Effects of stratification and mesoscale eddies on Kuroshio path variation south of Japan

ARTICLE IN PRESS Deep-Sea Research I 55 (2008) 997– 1008

Contents lists available at ScienceDirect

Deep-Sea Research I journal homepage: www.elsevier.com/locate/dsri

Effects of stratification and mesoscale eddies on Kuroshio path variation south of Japan Kazunori Akitomo  Department of Geophysics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

a r t i c l e in fo

abstract

Article history: Received 8 May 2007 Received in revised form 24 March 2008 Accepted 30 March 2008 Available online 29 April 2008

Bimodality of the Kuroshio current path south of Japan is investigated, focusing on the effects of stratification and mesoscale eddies. For this purpose, wind-driven numerical experiments are executed in barotropic and two-layered ocean models. Stratification has two effects on the path selection of the Kuroshio south of Japan. First, it makes an alongshore path stable at intermediate wind stress strength t0 by arresting an eddy southeast of Kyushu. This enables an alongshore path to appear in the entire experimental range of t0 . Second, the upper limit of t0 which allows a meandering path decreases from 4:75  101 N m2 (76  106 m3 s1 in the Sverdrup transport at the Tokara Strait) to 2:50  101 N m2 (40  106 m3 s1 ) as Dr=r0 increases from 2:0  103 to 4:0  103 . While an anticyclonic eddy imposed upstream (southeast of Kyushu) can cause the transition from an alongshore to a meandering path, it occurs most easily when t0 ¼ 1:522:0  101 N m2 (24232  106 m3 s1 ). The transition from a meandering to an alongshore path requires an eddy imposed downstream (east of the meandering segment) which suppresses redevelopment of the meandering segment and breaks the balance between the advective and beta effects. Applicability of the results to previously observed path variations is discussed. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Kuroshio Bimodality Stratification Mesoscale eddy

1. Introduction Bimodality of current path is a remarkable feature of the Kuroshio south of Japan. After entering the North Pacific from the East China Sea via the Tokara Strait south of Kyushu, the Kuroshio sometimes flows along the southern coast of Japan (hereafter called the alongshore path1), and at other times flows along an offshore detouring path off Enshunada (the meandering path or large meander). Both paths are relatively stable and maintained for several years to a decade once formed (Fig. 1). Transitions between these paths are also remarkable. Preceding the transition from an alongshore to a  Tel.: +8175 753 3923; fax: +8175 753 3928.

E-mail address: [email protected] Although we used the term ‘straight’ path in our previous papers, ‘alongshore’ path is preferable because it better reflects the actual situation of current path. 1

0967-0637/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.dsr.2008.03.013

meandering path, a small meander is formed southeast of Kyushu, and it progresses eastward along the southern coast of Japan to develop into a large meander (e.g., Shoji, 1972). On the other hand, a meandering path changes into an alongshore path after the large meander progresses eastward over the Izu Ridge (e.g., Nishida, 1982). Many observational, theoretical and experimental studies to date have tried to determine the features and dynamics of the bimodality, and have concluded that the volume transport or current velocity is one of the crucial factors determining which current path the Kuroshio takes (e.g., Nitani, 1975; Saiki, 1982; White and McCreary, 1976; Masuda, 1982; Chao, 1984; Yasuda et al., 1985; Akitomo et al., 1991). Analyzing hydrographic data, Nitani (1975) showed that a meandering path can be interpreted as a stationary Rossby wave which stagnates along the southern coast of Japan in balance between the planetary beta and advective effects. However, observational studies, including his own,

ARTICLE IN PRESS K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

Transport (x106m3s-1)

998

50

40

30 1900

1920

1940

1960 Time (year)

1980

2000

Fig. 1. Periods of meandering path after 1900 (shaded region) based on coastal tide gauge records (e.g., Kawabe, 1995), and the time series of the Sverdrup transport at the Tokara Strait (1301E, 30.51N) based on the NCEP/NCAR reanalysis wind stress data for 1948–2006 (solid line; Kalnay et al., 1996). Thick solid lines represent the mean values for 1960–1975 (first period), 1976–1990 (second period), and 1991–2006 (third period).

led to no decisive conclusion about the dependence of path selection on current velocity (volume transport). When the Kuroshio took a meandering path, the volume transport was small south of Japan (e.g., Nitani, 1975), but large in the upstream regions such as the East China Sea or the Tokara Strait (e.g., Saiki, 1982). This discrepancy is partly attributed to the assumption of a no-motion reference level which may have caused significant error in estimates of the volume transport (Saiki, 1985). Errors may also arise from uncertainties in the determination of current width. Recirculation gyres appearing on either side of the main current such as an anticyclonic one south of Shikoku and a cyclonic one off Enshunada, may induce this type of error (e.g., Qiu and Joyce, 1992). White and McCreary (1976) were the first to propose a scenario for this bimodal behavior based on the theory of stationary Rossby waves. A meandering path is sustained as a Rossby lee wave formed downstream of Kyushu Island when the current velocity is low. With increased current velocity, however, an alongshore path takes the place of the meandering path since its ‘wavelength’ becomes longer than the distance between Kyushu and the Izu Ridge. Using a nonlinear path equation, Masuda (1982) supported this idea and further pointed out that alongshore and meandering paths can each exist at low velocities (multiple equilibrium regime). The southern coast of Japan being inclined relative to the zonal direction is another factor controlling the path selection. It makes an alongshore path possible at low velocities by acting as a western boundary along which the linear Munk-layer balance can be established (Chao, 1984). As a result, dependence of the path selection on current velocity is entirely reversed, i.e., an alongshore (meandering) path at lower (higher) velocities, from that in the case with a zonal coastline (Yoon and Yasuda, 1987). Stratification and bottom topography also tend to stabilize an alongshore path for a wider range of current velocity (Masuda et al., 1999). Although various factors have been proposed to have effects on the bimodal behavior of the Kuroshio, so far, comprehensive understanding of this problem is incomplete in inflow-outflow model experiments. For example, there is no explanation for the fact that a meandering path appears at higher velocities in

