A numerical experiment on the path dynamics of the Kuroshio with reference to the formation of the large meander path south of Japan

Deep-SeaResearch,Vol. 37, No. 3, pp. 359-380, 1990

0198-0149i90 $3.00 + 0.00 ~) 1990 Pergamon Press plc

Printed in Great Britain.

A numerical e x p e r i m e n t on the p a t h d y n a m i c s o f the K u r o s h i o with

reference to the formation of the large meander path south of Japan YOSHIHIKO SEKINE*

(Received 18 December 1986; in revisedform 30 July 1989; accepted 8 September 1989) Abstract--Path dynamics of the Kuroshio south of Japan are investigated with reference to the formation of the large meander of the Kuroshio south of Japan. The observed formation process is a composite of two subprocesses: generation of a small meander off eastern Kyushu (process I) and amplification of the small meander south of central Japan (process II). Particularly, we have focused upon the observed evidence that the amplification of the small meander (process I) has a tendency to occur in a fiat part of the Shikoku Basin, while a small meander staying on the continental slope decays in a short time without process II. On the basis of this evidence, a numerical experiment on the formation process of the large meander of the Karoshio is carried out. A two-layer model is assumed and a realistic bottom topography south of Japan is modeled. In the numerical experiments, 10 runs with different inand outflow transport, initial current path and/or bottom topography are performed. It is shown that if the inflow volume transport is less than 60 Sv, the current path is forced to flow along the coastal boundary due to the topography of the continental slope and the planetary ~ effect. Even if a small meander is given in the initial current path with inflow of 30 Sv, the small meander decays in a short time and the current path resumes a no-meander path. However, in the model with inflow greater than 60 Sv, the large meander path is formed. If a small meander path is given initially in the same model, a larger meander and a cyclonic eddy are formed with spin-up and spin-down processes; the results agree with the observational features of the cyclonic cold water mass south of Japan. The amplification of the large meander is carried out in a fiat region. The spin-up of the large meander path and cold water mass is mainly due to the stretching of the water column when the meander shifts westward from the shallower west side slope of the lzu Ridge to the deeper region in the Shikoku Basin. If the topography of the Izu Ridge is excluded in the numerical model, the large meander is not formed. The bimodal path characteristics of the Kuroshio are discussed on the basis of the numerical results.

INTRODUCTION

IT has been widely accepted that the Kuroshio takes one of two stable paths south of Japan (e.g. STOMMELand YOSmDA, 1972; NrrAm, 1975; NISHIDA, 1982; IsHn et al., 1983). One path is rather straight and is referred to as the no-meander path. Another path exhibits a large meander south of Japan and is referred to as the large meander path (Fig. 1). KAWAaE (1985) showed by analysis of sea level variations at the southern coast of Japan and Izu Islands that the Kuroshio takes a large meander path about 40% of the time, and a no-meander path is further divided into two types by offshore distance over the Izu Ridge. In periods of a large meander path, a large cold water mass is formed on the coastal side of the main current axis. SEKIm~ et al. (1985) found that the cold water mass repeats spin-down and spin-up in response to the seasonal variation of the Kuroshio. * Institute of Oceanography, Faculty of Bioresources, Mie University, 1515, Kamihamacho, Tsu, Mie, 514 Japan. 359

