outside the boundary layer in our stratified model since topographic *β* will be reduced by the JEBAR term. In other words, the cross-isobath transport is permitted when the stratification acts as a buffer between transport and topography (Anderson and Killworth 1977). Equations (10) and (11) mean that large JEBAR permits the large amount of the cross-isobath transport. Hence the JEBAR term reduces the topographic effect because of stratification.

Equations (8) and (10) are integrated numerically in order to obtain the solution with the boundary and initial conditions described below.

The total volume transport (*ψ*_{o}) of 27.5 Sv enters through segment I–H in Fig. 5. The main part of the volume transport (25 Sv) exits segment G–F, which mimics the Kuroshio through Tokara Strait (see Fig. 1 for reference). The remainder (2.5 Sv) passes through the segment C–D, which represents the Tsushima Warm Current through the Tsushima/Korea Strait. The streamfunction is constant along other segments (i.e., I–J–A–B–C, D–E–F, and G–H), prohibiting volume transports across them. The streamfunctions along C–D and G–F segments change linearly. The boundary condition for *ψ* is

along I–H except the values at I and H.

We set a boundary condition of the upper-layer thickness along I–J–A–B–C with a constant value (*h**). We call *h** “ambient upper-layer thickness” here. In addition, the upper-layer thickness in the flat region is restored to *h** with a timescale of 100 days. This procedure is introduced to avoid the intersection of the interface with the bottom. In this model, the mean upper-layer thickness in the shelf region is adjusted by the value of *h**.

Along I–H, the upper-layer thickness (*h*_{1}) increases from *h** to *h*_{o}. The offshore pycnocline depth *h*_{o} of Kuroshio is fixed at 300 m in this study. The distribution of *h*_{1} along I–H is determined by Eqs. (12)–(16). It is assumed that the upper-layer thickness along I–H retains geostrophy with a constant velocity in the lower layer. The velocities in the lower layer are

As shown in Eq. (12), we set the constant lower-layer velocity *u*_{b} along the upstream condition of the Kuroshio, which is predetermined by *ψ* and *h*_{1} at I and H. This value varies around 40–50 cm s^{−1} in this model, depending on the value of *h**. In fact, Kaneko et al. (1990) observed the Kuroshio in the East China Sea using ADCP, and found the lower-layer velocity around 40 cm s^{−1} just above the bottom of the shelf slope (see their Fig. 10).

The upper-layer thickness along H–G is fixed to be *h*_{o}. Along the C–D–E–F–G, we impose

where **n** is the unit vector perpendicular to the segment.

The upper panel of Fig. 6 shows the initial condition of the upper-layer thickness when *h** is set to 50 m (i.e., the case of autumn). The lower panel of this figure shows the initial condition of the streamfunction, which is the steady-state solution of the one-layer model without the stratification. The streamfunction should be along the isobath with some modifications due to dissipation. In this case, an exit of the Kuroshio is located at the lower boundary so that the Kuroshio turns to the deeper area. The separation branch of the Kuroshio cannot be seen at the right-hand side of the model domain. The volume transport in the shelf region originates at the left boundary of the model domain.

Time integration of Eq. (8) is conducted using a leapfrog scheme with the Matsuno scheme done every 25 time steps. Equation (10) is solved by a simple iteration (Richardson scheme). As shown later, the solution is close to steady state after 100–200 days from the beginning of the calculation. However, time integration is continued until 1000 days in order to remove the temporal variability sufficiently.

## 4. Results

We first obtain the solution with *h** of 50 m as in autumn. Before showing the results with the boundary condition described above, another case is calculated for comparison. In this case, the volume transport of the Kuroshio flows through the right wall of the shelf slope (D–E in Fig. 5) instead of G–F. Results are shown in the upper panels of Fig. 7. As expected intuitively, the streamfunction and upper-layer thickness are distributed along the isobath except in the boundary layer near the left wall although some modifications can be seen due to the dissipation process. The distribution pattern of the streamfunction is nearly the same as that of the one-layer model (not shown). Thus the two-layer structure hardly changes the path of the current in this case.

However, the results change drastically when the Kuroshio flows out through the lower side of the shelf slope. The lower panel of Fig. 7 shows the distribution patterns of the streamfunction and the upper-layer thickness in the steady state. A hump (indicated by an arrow in the lower left panel) develops around the exit of the Kuroshio on the shelf slope. This hump extends toward the shallow shelf region along the broken line in this panel. The volume transport enters the model domain from the left boundary of the shelf slope. The main part of the volume transport turns to the lower side around the exit of the shelf slope. However, a part of the transport turns to the opposite direction, that is, toward the shelf. This distribution pattern is similar to that of the Kuroshio Front and the surface current fields in autumn. A separation branch is generated when the Kuroshio is forced to turn to the deeper area. Thus one of the critical conditions to make a separation branch is that, the Kuroshio turns to the east and leaves the shelf slope southwest of Kyushu.