some experiments, which is inconsistent with the scenario based on stationary Rossby waves. Without disturbances, the transitions between alongshore and meandering paths never occur in the multiple equilibrium regime. Instead, the transition from an alongshore (meandering) to a meandering (alongshore) path occurs only when the current velocity increases (decreases) beyond the upper (lower) limit allowing an alongshore (meandering) path. A recent concern is the interaction of the Kuroshio and mesoscale variabilities (eddies). Technological advances such as satellite altimetry have made it possible to detect mesoscale eddy activity in the ocean (e.g., Le Traon and Morrow, 2001) and huge computational resources have enabled the resolution of such phenomena in numerical models (e.g., Semtner and Chervin, 1992). These advanced technologies have attracted interest in the effects of mesoscale phenomena (eddies) on the Kuroshio path variation, since some short-term variations of current velocity have been said to be related to the path transitions (e.g., Kawabe, 1995; Akitomo et al., 1996). Idealized model studies have suggested that shortterm variations of current velocity or mesoscale eddies may trigger the transition from an alongshore to a meandering path in the multiple equilibrium regime (Akitomo et al., 1997; Akitomo and Kurogi, 2001; Endoh and Hibiya, 2001). Sea surface height derived from satellite altimetric data has revealed the close relationship of mesoscale eddy activity to Kuroshio transport in the Tokara Strait (Ichikawa, 2001) and the behavior of small meanders which could trigger the path transition under certain conditions (Ebuchi and Hanawa, 2003). Further, data assimilation experiments with highresolution general circulation models have confirmed that the transition from an alongshore to a meandering path can occur by the action of mesoscale eddies in the actual ocean (e.g., Waseda et al., 2003; Miyazawa et al., 2004). However, the mechanism for the reverse transition is still unknown. As for the unresolved problem of what enables two types of the Kuroshio path, i.e., alongshore and meandering paths, to be stable south of Japan, Kurogi and Akitomo (2003) (hereafter, KA03), executing two-layered

ARTICLE IN PRESS K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

The purpose of this study is to resolve some remaining questions about the effects of stratification and mesoscale eddies on the Kuroshio path selection and variation, through numerical experiments with barotropic and two-layered ocean models. The questions include: (1) What factors have changed the range of wind stress strength (volume transport) for an alongshore path to be possible among previous model studies? (2) How does the upper limit of wind stress strength for a meandering path depend on stratification? (3) What kind of eddies trigger the transition from a meandering to an alongshore path? The experiments are executed for wide ranges of wind stress strength and density difference between the two layers. Applicability of the results to the actual situation is also discussed.

model experiments with various zonal and meridional distributions of wind stress, recently showed a possibility that the wind stress field over the subtropical region in the North Pacific may provide a (sufficient) condition for the bimodal behavior of the Kuroshio. According to them, an alongshore (meandering) path tends to be stable when the wind-induced pressure difference between the two ends of the southern coast of Japan, Kyushu Island and Boso Peninsula, is large (small), and at intermediate pressure differences there is a multiple equilibrium regime in which both paths can exist. The actual wind field induces such intermediate pressure differences in the subtropical region of the North Pacific. Another finding by KA03 is that four types of stable path are possible south of Japan: two types of alongshore path (called N1 and N2 paths) and two types of meandering path (A1 and A2 paths). The N1 path runs along the southern coast of Japan, and the N2 path turns toward the south near the Izu Ridge. The former appears for any wind stress strength t0 and closely resembles observed alongshore paths while the latter appears only for the very narrow range of t0 . The A1 path runs near the southern coast of Shikoku, and the A2 path runs far from that coast although the maximum distance from the southern coast of Japan (meander amplitude) is almost unchanged between both paths when t0 is the same. The A1 path tends to appear at lower t0 while the A2 path does at higher t0. Further, Kurogi and Akitomo (2006) (hereafter, KA06) examined the effect of stratification on the bimodal behavior of the Kuroshio, and showed that the upper limit of wind stress strength allowing a meandering path (or the multiple equilibrium regime) largely depends on the stratification (i.e., density difference between the two layers) since the ‘interfacial beta effect’ which is induced by variation of the upper layer thickness along the current axis acts to change the zonal scale of a meandering path (wavelength of a stationary Rossby wave). Based on experimental results, they speculated that enhanced stratification after the late 1980s is a possible reason for the alongshore-path years in the 1990s. These studies are the first to show that Kuroshio path variation can be controlled not only by current velocity (volume transport) but also by the wind stress distribution and stratification in the subtropical region.

Y (km)

2000

Honshu Shikoku Kyushu Enshunada East Tokara China Strait Sea Nansei Islands

1000

999

2. Numerical model 2.1. Model basin and governing equations The model ocean of 10,000-km length and 2300-km width is the same as in KA06 (Fig. 2). A simplified coastal geometry and islands of the western North Pacific are located on the left-hand side of the basin. The eastern coasts of Taiwan and the Philippines are located near the southwestern corner of the domain, from which the coastline extends northeastward along the continental margin in the East China Sea to the west of Kyushu. It then continues along the southern and eastern coasts of Japan to the north end of the domain (about 381N). The Nansei (Ryukyu) Islands are simply expressed by two long islands, and Hachijo Island on the Izu Ridge is a square of 20 km  20 km. The experiments are executed in a barotropic and twolayered ocean on a beta-plane under assumptions of hydrostatic balance and rigid sea surface. Variable bottom topography is set in the two-layer ocean (shades in Fig. 2) while a flat bottom is set in the barotropic ocean. The governing equation in the flat-bottom barotropic ocean is the vorticity equation given by qz qc qz qc qz qc  þ þb qt qy qx qx qy qx !   2 2 q z q z 1 qty qtx ¼ nh  , þ þ r0 h qx qy qx2 qy2

(1)

Hachijo Island North Pacific Izu Ridge

0 0

1000

2000

3000 X (km)

10000

0 g (y)

Fig. 2. Model basin and meridional profile of wind stress field used in the present experiment. Shaded regions show water depths of 1200, 2000, 3000, 4000 m from lighter to darker.