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So far, many theoretical studies on the bimodal path characteristics of the Kuroshio have been carried out (e.g. ROBINSON and TAFr, 1972; WHITE and MCCREARY, 1976; CHAOand MCCREARY,1982). In these studies, because the large meander of the Kuoshio is considered essentially as a Rossby wave in the zonal mean flow, the Kuroshio takes the large meander path when the velocity and/or volume transport of the Kuoshio is relatively small. However, some theoretical studies show a remarkable multi-equilibrium state between the no-meander and large meander paths (e.g. MASUDA, 1982; CHAO, 1984; YASUDA et al., 1985; YAMAGATA and UMATANI, 1989). Recently, YooN and YASUDA (1987) and SEKINE (1988) have demonstrated by numerical experiments that if t h e deviation of the coastline south of Japan from the west-east direction is considered, the large meander path is formed when the volume transport is relatively large. Because we have no long-term observational Kuroshio current velocity data due to the lack of direct current measurements, the results of these theoretical studies cannot be checked against observational data. Most of the historical data of the current velocity and volume transport depend on geostrophic calculations or GEK data. Some problems in the geostrophic calculation of the Kuroshio south of Japan were pointed out by Isrm et al. (1983) with reference to the assumption of level of no motion. MmAMI et al. (1978, 1979) pointed out that historical meridional geostrophic flow estimation across the large meander path south of Japan under-estimates the Kuroshio transport due to neglect of the meridional velocity component and to the short observational line not covering the southern part of the Kuroshio flow. The formation of the:large Kuroshio meander is studied in the present paper. The observational formation process of the large meander path is divided into two subprocesses; process I is generation of a small meander off the eastern coast of Kyushu and process II is an abrupt amplification of the small meander into a large meander south of central Japan (SErdrCE, 1989). Schematic representation of processes I and II are shown in Fig. 2. Although process I occurs every winter or early spring, most of the small meanders decay without process II. SEKINEand TOBA (1981a) pointed out that an abrupt increase in GEK velocity is commonly observed prior to or during the occurrence of process I. Furthermore, SEKINE and TOBA (1981b) showed by a numerical experiment that the nonlinear effect due to the abrupt increase in current velocity advects the current path offshore and causes the separation of the path from the coast. In particular, the formation of the cyclonic Tanegashima Cold Water (Fig. 2a) is explained by stretching of the water column when it is advected deeper offshore. For process II, SEKINE (1989) demonstrated that the amplification of the small meander has a tendency to take place over a flat area in the northern part of the Shikoku Basin, near the Izu Ridge, while small meanders staying on the continental slope off Kyushu are stable and decay in a short time without the occurrence of process II. The dynamics behind process II were partly investigated by use of a very simple model (SEKIm~, 1989), and the effect of the topography of the continental slope on the time evolution of the small meander has been suggested to be important. However, since SEKINE (1989) used a very simple model, a more realistic condition of the formation process is needed to draw a firm conclusion on this problem. Therefore, the formation process of the large meander of the Kuroshio is studied by use of a numerical model with realistic bottom topography.

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MODEL

FORMULATION

Figure 3 shows a bathymetric chart of the region south of Japan and three cases of bottom topography employed in the present study. The system is driven by in- and outflow through the boundary. The inflow is given at the western boundary corresponding to Tokara Strait where the Kuroshio flows into Shikoku Basin, and the outflow is placed on the eastern side of the Izu Ridge (Fig. 1). As is shown in Fig. 3, the main topographic features south of Japan are considered in model I, while only the bottom topography of Izu Ridge is excluded in II and a flat bottom is assumed in III. The latter two models are used to see the effect of the Izu Ridge and other topography. A two-layer model is assumed (Fig. 4). The quasi-geostrophic approximation is not assumed in the present model because of the remarkable spatial change in upper layer thickness due to the large thermocline gradient in the Kuroshio south of Japan. A Cartesian coordinate system on a 13-plane is used as shown in Fig. 3. Since the direction of the deviation of the coastline from the west--east direction plays an important role in the bimodal path dynamics of the Kuroshio (YooN and YASUDA, 1987; SEKIr~, 1988), the basic coordinate system (x,y) of the rectangular model is rotated 30° counterclockwise. The vertically integrated equations appropriate for a two-layer Boussinesc fluid in hydrostatic balance are

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time velocity toward x-axis velocity toward y-axis layer thickness interface deviation positive downward from average interface depth total model ocean depth average upper layer thickness surface deviation from average surface level Coriolis parameter linear change rate of the Coriolis parameter along x-axis linear change rate of the Corinlis parameter along y-axis acceleration due to gravity reduced gravity g* ffi (Ap/p)g upper layer density density difference between layers horizontal eddy viscosity coefficient maximum in- and outflow velocities width of the in- and outflow quantifies in the upper and lower layers, respectively

(11)

366

Y. SEKINE

and the shear equation for the baroclinic mode: OSu Ot.