## 5. Discussion

### a. Processes generating a separation branch

As shown in the lower panel of Fig. 6, a separation branch crossing the isobath never appears in the one-layer model. However, the stratification acts as a buffer to shield effect of topography and permits cross-isobath transport outside the sidewall boundary layer. Figure 8 shows the distribution of the JEBAR term, indicating the buffer ability of the stratification. The region of the large and positive JEBAR terms is located around the left-hand side of the hump. A separation branch crossing the isobath is permitted around the region with a large and positive JEBAR term since the negative vorticity acquisition due to the transport toward the shallow shelf region is reduced by the JEBAR term. Now, we consider why a hump appears around the exit in the shelf slope and why it extends to the shelf region.

As mentioned previously, the distribution pattern of the upper-layer thickness is determined through three processes: advection due to the depth-averaged flow, dissipation, and upwelling or downwelling due to the lower-layer flow impinging on the bottom slope. Figure 9 shows these contributions along a hump in the shelf region in the steady state. Since the impinging term is negative, this term does not increase the upper-layer thickness in the shelf region. On the other hand, dissipation and advection terms are positive, which maintain the hump in the shelf region. Next, we show the temporal variation of each term from the initial state in order to explain how the hump develops on the shelf slope, and how a hump extends to the shelf region through the dissipation and advection processes.

Figure 10 shows the temporal variation of the upper-layer thickness (*h*_{1}), streamfunction (*ψ*), and three terms of Eq. (8) in the shelf slope until 300 days from the beginning of the calculation. Although contours of *h*_{1} and *ψ* change slightly after 100 days, they are close to a steady state. It is found that the upper-layer thickness increases in the right-hand side of the line along the shelf slope, making a hump around the exit. The advection term is a negative contribution, while the impinging term deepens the upper layer. Since the dissipation term is small compared to other two terms, its contribution is negligible. Thus the impinging term makes a hump in the shelf slope, which is induced by the lower-layer flow impinging on the bottom slope around the exit. A positive impinging term means the existence of the lower-layer flow heading toward the deep area.

Figure 11 shows the same variation as Fig. 10 except the line is along an isobath in the shelf region. The upper-layer thickness increases on the right-hand side of the shelf region until 100 days from the beginning of the calculation. In the early stage (0–40 days), the dissipation process contributes to increasing the upper-layer thickness. The large contribution especially in the right-hand side is due to the dissipation of a hump around the exit in the shelf slope. The increase of the upper-layer thickness on the right-hand side of the shelf region permits cross-isobath transport. This is because the JEBAR term becomes large as the horizontal gradient of the upper-layer thickness increases in *x* direction. Therefore the volume transport toward the shallow shelf region gradually develops (see the streamfunction in the early stage). This transport carries “warm” water to the shelf region, which also contributes to increasing the upper-layer thickness and to extending a hump toward the shallow shelf region. In fact, around 80 days, the major positive contribution term is changed to advection instead of dissipation. Then the increase of the upper-layer thickness on the right-hand side of the shelf region further induces a large cross-isobath transport (see the streamfunction after 80 days).

Thus a separation branch is generated around an extended hump in the shelf region, induced by the combination of the dissipation and the advection processes of the upper-layer thickness.

It is found that a hump extends toward the upper left in the shelf region (see the broken line in Fig. 7). We can understand this reason through Eq. (8) rewritten as follows:

Note the characteristic velocities of *h*_{1} shown in the bracket of the second and third terms in the left-hand side. The characteristic velocities are determined by the depth-averaged flow and the velocity along the isobath with the shallow water on the right-hand side. Therefore the upper-layer thickness is carried to the upper left in the shelf region as shown in Fig. 12 schematically.

### b. Response to the ambient upper-layer thickness in the shelf region

As shown in the observed density and surface current fields, it is difficult to detect a separation branch southwest of Kyushu in winter and spring. The reason for such seasonality is considered in this section.

We change the mean upper-layer thickness in the shelf region since its seasonal variation is in phase with the branching. The ambient upper-layer thickness is set to be 0 m in order to accomplish the thin upper layer in the shelf region as in winter and spring. The results in the steady state are shown in Fig. 13. We can see that the mean upper-layer thickness decreases compared to the result in Fig. 7. Although a hump appears in the shelf slope around the exit, it does not extend to the shelf region. A separation branch is difficult to identify in this case as in the real ocean in winter and spring.

In this case, the dissipation process ought to retain its ability to extend a hump from the shelf slope to the shelf region. This is because the damping coefficient is the same as in the case of Fig. 7 and because horizontal gradient of the upper-layer thickness in *y* direction increases compared to the case of Fig. 7. As mentioned previously, the extension of a hump is due to the combination of dissipation and advection processes. Therefore, it is considered that the advection process becomes weak in this case.