ARTICLE IN PRESS 1000

K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

where !

z¼

1 q2 c q2 c þ 2 . h qx2 qy

(2)

c and z are the volume transport function and the vertical component of vorticity, respectively, b the beta parameter (2  1011 m1 s1 ; meridional variation of the Coriolis parameter), r0 sea water density (1:03  103 kg m3 ), nh horizontal eddy viscosity (5  102 m2 s1 ), h constant water depth (600 m), and ðtx ; ty Þ is the wind stress vector. A no-slip condition is imposed on all lateral boundaries while the bottom is slippery. The governing equations in the two-layered model are the same as in KA06. Total water depth H is a function of x and y, changing from 1200 to 4000 m. Thickness of the upper layer at rest H1 is 600 m, and that of the lower layer H2 is H  H1 . Other physical parameters are the same as in the barotropic model. These governing equations are temporally integrated by the finite difference method with grid sizes Dx and Dy of 20 km and time increment Dt of 7200 s (barotropic experiments) or shorter (two-layered experiments).

from one value to another over 1000 days, time integration is continued to obtain a (quasi-)steady meanderingor alongshore-path state for another 10,000 days or more. Although four types of stable path are possible south of Japan, the N2 path is excluded in this study because it appears only for the very narrow range of t0 (KA03). Therefore, an alongshore path corresponds to the N1 path.

3. Stable paths of the Kuroshio 3.1. Barotropic experiment Fig. 3a shows dependence of stable paths on t0 in the barotropic experiment. When t0 is small (o1:0 101 N m2 ), only an alongshore path appears. A meandering path begins to appear at t0 ¼ 1:0  101 N m2 and takes the place of an alongshore path for 1:25 101 N m2 pt0 p2:25  101 N m2 . Thus, a multiple equilibrium regime (one alongshore and one meandering path) is found only at t0 ¼ 1:0  101 N m2 . While the meandering path which is close to the southern coast of

ðtx ; ty Þ ¼ ðt0  f ðxÞ  gðyÞ; 0Þ,

(3)

where t0 is the magnitude of wind stress, and f ðxÞ and gðyÞ the zonal and meridional distributions, respectively. The same distributions of f ðxÞ and gðyÞ are adopted as in KA06. That is, ( 0 ð0oxoX 2 Þ; f ðxÞ ¼ 1 (4) ðX 2 oxoX 1 Þ; 3 and gðyÞ is given so that the ratio of the Sverdrup transport at the eastern end of Honshu to that at the southern end of Kyushu Rc is 0.6 (Fig. 2).   8 py > > 0pyoY 4 ; >  cos Y ; > > 2 > >   >  2 > > py py > > þ b1 Y 4 pyoY 3 ; þ c1 ; > a1 < Y2 Y2 gðyÞ ¼  2   > py py > > þ b2 Y 3 pyoY 2 ; þ c2 ; a2 > > > Y2 Y2 > >     > > > Y1  Y2 pðy  Y 2 Þ > > 1 þ cos ; Y 2 pypY 1 ; :d þ Y1  Y2 Y2 (5) where ða1 ; a2 ; b1 ; b2 ; c1 ; c2 ; dÞ ¼ ð0:242; 0:629; 1:87; 3:95; 2:35; 5:16; 1:05Þ, and ðX 1 ; X 2 ; Y 1 ; Y 2 ; Y 3 ; Y 4 Þ ¼ ð10; 000; 3000; 2300; 2100; 1800; 1280 kmÞ. While KA06 examined the effect of stratification with density difference Dr=r0 ¼ 2 and 3  103 , here we consider six cases with Dr=r0 of 2.0, 2.5, 2.75, 3.0, 4.0, and 5:0  103 in addition to the barotropic one. The model ocean is initially at rest. Spin-up and searching for stable paths follow the previous studies (e.g., KA03). After t0 is linearly increased or decreased

600

400 vacillating 200

0

Meander amplitude (km)

To facilitate the study, we use an idealized wind stress field consisting of only the zonal component,

Meander amplitude (km)

2.2. Experimental cases: wind stress field and stratification

0.5

1.0

2.5 1.5 2.0 τ0 (x10-1 Nm-2)

3.0

3.5

0.5

1.0

2.5 1.5 2.0 τ0 (x10-1 Nm-2)

3.0

3.5

600

400

200

0

Fig. 3. Time-averaged distance of the Kuroshio axis from the southern coast of Japan (or meander amplitude). Solid circle indicates an alongshore path, and open circle and triangle meandering paths A1 and A2 , respectively, with error bars showing the standard deviation of the temporal variation. (a) Barotropic experiment and (b) two-layer experiment with Dr=r0 ¼ 3  103 (KA06). See text for detail.

ARTICLE IN PRESS K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

Shikoku is possible at low t0 (p1:75  101 N m2 ), that which is far from that coast is possible at high t0 (X1:75  101 N m2 ). The former corresponds to the A1 path and the latter to the A2 path in the two-layer experiment (KA03). Thus, two types of meandering paths are also possible in the barotropic ocean. This result is different from those in previous inflow–outflow models (Chao, 1984; Akitomo et al., 1991). The absence of an alongshore path at intermediate t0 (1:25  101 N m2 pt0 p2:25  101 N m2 ) is due to the action of eddies formed southeast of Kyushu. The eddies repeatedly appear, progress eastward one after another, and finally lead to the formation of a meandering path (Akitomo et al., 1991). So no steady alongshore path exists for the intermediate t0 . As a southward protrusion, the geometry of Kyushu Island is essential to the formation of these eddies since it compels the Kuroshio to turn toward the south when entering the North Pacific. This may explain why an alongshore path always appeared in the experiment by Chao (1984) where Kyushu Island was modeled as a geometrical step not a protrusion. The narrower range of the multiple equilibrium regime (or an alongshore path disappearing at lower t0 ) than in previous inflow–outflow model experiments is partly because the Sverdrup transport ratio between the two ends of the southern coast of Japan, Rc , is 0.6 in the present experiment while it corresponds to 1.0 in the inflow-outflow model experiment. The smaller the Rc , the more unstable an alongshore path (KA03). As described below, it is another factor affecting the stability of an alongshore path that the wide model basin allows higher variabilities (eddy activity) in the downstream region. Another difference from previous studies is found at higher t0. After t0 exceeds 2:25  101 N m2 , the current path begins to vacillate between meandering- and alongshore-path states, and only an alongshore path survives when t0 becomes 3:0  101 N m2 . As a result, an alongshore path separately appears in the two ranges with lower and highest t0 . There are two mechanisms by which an alongshore path is maintained south of Japan, the linear western boundary current along which the viscous effect balances the beta effect (e.g., Chao, 1984) and the nonlinear one along which the viscous, beta, and advective effects together balance one another (e.g., Yoon and Yasuda, 1987). While the alongshore path at lower t0 is basically the linear western boundary current along the inclined coastline, that at higher t0 is the nonlinear one which reappears since the ‘wavelength’ of the meandering path becomes too long to be sustained as a stationary Rossby wave along the southern coast of Japan (e.g., White and McCreary, 1976). While the alongshore path appeared at higher velocities than the meandering path did in Chao (1984), such a result was not obtained in Akitomo et al. (1991). This is because the experimental range of current velocity was too low for an alongshore path to recur at higher velocities in the latter study. (The maximum current velocity of 1:3 m s1 in Akitomo et al. (1991) corresponds to 2:5  101 N m2 in t0 here.) The vacillation of the current path at t0 ¼ 2:5 and 2:75  101 N m2 is also due to the action of eddies. A meandering path at these t0 ’s is unstable since its