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A viscous boundary condition was imposed at the western and northern boundaries. The model parameters are tabulated in Table 2. Equations (11)-(17) are solved numerically with a square grid resolution of 18 km. This grid resolution is smaller than the scale of internal radius of deformation of the system about 40 kin. The space difference scheme is similar to that proposed by Lna:L (1965) for the vorticity equation and the generalized Arakawa scheme (A~I~WA, 1966) for the shear equation. The latter scheme conserves kinetic energy, averaged vorticity and enstrophy (e.g. Gm~tMEL~¢EDT, 1968). A leap frog scheme was basically used in the finite form for the local time change term and an Euler backward scheme (MATStmO, 1966) was employed at every 20th time step to suppress:the growth of the computational modes. The runs with different initial condition and/or the bottom topography were performed (Table 3). In the first phase, the nonlinear effect due to the intensity of the current velocity on the formation of the large meander path is examined by runs 1-6, in which only the volume transport of the in- and outflow is varied from 20 to 70 Sv (Table 3). Although it is very interesting to see the time change in the volume transport (CrlAO, 1984; YASUDAet al., 1985), the stational inflow was given in all runs. This is because the time change of the interface at the boundary yields remarkable artificial boundary influence on the numerical solution. The inflow was given in the upper layer and no inTable 2. Basicmodel constants Reduced gravity Coriolis parameter

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367

Path dynamics of the Kuroshio

Table 3. Parameters and model conditions for the experiments Run no.

Volume transport of in- and outflow (Sv)

Maximum velocity of inflow, Uo (cm s-1)

Initial current path

Bottom topography

1 2 3 4 5 6 7 8 9 10

20 30 40 50 60 70 30 60 60 60

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No meander (Fig. 5a) No meander No meander No meander No meander No meander Small meander (Fig. 5b) Small meander No meander No meander

Realistic (Fig. 3b,I) Realistic Realistic Realistic Realistic Realistic Realistic Realistic No ridge (Fig. 3b,II) Flat (Fig. 3b,III)

and outflow was assumed for all runs listed in Table 3. The initial flow in the upper layer had a sinusoidal horizontal distribution of current and the following boundary conditions were imposed along the in- and outflow boundaries:

(u2, v2) -- (0, 0),

(19)

where L (= 108 kin) is the width of inflow and Uo is the maximum velocity at the center of the inflow. Here, u0 for each run is listed in Table 3, which is a function of the total inflow transport. In runs 1-6, the initial condition shown in Fig. 5a was employed, giving a coastal flow with no meander. In the second phase of the numerical experiment, the effect of difference in the initial current path was investigated by runs 7 and 8. The initial current path of these two runs shown in Fig. 5b has a small meander instead of the coastal flow shown in Fig. 5a. Because of the mechanism of process I, the abrupt increase in upper layer velocity is not employed in the numerical model (cf. SEgn,r~ and TOBA, 1981a,b) and a clear small meander with a clear cyclonic eddy corresponding to the Tanegashima Cold Water (Fig. 2a) is not formed in the numerical model. Therefore, to include process I, the cyclonic eddy was given as an initial condition of these runs. These two runs have different boundary inflow: 30 Sv for run 7 and 60 Sv for run 8 (Table 3). In the third phase, the topographic effects of the continental slope and the Izu Ridge were examined by use of two models with different bottom topography: runs 9 and 10 have bottom topographies shown in Fig. 3(II) and (III), respectively. To see the topographic effect of the Izu Ridge, the bottom topography of run 9 lacks the Izu Ridge. Results of run 9 are compared with those of run 5, of which other all model characteristics are the same as in run 9. A flat bottom with a depth of 4300 m was assumed in run 10, having depth equal to the average depth of the Shikoku Basin. NUMERICAL RESULTS

The effect of current intensity (runs 1-6) The results of runs 1 and 2 with relatively small inflow are shown in Fig. 6a and b, respectively. For both runs, the initial current paths are stable and they continue to flow

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Path dynamics of the Kuroshio

