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Roles of Mesoscale Eddies in the Kuroshio Paths
YASUMASA MIYAZAWA
Frontier Research System for Global Change/JAMSTEC, Yokohama City, Kanagawa, JapanXINYU GUO
Frontier Research System for Global Change/JAMSTEC, Yokohama City, Kanagawa, Japan, and Center for Marine Environmental
Studies, Ehime University, Matsuyama, JapanTOSHIO YAMAGATA
Frontier Research System for Global Change/JAMSTEC, Yokohama City, Kanagawa, Japan, and Department of Earth and Planetary
Science, Graduate School of Science, The University of Tokyo, Tokyo, Japan(Manuscript received 11 June 2002, in final form 8 April 2004)
ABSTRACT
A high-resolution ocean general circulation model is developed to simulate connections between the Kuroshio
path variations and mesoscale eddy activities as realistically as possible. The climatological mean of the modeled
Kuroshio takes a nearshore nonlarge meander path. It is found that the model is capable of simulating two typesof nonlarge meander state and a possible version of the large meander state. The offshore nonlarge meander isgenerated through interaction between the Kuroshio and an anticyclonic eddy. The large meander occurs justafter significant intensification of the anticyclonic Kuroshio recirculation; successive intrusion of anticycloniceddies from the upstream region is responsible for this process. Those anticyclonic eddies are advected by the
Kuroshio from the region northeast of Luzon Island and increase the upstream Kuroshio volume transport on
an interannual time scale. The cyclonic eddies propagating from the Kuroshio Extension region, on the other
hand, weaken the Kuroshio meander after the merger. The Kuroshio path variations south of Japan thus seemto be closely related to eddy activities in the subtropical gyre system.

1. Introduction
The Kuroshio is one of the most energetic westernboundary currents associated with high mesoscale eddy
activity. It is unique among various western boundary
currents in that the Kuroshio has three typical paths
along the southern coast of Japan. As shown in Fig. 1,
these are the large meander path, the nearshore nonlarge
meander path, and the offshore nonlarge meander pathaccording to the definition given by Kawabe (1985).
The large meander and nonlarge meander paths persist
from a few years to a decade, suggesting a link withbasinwide climate variations. The large meander pathhas not been observed during the last decade. However,
the transition between the nearshore nonlarge meander
path and the offshore nonlarge meander path has beenfrequently observed; the primary period of the path transition is 1.6–1.8 yr (Kawabe 1987).
Recent studies suggest that the transition between the
Corresponding author address: Yasumasa Miyazawa, Frontier Research System for Global Change/JAMSTEC, 3173-25 Showamachi,
Kanazawa-ku, Yokohama City, Kanagawa 236-0001, Japan.
E-mail: miyazawa@jamstec.go.jp

q 2004 American Meteorological Society

nearshore and the offshore nonlarge meander paths during the last decade is influenced by mesoscale eddy
activity (Ebuchi and Hanawa 2000, 2003; Mitsudera etal. 2001). Analyzing satellite altimetry data, Ebuchi and
Hanawa (2003) suggested that anticyclonic/cyclonic eddies trigger the offshore nonlarge meander observed
from 1993 to 1999. Several numerical experiments havebeen performed recently to examine how an anticyloniceddy inserted artificially in ocean models triggers thepath transition from the nearshore to the offshore nonlarge meander path (Mitsudera et al. 2001) or to thelarge meander path (Endoh and Hibiya 2001; Akitomo
and Kurogi 2001). However, the inflow/outflow models(Mitsudera et al. 2001; Endoh and Hibiya 2001) or noneddy-resolving models (e.g., Akitomo and Kurogi 2001)
cannot capture the mesoscale eddy activity linked tobasin-scale processes.
Recent observational studies suggest that two kindsof mesoscale eddy activity exist in this region. The firstis westward-propagating eddies with a spatial scale of
500 km and a time scale less than 3 months, probably
originating in the Kuroshio Extension and entering theKuroshio recirculation region at 308N (Ebuchi and Han-

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FIG. 1. Tide gauge stations and typical paths (LM: large meander
path, oNLM: offshore nonlarge meander path, and nNLM: nearshore
nonlarge meander path) of the Kuroshio. The numbers denote thetide stations and the abbreviations represent locations (1: Naze, 2:
Nishinoomote, 3: Kushimoto, 4: Uragami, 5: Hachijojima, Ki: Kii
Peninsula, S: Shikoku, Ky: Kyushu, and IOR: Izu–Ogasawara Ridge).
We note that Uragami (4) is located slightly downstream of Kushimoto (3). Labels PN and ASUKA denote the CTD line of the Nagasaki
Marine Observatory and the line of the ASUKA observation group,
respectively.