1001

‘wavelength’ exceeds the length of the southern coast of Japan, and it shrinks into an alongshore path after southward elongation (Figs. 4a and b), cyclonic-eddy shedding (Fig. 4c), and eastward progression (Figs. 4d–f). It is notable that after the eddy shedding the zonal scale of recirculations decreases and cyclonic and anticyclonic eddies become significant south of the recirculation region (Figs. 4e–h). When an alongshore path is established, the transition back to a meandering path is already prepared. That is, a cyclonic eddy is formed east of Kyushu (Fig. 4h). Successive formation and eastward progression of such eddies leads to the transition to a meandering path again. Fig. 5 shows the transition phase starting on day 19,520 (about 2 years after the alongshore path is established). During this transition, mesoscale eddies which are formed in the Kuroshio Extension region propagate westward to interact with the main current of the Kuroshio. In particular, cyclonic eddies pass just south of the recirculations and approach Kyushu (eddies A–C). Eddy A merges with the small meander southeast of Kyushu on day 19,520 (Fig. 5d), and eddy C interacts with the Kuroshio just before a meandering path sets in (day 19,550; Fig. 5g). On the contrary, anticyclonic eddies pass south of the cyclonic eddies and do not interact with the Kuroshio so much (eddy X on days 19,530 and 19,540; Figs. 5e and f). Thus, cyclonic eddies propagating westward from the downstream region are deeply related to the transition from an alongshore to a meandering path in this barotropic experiment. The propagation speed of the eddies is about 0:25 m s1 which is similar to the propagation speed of barotropic Rossby waves with wavelength of 800 km, about 0:16 m s1 . The total duration of the meandering-path state is twice that of the alongshore-path state when t0 ¼ 2:5  101 N m2 , and it decreases to half when t0 ¼ 2:75  101 N m2 . 3.2. Two-layer experiment As seen in Fig. 3b, an alongshore path appears for the entire experimental range of t0 in a two-layered ocean with Dr=r0 ¼ 3:0  103 (KA06). The two types of alongshore path are merged in this case since an eddy is stagnant southeast of Kyushu. Stratification makes the eddy stagnate behind Kyushu and bottom topography makes it hard to develop into a large meander even if it progresses eastward along the southern coast of Japan (Masuda et al., 1999). These factors overcome the destabilizing effect of Kyushu to make an alongshore path appear for all t0 . As a result, the transition to a meandering path needs some disturbances such as a short-term velocity increase (Akitomo et al., 1997) or the action of eddies (e.g., Akitomo and Kurogi, 2001). Differences from the barotropic experiment include an increase in the upper limit of wind stress strength tmax 0 allowing stable meandering paths to 2:75  101 N m2 while the lower limit tmin of 1:0  101 N m2 does not 0 change. This is because interfacial depth changes along a current axis and shortens the wavelength of a stationary

ARTICLE IN PRESS

Y (km)

1002

K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

2000

2000

1600

1600

1200

1200

800

800 1000

1500

2000

2500

3000

3500

1000

1500

2000

2500

3000

3500

1000

1500

2000

2500

3000

3500

1000

1500

2000

2500

3000

3500

1000

1500

2000

2500

3000

3500

X (km)

2000

2000

1600

1600

1200

1200 800

800 1000

1500

2000

2500

3000

3500

2000

2000

1600

1600

1200

1200

800

800 1000

1500

2000

2500

3000

3500

2000

2000

1600

1600

1200

1200

800

800 1000

1500

2000

2500

3000

3500

Fig. 4. Time evolution of stream function c for the transition from a meandering to an alongshore path in the barotropic experiment when t0 ¼ 2:5  101 N m2 . (a) Day 18,620, (b) day 18,640, (c) day 18,660, (d) day 18,670, (e) day 18,680, (f) day 18,740, (g) day 18,760, (h) day 18,780. Solid (dotted) contour lines indicate positive (negative) value of c. Contour interval is 10  106 m3 s1 .

Rossby wave (the along-coast scale of a large meander south of Japan) by inducing an additional beta effect (the interfacial beta effect) of the same sign as the planetary one (KA06). The interfacial beta effect becomes more significant as stratification weakens, or the density gap between two layers Dr becomes smaller. In KA06, tmax 0 increases from 2:75  101 N m2 to 4:75  101 N m2 as Dr=r0 decreases from 3:0  103 to 2:0  103 when the upper layer thickness is 600 m.

Fig. 6 shows dependence of tmax and tmin 0 0 , or the range of t0 allowing meandering paths, on stratification for 2:0  103 pDr=r0 p5:0  103 , compared with the barotropic case. Since an alongshore path exists at all t0 for each stratification except the barotropic case, the range of t0 for meandering paths gives that for the multiple equilibrium regime. As seen in Fig. 6, the upper limit tmax for a meandering 0 path decreases much more abruptly with stratification

ARTICLE IN PRESS

Y (km)

K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

2000

2000

1600

1600

1200

C

B

A

1003

1200 Y

X

A

Z

800

C

B X

Z

Y

800 1500

1000

2500

2000

3000

3500

1500

1000

2500

2000

3000

3500

2500

3000

3500

X (km)