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371

Path dynamics of the Kuroshio

along the northern boundary. There is no apparent difference between the two runs and no meander path is formed in either case. The results of runs 3 and 4 (Fig. 7) are similar to those of runs 1 and 2, and a large meander path is not generated. However, an anticyclonic eddy is formed on the offshore side of the main current axis; the anticyclonic eddy is larger in run 4. A weak separation of the pycnocline from the northern boundary is detected from the distribution of the upper layer thickness of run 4. The velocity fields show that lower layer flow has a tendency to flow along depth isopleths as a manifestation of the bottom intensified mode (e.g. RrnNES, 1970; SUOn~O~L~RA,1981). This tendency is weak in the upper layer owing to the predominance of the surface mode. The vorticity balance for runs 2 and 4 at day 100 (Fig. 8) shows that the main vorticity balance over the bottom slope is between the divergence and coupling term, which Divergence

Friction

Tote I, change

Beta term

F"

Advection

loj,,

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"=1 (a)

Divergence

Friction

TotoL change

Beta term

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(b) Fig. 8. Spatial distribution of important term contributions at day 100 in the vorticity equation (11). (a) R u n 1, (b) run 4. The contour interval is 5 x 10-12 s- 2 and the regions less than-5 x 10-12 s-2 are stippled.

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indicates the barotropic and baroclinic adjustment of the flow to the effect of the bottom topography. However, Fig. 8 shows that two topographic terms balance each other, and the total time change in the relative vorticity is small. Under this vorticity balance, the current path is forced to flow along depth isopleths without apparent change in the relative vorticity. Because the current must cross geostrophic contours (f/D), approximated depth isopleths, to make a meander path (Fig. 1), the two-term balance suppresses meander formation. Figure 8 also shows that the friction term is prominent in the narrow region along the northern boundary. This is due to the large lateral shear in this area owing to the viscous boundary condition. The advection term is important along the main current axis. It is concluded from these runs that if the in- and outflow is relatively small (< 50 Sv), only the no-meander path is formed due to the dominant topographic effect of the continental slope. In both runs 5 and 6 (Fig. 9) a small meander appears in the inflow region off Kyushu. The small meander develops gradually and an anticyclonic eddy is formed east of it. The difference between runs 5 and 6 is in the time evolution of the anticyclonic eddy: in run 5, the anticyclonic eddy stays east of the small meander path. But, in run 6, the anticyclonic

200 Days

(a)

Fig. 9a.

200 Days

373

Path dynamics of the Kuroshio

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S"

200 Days (b) Fig. 9.

Same as for Fig. 6 but for (a) run 5 and (b) run 6. Volume transport contour intervals are

10 Sv. eddy shifts eastward and arrives at the western side of the Izu Ridge. During 100-200 days, a weak cyclonic eddy appears west of the Izu Ridge and moves southwestward. In this process, because the cyclonic eddy shifts to a deeper region, it develops by stretching of the water column and a large meander of the current path is formed. The large meander path shows no apparent time variation in the following time stage (Fig. 9b). The velocity fields of run 6 show a large gentle meander in the upper layer and a cyclonic circulation in the lower layer. These flow patterns are similar to those of the observed large meander of the Kuroshio south of Japan (e.g. NISHIDA, 1982; IsI-m et al., 1983). Formation of the large meander path results in run 6. Conversely, in run 5 a small meander off Kyushu is formed, but it does not develop into a large meander. These results show that even if a small meander off Kyushu is formed it cannot evolve into the large meander path if the volume transport is relatively small, less than 60 Sv. The term balance of runs 5 and 6 is compared in Fig. 10. In run 5, good vorticity balance is achieved among divergence, coupling and advection terms and the time change is relatively small. In contrast, in run 6 the two topographic terms balance each other and a relatively large time change is generated by the advection term. Therefore, the formation of the large meander path in run 6 is associated with large time change due

374

Y. Serar~ Divergence

Friction

Total change

Beto term

CoupLing

Advection

to) Divergence

Friction

Total change

(b)

Fig. 10. Same as for Fig. 8 but for (a) run 5 and (b) run 6. Contour intervals are 10 times larger than in Fig. 8.

to advection, while the balance among the two topographic and advection terms yields no development of the small meander off Kyushu. It is thus concluded by these experiments that large volume transport of the inflow is needed for the formation of the large meander path. This conclusion agrees with the observational evidence that the maximum surface velocity is suggested by the sea level difference across Tokara Strait and horizontal temperature gradient south of Japan (SEIcn~, 1989).