Figure 14 shows the temporal variation of the difference of the upper-layer thickness and the JEBAR term averaged along the line A–B. Both cases with thick (*h** = 50 m) and thin (*h** = 0 m) ambient upper-layer thickness are plotted in the same figure. The difference of the upper-layer thickness in the case with a thin upper layer is larger than that of the thick upper-layer case until 150 days. Thereafter the difference is reversed in sign. However, the JEBAR term in the case of the thin upper layer is always small compared to that of thick upper layer. This is because the JEBAR term is not proportional to the horizontal gradient of the upper-layer thickness, but the gradient of upper-layer thickness squared. Therefore the JEBAR term cannot be large when the upper layer is thin. Cross-isobath transport toward the shelf region cannot develop when the JEBAR term is small. Therefore an extended hump and its related separation branch never appear southwest of Kyushu when the upper layer is thin in winter and spring.

The transition to the branching pattern is a time-dependent problem in the real ocean, while the present study obtains steady-state solutions in order to interpret the branching mechanism. However, as we can see in the lower panels of Fig. 11, the main processes forming the branching are completed within 100 days from the beginning of the calculation. Therefore it is anticipated that a transition to the branching pattern occurs within the timescale from summer to the end of autumn. Needless to say, a time-dependent experiment should be done in order to understand the branching process more clearly. Using another model, we will investigate this problem in the near future.

### c. Response to the damping coefficient

A hump and a separation branch develop through the combination of the dissipation and the advection processes of the upper-layer thickness. In the previous subsection, the dependency of the latter process on the result was examined. In this subsection, we show the dependency of the former process.

The calculation is performed with the same condition and parameters (as in the lower panels of Fig. 7) except that the damping coefficient is changed from 0.4 × 10^{−6} s^{−1} to 2.4 × 10^{−6} s^{−1} with the interval of 0.4 × 10^{−6} s^{−1}. The contours of the volume transport of 2 Sv are shown in Fig. 15. It is found that the location of the separation moves to the left as we use the smaller damping coefficient. Namely, the result approaches that of the one-layer model (see the lower panel of Fig. 6) when the dissipation process is weak. Therefore a large damping coefficient is needed in order to produce a separation branch.

Figure 16 shows the divergence of the viscous part of the lower-layer velocity in the case of the lower panel of Fig. 7. It is found that the upwelling (downwelling) appears inside (outside) a hump. We can interpret that a hump, that is, a depression of the interface, extends into surrounding area due to the divergence of the viscous part of the lower-layer velocity although the present model expresses this process as the “diffusion” of the upper-layer thickness &lsqb≃e the first term in the right-hand side of Eq. (8)]. This implies that the Ekman suction velocity just above the bottom Ekman layer is required in the real ocean in order to extend the hump effectively onto the shelf.

## 6. Conclusions

The observed density and surface current fields clearly show a separation branch of the Kuroshio southwest of Kyushu in autumn. However, the separation branch disappears in winter and spring when a relatively homogeneous density structure develops with a thin upper layer. This is consistent with the results of Isobe (1999) who suggested that the Tsushima Warm Current is a part of the Taiwan–Tsushima Warm Current System except in autumn.

A scenario generating a separation branch in autumn is summarized below. The Kuroshio flowing along the shelf slope turns to the east abruptly and leaves the shelf slope around Tokara Strait. Then a hump is made by the lower-layer flow impinging on the bottom slope, which is expressed by the second term of the right-hand side of Eq. (8). The lower-layer flow in the same direction of the Kuroshio is needed in order to make a hump there. A hump in the shelf slope extends to the shallow shelf region due to the dissipation, which reduces the topographic *β* through the JEBAR term. The cross-isobath transport develops gradually around the hump extending to the shelf region. The cross-isobath transport also excites the hump through the advection of “warm” water from the deep shelf slope. The developed hump permits larger amounts of the cross-isobath transport toward the shelf region, and a separation branch is formed.

Thus the combination of dissipation and advection processes of the upper-layer thickness develops a hump and its related separation branch. When the thin upper layer obstructs the advection process in winter and spring, a separation branch disappears. Moreover a separation branch disappears when the dissipation process is weak using the small damping coefficient. Therefore, when modeling the separation of the Tsushima Warm Current from the Kuroshio southwest of Kyushu, a deep pycnocline in the shelf region is needed mimicking autumn condition. A short timescale of damping in the shallow shelf region is also needed to induce branching.

## Acknowledgments

The author expresses his sincere thanks to Prof. T. Yanagi and Mr. R. S. Balotro, Kyushu University for their critical reading of the manuscript. Thanks are also extended to the journal reviewers for useful suggestions on improving the manuscript. Data of the surface current were obtained through JODC Data Online Service System (J-DOSS) on their Web site.

## REFERENCES

## Footnotes

*Corresponding author address:* Dr. Atsuhiko Isobe, Department of Earth System Science and Technology, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1, Kasuga-Koen, Kasuga, 816-8580, Japan.