2000

2000

1600

1600

1200

A

X

A

1200

C

B

Z

Y

C

B

Z

Y

X 800

800 1000

1500

2000

2500

3000

1000

3500

2000

2000

1600

1600 C

B

1200

Y

X

Z 800

1500

2000

2500

3000

3500

2000

2000

1600

1600 C

1200

2000

C

1200

800 1000

1500

X

Z

Y

1000

1500

2000

2500

3000

3500

1000

1500

2000

2500

3000

3500

1200 Z

Y 800

800 1000

1500

2000

2500

3000

3500

Fig. 5. Same as in Fig. 4 but for the transition from an alongshore to a meandering path. (a) Day 19,490, (b) day 19,500, (c) day 19,510, (d) day 19,520, (e) day 19,530, (f) day 19,540, (g) day 19,550, (h) day 19,570.

when 2:0  103 pDr=r0 p3:0  103 than when Dr=r0 X is because the 3:0  103 . Such abrupt change of tmax 0 stability of the A2 path is much more sensitive to stratification than that of the A1 path (KA06). A slight decrease of Dr=r0 from 3:0  103 to 2.75103 (or an increase in water temperature by 1.25 K) results in a by 1:0  101 N m2 which significant increase of tmax 0 corresponds to a Sverdrup transport of about 20  106 m3 s1 at the Tokara Strait. Based on this, KA06 speculated that continuation of an alongshore-path state for 1990–2004 might have been caused by enhanced

stratification which began in the late 1980s. Detailed examination here shows that the abrupt change of tmax 0 occurs in the range of 2:0  103 pDr=r0 p3:0  103 which encompasses the actual stratification. This means that stratification can be a major factor controlling the path variation in the actual ocean. This will be discussed further in Section 5. As Dr=r0 exceeds 3:0  103 , tmax ceases to decrease 0 abruptly and remains 2:5  101 N m2 when Dr=r0 X ¼ 2:5  101 N m2 is almost 4:0  103 . The value of tmax 0 the same as in the barotropic experiment, showing that

ARTICLE IN PRESS K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

6

τ0 (x10-1 Nm-2)

5 4 3 2 1 0 2

3

4 5 Δρ/ρ0 (x10-3)

∞ (barotropic)

Fig. 6. Range of t0 for a meandering path to be possible depending on Dr=r0 . Black bar with circles (gray bar with triangles) represents the range of the A1 (A2 ) path. Shaded region indicates the range of wind stress giving the actual (Sverdrup) transport at the Tokara Strait ð30250  106 m3 s1 Þ.

the interfacial beta effect is negligible when Dr=r0 X

(eddy H) for a meandering-path state (Fig. 7). Experimental cases and results are shown in Tables 1 and 2. Eddy strength (r 0 ; jZ0 jÞ is changed from (100 km, 100 m) to (250 km, 250 m), considering recent observations by satellite altimeter that the eddy scale is 2002400 km in diameter (e.g., Ebuchi and Hanawa, 2003; Waseda et al., 2003). The A1 path is used for the initial condition if there are two types of meandering path because the A1 path represents actual meander events more realistically. The A2 path changes into the A1 path when eddy H is imposed, or it changes the alongshore path via the A1 path when t0 exceeds tmax . 0

2000

1600 Y (km)

1004

eddy H

1200

4:0  103 .

eddy K 4. Path transitions due to mesoscale eddies

800

1500

1000

2000

2500

X (km) The transitions between alongshore and meandering paths occur in a relatively short time, several months to half a year. While it has been suggested that short-term variations of current velocity or mesoscale eddies can trigger the transition from an alongshore to a meandering path (e.g., Kawabe, 1995; Akitomo et al., 1996, 1997; Masuda and Akitomo, 2000; Akitomo and Kurogi, 2001; Ichikawa, 2001; Endoh and Hibiya, 2001), the mechanism of the reverse transition is still unclear. This transition does not occur by the action of the same eddies that trigger the transition from an alongshore to a meandering path when they are imposed upstream, east of Taiwan or southeast of Kyushu (Akitomo and Kurogi, 2001). Although KA06 proposed a scenario for the long-term path variation (regime shift) from a meandering- to an alongshore-path period occurring around 1990 based on a modified theory of stationary Rossby waves, short-term path transitions require a different explanation. The most promising candidate is the activity of mesoscale eddies prevailing in this region. Thus, we examine a possible transition process from a meandering to an alongshore path due to the action of mesoscale eddies imposed in the downstream region, covering the whole range of t0 for the multiple equilibrium regime, i.e., t0 ¼ 1:0, 1.5, 2.0 and 2.5101 N m2 , in the case with Dr=r0 ¼ 3:0  103 . The transition process from an alongshore to a meandering path due to eddies imposed upstream is also examined for this wide range of t0 . Akitomo and Kurogi (2001) investigated this process only for t0 ¼ 1:75  101 N m2. The mesoscale eddy is given as a Gaussian eddy with a radius of r 0 and an interfacial displacement of Z0 (positive for cyclonic rotation), as in Akitomo and Kurogi (2001). Its initial position is southeast of Kyushu (called eddy K) for an alongshore-path state and southeast of Hachijo Island

Fig. 7. Initial positions of a mesoscale eddy imposed southeast of Kyushu (eddy K) and that east of the Izu Ridge (eddy H).

Table 1 Transition from an alongshore to a meandering path due to eddy K Strength of eddy ðr 0 ; jZ0 jÞ

t0 ð101 N m2 Þ 1.0

(200 km, 200 m) (175 km, 175 m) (150 km, 150 m) (125 km, 125 m) (100 km, 100 m)

1.5

2.0

2.5

C

AC

C

AC

C

AC

C

AC

    

    

    

    

    

    

    

    

Circles and crosses indicate transition and non-transition cases, respectively, when a mesoscale eddy with ðr0 ; jZ0 jÞ is initially imposed southeast of Kyushu, eddy K, in case with Dr=r0 ¼ 3  103 . C (AC) represents cyclonic (anticyclonic) rotation.

Table 2 Transition from a meandering to an alongshore path due to eddy H Strength of eddy ðr 0 ; jZ0 jÞ

t0 ð101 N m2 Þ 1.0

(250 km, 250 m) (200 km, 200 m) (150 km, 150 m) (100 km, 100 m)

1.5

2.0

2.5

C

AC

C

AC

C

AC

C

AC

   

   

   

   

   

   

   

   

Same as in Table 1, but a mesoscale eddy is initially imposed east of the Izu Ridge, eddy H.