The effect of a small initial meander path (runs 7 and 8) The results of runs 7 and 8 with a small meander path in the initial condition are shown in Fig. 11. In run 7, the initial small meander off Kyushu decays in a short time and the current resumes the no-meander path along the coastal boundary. The total flow pattern of run 7 is similar to that of run 2, with the same inflow of 30 Sv. This shows that if the volume transport is relatively small, the small meander path cannot evolve into the large meander as in run 2 without a small meander in the initial condition. In run 8, an initial small meander decays in a short time but a large anticyclonic circulation is formed to its east. When the eastern part of the anticyclonic circulation

375

Path dynamics of the Kuroshio

/

Upper loyer

~

IOOcm s -j 200 Days

~

/ V

Lower loy¢l" ~50cm s "l 200 Doys

(a)

200 Ooys

200 Ooys

(b)

Fig. 11. Same as for Fig. 6 hut for (a) m n 7 and (b) run 8. Volume transport contour intervals are 5 Sv in (a) and I0 Sv in (b).

376

Y. S~rar,m

Fig. 12.

Sequential patterns of volume transport of run 8. Contour interval is 10 Sv.

shifts westward, a large meander path with a cycloniceddy on its coastal side is formed. After thisperiod, the cycloniceddy and the large meander path repeat spin-down and spin-up. Figure 12 shows one cycle of spin-down and spin-up of the large meander path. The large meander path of the Kuroshio begins to diminish from 400 days and the cold eddy is cut-offat 440 days. The inflowpatterns of thisperiod are similarto the observed cut-offof the cold water mass of the Kuroshio in 1977 (KAMImRA et al., 1979). Figure 12 shows that aftercut-offof the cold water mass, the large meander path is not clear for several days but it reappears at about 500 days and redevelops gradually. The flow patterns at day 540 resemble those of day 340 displayed above, completing one cycle of spin-down and spin-up.The cycle period is about 200 days. These variationsare similar to the observed feature revealed by SFICn,~ et al. (1985): the observed large meander of the Kuroshio repeats spin-up and spin-down; during spin-up a large meander with expanded cold water mass is observed, while a diminished cold water mass is observed during spin-down. If we compare the result of run 8 to that of run 5 with the same model characteristics but for no small meander path in the initial condition (Table 3), it is suggested that a small initial meander path is needed to develop a large meander path. This agrees with the observational evidence that a small meander with a cyclonic eddy called the Tanegashima Cold Water is commonly observed prior to formation of the large meander path (Fig. 2a). On the whole, the results of run 8 successfully simulate the observational features of the large meander of the Kuroshio south of Japan.

Topographic effects of the Izu Ridge and continental slope (runs 9 and 10) The topography of the Izu Ridge is excluded in run 9 and a fiat bottom is employed in run 10 (Fig. 13). Figure 13a shows that the coastal flow is well maintained, and the flow

Path dynamicsof the Kuroshio

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pattern is similar to that of run 5 with the same in- and outflow, but different from runs 6 and 8 mentioned above. From these experiments, it is suggested that the topographic effect of the Izu Ridge is necessary for the formation of the large meander path and for a small meander given as an initial condition to grow into a large meander. That is, the Izu Ridge is necessary to make a cyclonic eddy by its stretching effect shown in run 6 and for

378

Y. SEKl~re

Divergence

Friction

eta term

Coupting

Fig. 14.

Total change

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Same as for Fig. 8 but for day 25 of run 10.

the small meander to generate a larger anticyclonic circulation that generates a large meander path by its westward shift (runs 6 and 8). The result of run 10 is quite different from those of all previous runs (Fig. 13b). The current path is unstable and an unstationary large meander path is formed. The vorticity balance of this run is shown in Fig. 14. Because a flat bottom is assumed in this model, the two topographic terms disappear. The predominance of the advection term with weak modification of the planetary I~term controls the total vorticity balance, resulting in a large vorticity change. Because the friction is relatively small, the basic flow has a barotropic and baroclinic instability (P~DLOSKV, 1979). The results of run 10 explain the observational evidence that amplification of a small meander path, process II, is carried out over a flat region in the Shikoku Basin. CONCLUSION AND DISCUSSION