ARTICLE IN PRESS K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

Y (km)

The strength of eddy K needed for the transition from an alongshore to a meandering path depends on the magnitude of t0 and the rotation of the eddy. When t0 is 1.5 and 2.0101 N m2 , the transition occurs easily regardless of the rotation. On the contrary, cyclonic (anticyclonic) eddies hardly trigger the transition when t0 is 1:0  101 ð2:5  101 Þ N m2 . When t0 is 1:0 101 N m2 , the main current is too weak for a small meander (imposed cyclonic eddy) to develop into a large meander while an anticyclonic eddy induces a large meander separating the main current from the coast by its own nonlinear (advective) effect. When t0 is 2:5  101 N m2 , the strong main current compels the small meander induced by the imposed anticyclonic eddy to escape eastward while the small meander originating from the imposed cyclonic eddy effectively develops into a larger meander. As a result, the transition is most likely to occur when t0 ¼ 1:522:0  101 N m2 giving a realistic value of 24232  106 m3 s1 in Sverdrup transport at the Tokara Strait. The relative effectiveness of cyclonic eddies is the same as in Akitomo and Kurogi (2001).

While eddy K never leads to the transition from a meandering to an alongshore path as in Akitomo and Kurogi (2001), eddy H does in some cases when it is anticyclonic (Table 2). Fig. 8 shows the time evolution of a ‘pseudo’ stream function c1 in the upper layer during the transition from a meandering to an alongshore path with t0 ¼ 2:50  101 N m2 when an anticyclonic eddy H with ðr 0 ; jZ0 jÞ ¼ ð200 km; 200 mÞ is imposed on day 19,000. c1 is defined by c1 ðP; P0 Þ ¼ k 

P P0

0

ðh1 u1  dlÞ;

(6)

0

2000

1600

1600 C

B

A

Z

where u1 and h1 are the horizontal velocity vector and thickness of the upper layer, respectively, dl a line element vector along the integral path, and k is the upwarddirected unit vector (Akitomo and Kurogi, 2001). A similar time series of c1 , but for the case without the eddy, is shown in Fig. 9 for comparison. While elongation of the meandering segment (Fig. 8a), eddy shedding (Fig. 8b), and reduction of the meander amplitude (Fig. 8c) are similar to those in the no-eddy case (Figs. 9a–c), the

2000

1200

1005

1200 Y

X

Z

800

C

B A

X

Z

Y

800 1000

1500

2500

2000

3000

3500

1500

1000

2500

2000

3000

3500

2500

3000

3500

2500

3000

3500

X (km)

2000

2000

1600

1600

1200

A

X

A

1200

C

B Y

C

B

Z

Z

Y

X 800

800 1000

1500

2000

2500

3000

1000

3500

2000

2000

1600

1600 C

B

1200

Y

X

Z 800

1500

2000

2500

3000

3500

2000

C

1200

800 1000

1500

X 1000

Z

Y 1500

2000

Fig. 8. Time evolution of ‘pseudo’ stream function c1 in the case of an anticyclonic eddy with ðr 0 ; jZ0 jÞ ¼ ð200 m; 200 kmÞ imposed east of the Izu Ridge (eddy H) on day 19,000 when the Kuroshio is in a meandering state with t0 ¼ 2:5  101 N m2 and Dr=r0 ¼ 3  103 . (a) Day 19,190, (b) day 19,220, (c) day 19,240, (d) day 19,280, (e) day 19,370, (f) day 19,410. Solid (dotted) contour lines indicate positive (negative) value of c1 . Contour interval is 10  106 m3 s1 .

ARTICLE IN PRESS

Y (km)

1006

K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

2000

2000

1600

1600

1200

C

B

A

1200 Y

X

A

Z

800

C

B X

Z

Y

800 1000

1500

2500

2000

3000

3500

1500

1000

2500

2000

3000

3500

2500

3000

3500

2500

3000

3500

X (km)

2000

2000

1600

1600

1200

A

X

A

1200

C

B

Z

Y

C

B

Z

Y

X 800

800 1000

1500

2000

2500

3000

1000

3500

2000

2000

1600

1600 C

B

1200

Y

X

Z 800

1500

2000

2500

3000

3500

2000

C

1200

800 1000

1500

X 1000

Z

Y 1500

2000

Fig. 9. Same as in Fig. 8 but for the case without the eddy. (a) Day 19,130, (b) day 19,160, (c) day 19,190, (d) day 19,230, (e) day 19,320, and (f) day 19,360.

subsequent process proceeds differently. The reduced meander does not redevelop so much (Fig. 8d) but propagates eastward (Fig. 8e), and an alongshore path is established (Fig. 8f). This is in contrast to the no-eddy case where the normal meandering-path state is reestablished after the meandering segment significantly redevelops before reaching the eastern end of the southern coast of Japan (Figs. 9d and f). Although the transition process to an alongshore path is similar to that which occurs when t0 exceeds tmax 0 (KA06), it is a key process in the multiple equilibrium regime here that the imposed eddy acts to suppress development of the meandering segment. This allows the advective effect of the Kuroshio main current to overcome the beta effect and sweep away the meandering segment eastward. The suppression is caused by enhanced recirculations south of the Kuroshio (compare Fig. 8a with Fig. 9a). The enhanced recirculations delay the shedding of the cyclonic eddy and increase its magnitude (compare Fig. 8b with Fig. 9b). Further, the recirculation east of the Izu Ridge suppresses the growth of the meandering segment as it progresses eastward (compare Figs. 8c, d with 9c, d). The same path transition occurs in cases with lower t0 (1.5 and 2:0  101 N m2 ) although it requires a

stronger eddy (Table 2), and when an anticyclonic eddy with ðr 0 ; jZ0 jÞ ¼ ð200 km; 200 mÞ is imposed 300 km south of eddy H (or at the same latitude with eddy K; not shown). On the contrary, enhancement of the recirculations is not observed and no transition occurs when eddy H is cyclonic. The enhancement and path transition do not occur when eddy K is imposed (either cyclonic or anticyclonic) although it induces the eddyshedding (e.g., Akitomo and Kurogi, 2001). Despite the rather artificial situation, it is concluded that the transition from a meandering to an alongshore path can occur in the multiple equilibrium regime when the recirculations off the Kuroshio main current are enhanced by some disturbances. Such enhancement is induced by anticyclonic eddies imposed downstream in the present experiment.