On the basis of the observational evidence of the formation process of the large meander of the Kuroshio (SEr,n~E, 1989), a numerical experiment has been carried out. The main results are summarized as follows: (1) The large meander path is not formed if the volume transport is less than 60 Sv. This is due to the dominant topographic effect of the continental slope, which stabilizes the current path and forces it to flow along depth isopleths. (2) The large meander path is formed ff the volume transport exceeds 60 Sv. Before the formation of the large meander path, a small meander path with a cyclonic eddy appears when the anticyclonic eddy shifts westward from the western side slope of the Izu Ridge. This is due to the stretching of the water column by its shift to a deeper region. If the Izu Ridge is excluded from the model ocean, the large meander is not formed. (3) A flat area is needed to form a large meander path. If a flat bottom model is assumed, a barotropic and baroclinic instability of the current path occurs and a prominent meander of the current path is generated. This agrees with the observational evidence that amplification of a small meander is commonly observed in a flat region in

Path dynamics of ~.heKuroshio

379

the Shikoku Basin, while a small m e a n d e r staying on the continental slope decays in a short time without further amplification. (4) The existence of a small m e a n d e r in the initial position is necessary for f o r m a t i o n of a large meander path. If the coastal path is given in the initial condition, f o r m a t i o n of the large meander path is suppressed. This result agrees with the observational evidence that a small meander with a cyclonic eddy, the T a n e g a s h i m a Cold Water, is c o m m o n l y observed prior to formation of the large m e a n d e r of the Kuroshio south of Japan. (5) Finally, in the formation process of the large m e a n d e r path, volume t r a n s p o r t greater than 60 Sv is needed to advect a current path to offshore regions and to separate it from the continental slope. This result contradicts the theory that the large m e a n d e r of the Kuroshio appears when the v o l u m e transport is relatively small, in which the large meander is considered as the planetary Rossby wave in a m e a n flow. T h e cause of the contradiction is the neglect of the topographic effect of the continental slope in the latter case. Most of the models of the Kuroshio path so far p r o p o s e d have assumed a flat bottom, which is similar to run 10 in the present study. Although the p a t h characteristics in run 10 are similar to those of YOON and YASUDA (1987) and SErm~ (1988), it is pointed out from the present study that the effect of the continental slope should be included in the discussion of the bimodal p a t h characteristics of the Kuroshio.

Acknowledgements---I would like to thank Profs Y. Toba of Tohoku University, K. Takano of Tsukuba University, Y. Nagata and N. Suginohara of University of Tokyo and Drs H. Nishida of Maritime Safety Agency of Japan, A. Masuda and T. Yamagata of Kyushu University, J. H. Yoon and M. Fukasawa of University of Tokyo for helpful comments and discussions during the course of this work. Thanks are extended to Dr H. Solomon for valuable comments and careful correction of the manuscript. REFERENCES AP.~r,AWA A. (1966) Computational design for long-term numerical integration of the equation of fluid motion: two dimensional imcompressible flow. Part I. Journal of Computational Physics, l, 119-143. CHAOS.-Y. (1984) Bimodality of the Kuroshio. Journal of Physical Oceanography, 14, 92-103. CHAOS.-Y. and J. P. MCCRF~RY(1982) A numerical study of the Kuroshio south of Japan. Journal of Physical Oceanography, 12, 680-693. GRAMMELTVEDTA. (1968) A survey of finite difference schemes for the primitive equations for a barotropic fluid. Monthly WeatherReview, 97, 384-404. Isml H., Y. SEKINEand Y. TOBA(1983) Hydrographic structure of the Kuroshio large-cold water mass region down to the deeper layers of the ocean. Journal of the Oceanographical Society of Japan, 29, 240-2.50. KAMmI~ E., H. M ~ , H. ISmZAKIand J. NIsmzAwA(1978) The cut-off phenomenon of the large cold water mass off Tokaido. Bulletin of Kobe Marine Observatory, 195, 1-15. IC~WABEM. (1985) Sea level variation at the Izu Island and the typical stable path of the Kuroshio. Journal of the OceanographicalSociety of Japan, 41, 307-326. LILLY D. K. (1965) On the computation stability of the numerical solution of time-dependent nonlinear geophysical fluid dynamics problem. Monthly Weather Review, 93, 11-26. MASUDAA. (1982) An interpretation of the bimodal character of the stable Kuroshio path. Deep-Sea Research, 29, 471--484. MATSUNOT. (1966) Numerical integration of the primitive equation by a simulated backward difference method. Journal of the Meteorological Society of Japan, 44, 76--84. MINAMIH., E. KAMmIRA,H. EOUCHIand J. NlSmZAWA(1978) Statistical feature of the oceanographic condition south of Honshu, Japan (Part 1; summer and winter off Kii Peninsula). Umi to Sofa, 53, 147-156 (in Japanese). MINAM1H., E. KAMmmA, K. KOMURA, H. EGUCHIand J. NISI-HZAWA(1979) Statistical feature of the oceanographic condition south of Honshu, Japan (Part 2; spring and autumn off Kii Peninsula). Bulletin of Kobe Marine Observatory, 197, 1-11 (in Japanese). NISHIDAH. (1982) Description of the Kuroshio meander in 1975-1980---large meander of the Kuroshio in 1975--1980(I). Report of Hydrographic Researches, 17, 181-207. NrrANI(1975) Variation of the Kuroshio south of Japan. Journal of the Oceanographical Society of Japan, 31, 154-173.

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PEDLOSKYJ. (1979) Geophysicalfluid dynamics. Springer Verlag, New York, 624 pp. RI-IINESP. (1970) Edge-, bottom and Rossby wave in a stratified fluid. GeophysicalFluidDynamics, 1,273-302. ROnINSONA. R. and B. TAFr (1972) A numerical experiment for the path of the Kuroshio. Journal of Marine Research, 30, 65-101. SEIO~ Y. (1988) Coastal and bottom topographic effects on the path dynamics of the western boundary current with special reference to the Kuroshio south of Japan. La Mer, 26, 99-114. SEltm'EY. (1989) Formation process of the large meander of the Kuroshio south of Japan. Deep-Sea Research, submitted. SEKI~ Y. and Y. TOBA(1981a) Velocity variation of the Kuroshio during formation of the small meander south of Kyushu. Journal of the Oceanographical Society of Japan, 37, 87-93. SEKI~ Y. and Y. TOBA(1981b) A numerical study on the generation of the small meander path of the Kuroshio off southern Kyushu. Journal of the OceanographicalSociety of Japan, 37, 234-242. SEKIt~ Y., H. ISHnand Y. TOnA(1985) Spin-up and spin-down processes of the large cold water mass of the Kuroshio south of Japan. Journal of the OceanographicalSociety of Japan, 41,207-212. STOM~IELH. and K. YOSI~A (1972) Kuroshio--ltsphysicalaspects. University of Tokyo Press, Tokyo, 517 pp. SUGINOHARAN. (1981) Quasi-geostrophic waves in a stratified ocean with bottom topography. Journal of Physical Oceanography, 11, 107-115. TAFT B. A. (1972) Characteristics of the flow of the Kuroshio south of Japan. In: Kuroshio--lts physical aspects, H. STOMMELand K. YOSmDA,editors, University of Tokyo Press, Tokyo, pp. 165-214. TAFr B. A. (1978) Structure of the Kuroshio south of Japan. Journal of Marine Research, 36, 78-117. TERAMOTO T. (1974) Meander of currents. In: Physical oceanography, Vol. 1, T. TERAMOTO, editor, University of Tokyo Press, Tokyo, pp. 161-207 (in Japanese). WHITEW. B. and J. P. McC'REARY(1976) The Kuroshio meander and its relationship to the large.scale ocean circulation. Deep-SeaResearch, 7,3, 33--47. YAMAGATAT. and S. UMATAm(1989) Geometry-forced coherent structure as a model of the Kuroshio large meander. Journal of Physical Oceanography, 19, 130-138. YASUDA I., J. H. YOONand N. SUGINOHARA(1985) Dynamics of the Kuroshio large meander--barotropic model. Journal of the Oceanographical Society of Japan, 41 259-273. YOON J. H. and I. YASUDA(1987) Dynamics of the Kuroshio large meander. Two-layer model. Journal of Physical Oceanography, 17, 66--81.