5. Summary and discussion In last three or four decades, many studies have revealed that various factors are related to the bimodal behavior of the Kuroshio path south of Japan, geometric features (Kyushu Island, the southern coast of Japan

ARTICLE IN PRESS K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

Weakly stratified Strongly stratified Actual range of wind stress

Meander amplitude

inclined relative to the zonal direction, and the Izu Ridge), wind stress over the North Pacific (its distribution and strength), stratification, and short-term (mesoscale) variations. The present study has investigated some remaining problems related to these factors. While there are two types of alongshore path, one of which is a linear western boundary current formed along the southern coast of Japan, and the other is controlled by the nonlinear dynamics, they are linked at intermediate t0 in the two-layer (stratified) ocean. This linkage is realized by the effects of stratification and bottom topography which stagnate an eddy formed behind Kyushu Island. Without these effects, the eddy progresses eastward to compel the transition from an alongshore to a meandering path, and the range of the multiple equilibrium regime becomes much narrower than that in previous inflow–outflow models. Stratification also controls the upper limit of wind stress strength tmax for a meandering path, or the multiple 0 equilibrium regime (KA06). tmax decreases from 4.75 to 0 2:50  101 N m2 as Dr=r0 increases from 2.0 to 5:0  103 while the lower limit tmin is unchanged (1:0 0 101 N m2 ). The abrupt change of tmax occurring between 0 Dr=r0 of 2.0 and 3:0  103 implies high sensitivity of the Kuroshio path selection to stratification in the actual situation. In terms of the Sverdrup transport, the range of t0 for the multiple equilibrium regime is from 16 to 40276  106 m3 s1 at the Tokara Strait in the present experiment. Thus, the actual Kuroshio transport (30250 106 m3 s1 ) is almost entirely within the multiple equilibrium regime (always when Dr=r0 p2:75  103 ). Mesoscale eddies are candidates for causing the transitions between alongshore and meandering paths in the multiple equilibrium regime. The transition from an alongshore to a meandering path can occur due to the action of mesoscale eddies imposed upstream (e.g., Akitomo and Kurogi, 2001), and this occurs most effectively when t0 ¼ 1:522:0  101 N m2 giving a value of 24232  106 m3 s1 in Sverdrup transport at the Tokara Strait. The reverse transition, on the other hand, is most effectively caused by an anticyclonic mesoscale eddy imposed downstream. On approaching the anticyclonic recirculations off the Kuroshio, the eddy enhances them and the enhanced recirculations in turn suppress redevelopment of the meandering segment after significant eddy-shedding. As a result, the advective effect of the Kuroshio main current overcomes the beta effect to sweep away the redeveloping meander eastward. The transition occurs more easily for larger t0. The enhancement of the recirculations is not induced by a cyclonic eddy or eddies imposed upstream. The results obtained here are schematically shown in Fig. 10. While an alongshore path can exist for any wind stress strength t0 , a meandering path can exist only at intermediate t0 . The upper limit of wind stress strength tmax for a meandering path decreases as stratification is 0 enhanced. If tmax is greater than the actual range of wind 0 stress strength, the path transitions can occur only by the action of some disturbances (mesoscale eddies). On the contrary, if tmax is in the actual range of wind stress 0 strength, the transition from a meandering to an alongshore path can occur when t0 exceeds tmax . 0

1007

meandering path

Transition due to disturbances (eddies)

alongshore path Wind stress 0 Fig. 10. Schematic view of current paths of the Kuroshio and their possible transitions south of Japan. While an alongshore path is possible for any wind stress strength t0 , a meandering path is possible only at intermediate t0 . The upper limit of wind stress strength tmax for a 0 meandering path changes with stratification. It exceeds the actual range of t0 when the ocean is weakly stratified (dashed line with open circles). Thus, transitions between alongshore and meandering paths occur due only to short-term disturbances (mesoscale eddies) in the multiple equilibrium regime (thick bidirectional arrow). On the contrary, tmax 0 drops within the actual range in the strongly stratified ocean (solid line with closed circles). In this case, the transition from a meandering to an alongshore path is also possible when t0 exceeds tmax (black unidirec0 tional arrow). Gray arrows show that the path transition is possible but never occurs as long as t0 is in the actual range.

It is worthwhile discussing possible scenarios of long-term and short-term path variations of the Kuroshio based on these results. As seen from Fig. 1, the long-term path variations have several features. Among them, alongshore-path and predominantly meandering-path periods appear alternately every 15 years after about 1960. Although such a long-term path variation has been said to be related to the current velocity (volume transport), the relationship is not straightforward to explain. While the Sverdrup transport was relatively low (30245  106 m3 s1 ) in the first period of 1960–1975 during which an alongshore path was dominant, it increased to 38253  106 m3 s1 in the second period of 1976–1990 during which a meandering path appeared frequently. Thus, the regime shift in 1975 from the first (alongshore-path) to the second (meandering-path) period has been considered to be caused by increased current velocity (volume transport). However, the present experiments indicate that the multiple equilibrium regime was possible in both periods. This means that the increased current velocity alone cannot explain the 1975 regime shift. Instead, it is a possible scenario that the increased current velocity activated mesoscale eddies which in turn worked as triggers for the path transitions between alongshore and meandering paths in the second period. This scenario is not inconsistent with the fact that the shorter periods of meandering- and alongshore-path years alternatively appeared in the 1980s.

ARTICLE IN PRESS 1008

K. Akitomo / Deep-Sea Research I 55 (2008) 997–1008

The higher transport continued after an alongshore path became dominant again in the third period of 1991–2006. KA06 speculated that the continuation of an alongshore path in the third period may have been caused by a decrease of tmax due to the enhanced stratification 0 which began in the late 1980s. Their speculation is reinforced by the present result that the upper limit of wind stress strength tmax abruptly decreases as Dr=r0 0 increases from 2.0 to 3:0  103 (Fig. 6). The higher transport in the third period, on the other hand, infers that mesoscale eddies were still activated. From this viewpoint, it is worthwhile noting that a ‘meandering’ path with a lifetime of less than 1 year was often induced by eddy action in the 1990s (e.g., Ebuchi and Hanawa, 2003), and that the meandering path formed in 2004 was maintained for only 1 year. Finally, a longer-term variation is detected in Fig. 1: the duration of the meandering-path period generally decreases with time. While the meandering-path period continued for more than 4 years before 1950, its duration was generally shorter, 1–3 years (4 years 7 months at most) after 1950. This trend may be related with the enhanced stratification (e.g., Levitus et al., 2005) and/or eddy activity in the subtropical region of the North Pacific. These scenarios are somewhat speculative. The longterm variations of stratification and eddy activity are not well known and the present two-layer model is not enough to represent actual stratification and bottom topography. Thus, further investigation from either the observational or experimental side is needed. Nevertheless, the effects of stratification and short-term disturbances (mesoscale eddies) can elucidate problems about Kuroshio path variation which have not been explained thoroughly by current velocity (wind stress strength) alone. References Akitomo, K., Kurogi, M., 2001. Path transition of the Kuroshio due to mesoscale eddies: a two-layer, wind-driven experiment. Journal of Oceanography 57, 735–741. Akitomo, K., Awaji, T., Imasato, N., 1991. Kuroshio path variation south of Japan. 1 Barotropic inflow–outflow model. Journal of Geophysical Research 96, 2549–2560. Akitomo, K., Ooi, M., Awaji, T., Kutsuwada, K., 1996. Interannual variability of the Kuroshio transport in response to the wind stress field over the North Pacific: its relation to the path variation south of Japan. Journal of Geophysical Research 101, 14057–14071. Akitomo, K., Masuda, S., Awaji, T., 1997. Kuroshio path variation south of Japan: stability of the paths in a multiple equilibrium regime. Journal of Oceanography 53, 129–142. Chao, S.-Y., 1984. Bimodality of the Kuroshio. Journal of Physical Oceanography 14, 92–103. Ebuchi, N., Hanawa, K., 2003. Influence of mesoscale eddies on variations of the Kuroshio path south of Japan. Journal of Oceanography 59, 25–36. Endoh, T., Hibiya, T., 2001. Numerical simulation of the transient response of the Kuroshio leading to the large meander formation south of Japan. Journal of Geophysical Research 106, 26833–26850.

Ichikawa, K., 2001. Variation of the Kuroshio in the Tokara Strait induced by meso-scale eddies. Journal of Oceanography 57, 55–68. Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu, Y., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K.C., Ropelewski, C., Wang, J., Leetmaa, A., Reynolds, R., Jenne, R., Joseph, D., 1996. The NCEP/NCAR 40-year reanalysis project. Bulletin of the American Meteorological Society 77, 437–471. Kawabe, M., 1995. Variations of current path, velocity, and volume transport of the Kuroshio in relation with the large meander. Journal of Physical Oceanography 25, 3103–3117. Kurogi, M., Akitomo, K., 2003. Stable paths of the Kuroshio south of Japan determined by the wind stress field. Journal of Geophysical Research 108 (C10), 3332. Kurogi, M., Akitomo, K., 2006. Effects of stratification on the stable paths of the Kuroshio and on their variation. Deep-Sea Research I 53, 1564–1577. Le Traon, P.Y., Morrow, R., 2001. Ocean currents and eddies. In: Fu, L.L., Cazenave, A. (Eds.), Satellite Altimetry and Earth Science. Academic Press, San Diego, pp. 171–215. Levitus, S., Antonov, J., Boyer, T., 2005. Warming of the world ocean, 1955–2003. Geophysical Research Letters 32, L02604. Masuda, A., 1982. An interpretation of the bimodal character of the stable Kuroshio path. Deep-Sea Research 29, 471–484. Masuda, S., Akitomo, K., 2000. Effects of stratification and bottom topography on the Kuroshio path variation south of Japan. Part II: Path transitions in a multiple equilibrium regime. Journal of Physical Oceanography 30, 1431–1449. Masuda, S., Akitomo, K., Awaji, T., 1999. Effects of stratification and bottom topography on the Kuroshio path variation south of Japan. Part I: Dependence of path selection on velocity. Journal of Physical Oceanography 29, 2419–2431. Miyazawa, Y., Guo, X.Y., Yamagata, T., 2004. Roles of mesoscale eddies in the Kuroshio paths. Journal of Physical Oceanography 34, 2203–2222. Nishida, H., 1982. Description of the Kuroshio meander in 1975–1980—Large meander of the Kuroshio in 1975–1980. Report of the Hydrographic Research 17, 181–207; Maritime Safety Agency, Tokyo. Nitani, H., 1975. Variation of the Kuroshio south of Japan. Journal of Oceanographical Society of Japan 31, 154–173. Qiu, B., Joyce, T.M., 1992. Interannual variability in the mid- and lowlatitude Western North Pacific. Journal of Physical Oceanography 22, 1062–1079. Saiki, M., 1982. Relation between the geostrophic flux of the Kuroshio in the Eastern China Sea and its large-meanders in south of Japan. Oceanographical Magazine 32, 11–18. Saiki, M., 1985. Transport of the Kuroshio. Marine Sciences Monthly (Kaiyo Kagaku) 17, 267–273 (in Japanese). Semtner, A.J., Chervin, R.M., 1992. Ocean general-circulation from a global eddy-resolving model. Journal of Geophysical Research 97, 5493–5550. Shoji, D., 1972. Time variation of the Kuroshio south of Japan. In: Stommel, H., Yoshida, K. (Eds.), Kuroshio—Its Physical Aspects. University of Tokyo Press, Tokyo, pp. 217–234. Waseda, T., Mitsudera, H., Taguchi, B., Yoshikawa, Y., 2003. On the eddy–Kuroshio interaction: meander formation process. Journal of Geophysical Research 108, 3220. White, W.B., McCreary, J.P., 1976. On the formation of the Kuroshio meander and its relationship to the large-scale ocean circulation. Deep-Sea Research 23, 33–47. Yasuda, I., Yoon, J.-H., Suginohara, N., 1985. Dynamics of the Kuroshio large meander—barotropic model. Journal of Oceanographical Society of Japan 41, 259–273. Yoon, J.-H., Yasuda, I., 1987. Dynamics of the Kuroshio large meander: two-layer model. Journal of Physical Oceanography 17, 66–81.