awa 2000). The second is mesoscale eddies located farther to the south near 238N. After being captured by theoffshore current of the Kuroshio south of Okinawa (theRyukyu Current), they are advected by the Kuroshio
itself to the Shikoku Basin, where they eventually merge
with the eddies mentioned above (Ichikawa 2001).
Many theoretical works have addressed mechanismsof the Kuroshio large meander since the pioneering workof Robinson and Taft (1972) (see references of Qiu andMiao 2000). Using an eddy-permitting, two-layer primitive equation model of the North Pacific Ocean, Qiu
and Miao (2000) have recently suggested that the accumulation of low potential vorticity water in the Kuroshio recirculation region influences the Kuroshio pathvariation. They renewed interest in possible connectionsof the Kuroshio large meander to the whole subtropicalgyre system including the low latitudes as well as therecirculation region, rather than considering the meander simply as a local nonlinear phenomenon (see also
Saiki 1982; Yamagata et al. 1985; Yamagata and Umatani 1987). Hurlburt et al. (1996), using an eddy-resolving, six-layer primitive equation model, also
showed that the basinwide structure of stratification andthe basinwide increasing/decreasing trend of the windstress change the frequency of the large meander paththrough baroclinic instability west of the Izu–Ogasawara Ridge. However, the explicit roles of the mesoscaleeddies south of Japan have not been clarified so far using
a basin-scale ocean general circulation model (OGCM).
The purpose of this paper is to investigate possible
connections between the Kuroshio path variations and

VOLUME 34

mesoscale eddy activity using an eddy-resolving
OGCM. The horizontal grid spacing of the model is 1⁄128
in both zonal and meridional directions, which corresponds to about 9 km in the Kuroshio region. This grid
spacing is much smaller than the first baroclinic Rossby
radius in the Northwest Pacific (see Emery et al. 1984).
The present model with forcing from 1992–1998 reproduces the offshore nonlarge meander path, the nearshore nonlarge meander path, and a possible version of
the large meander path.
This paper is organized as follows. In section 2, themodel configuration is described. In section 3, the meanstate and variability of the model are discussed. Thensea level variations are discussed in connection with the
Kuroshio path variation. The model skill for representing mesoscale eddy activities is also argued. In section
4, we describe details of the Kuroshio path variation inview of the interaction with mesoscale eddies. We also
examine effects of the mesoscale eddy activity on theintensity of the Kuroshio. Section 5 is devoted to summary and discussion.
2. Numerical model
The present model is based on one of the world community models, the Princeton Ocean Model (POM; Mellor 1996). The POM is a three-dimensional primitive
equation ocean model including thermodynamics. The
vertical coordinate of the POM is represented by a bottom-following (sigma coordinate) system. The horizontal grids are defined on spherical coordinates. The vertical viscosity and diffusivity are calculated using theMellor and Yamada (1982) level-2.5 turbulent closure
scheme. The horizontal viscosity is calculated by the
Smagorinsky-type formulation (Smagorinsky et al.
1965), which is proportional to the square of grid sizeand horizontal velocity shear with a coefficient of 0.05.
The horizontal diffusivity coefficient is assumed to be
one-half of the viscosity coefficient. The bottom stressis calculated by the quadratic formula with an empiricaldrag coefficient, the minimum value of which is 2.5 3
10 23 . Coastal boundary conditions are no slip as well
as no mass flux.
The model for the North Pacific (Fig. 2) is run inboth low-resolution (1⁄48–18) and high-resolution (1⁄128)
configurations. The bottom topography of the low-resolution model is created from the 1⁄128 global height data,
GETECH DTM5. This low-resolution basinwide model
ranges from 308S to 628N and from 1008E to 708W andhas 21 sigma levels in the vertical direction as in theprevious study (Guo et al. 2001). The horizontal resolution varies from 1⁄ 48 in the region corresponding to thehigh-resolution model to 18 near the boundary. The
high-resolution regional model, with uniform horizontal
resolution of 1⁄ 128, extends from 108 to 508N and from
1178E to 1808 (Fig. 2). This high-resolution model has
45 sigma levels (Table 1). The distribution of verticallevels is introduced to resolve the bottom and surface

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FIG. 2. Bottom topography. The nested area is indicated with a rectangle.

boundary layers. The bottom topography of the highresolution model is also created from the 1⁄ 128 data,
DTM5. In addition, the 500-m mesh bottom topography
provided by Hydrographic Department of Japan is embedded in the coastal sea around Japan.
The bottom topography in both models has beensmoothed to reduce the pressure gradient error (Mellor
et al. 1994). The maximum bottom slope between two
adjacent grid points is constrained by the inequality,( | H1 2 H 2 | )/( | H1 1 H 2 | ) # 0.2. To reduce the pressure
gradient error, we have adopted a Gaussian smootherwith ½8 scale for the low-resolution grid and with 1⁄ 128
scale for the high-resolution grid. A ‘‘zero forcing run’’with a horizontally uniform, stable stratification allows
TABLE 1. Sigma coordinate used in the high-resolution model.
LayersSigma coordinate

LayersSigma coordinate

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

0.000
20.00220.00520.01020.01520.02520.03520.04520.05520.06520.07520.08520.09520.10520.12020.13520.15020.16520.18020.19520.21020.22520.250

24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

20.27520.30020.32520.35020.37520.42520.47520.52520.57520.62520.67520.72520.77520.82520.87520.90020.92520.95020.97020.98020.99021.000

us to estimate the current induced by the pressure gradient error. The magnitude of the erroneous velocity due
to the pressure gradient error is less than a few centimeters per second for both of the models. We note herethat local topography such as the Koshu Seamount,which may influence the Kuroshio path dynamics southof Japan (Hurlburt et al. 1996; Endoh and Hibiya 2001),
is well resolved in the high-resolution model even after
the smoothing.
Northern and southern boundaries of the low-resolution model are treated as open boundaries, along
which a radiation condition is adopted on external mode
velocities, together with a one-sided advection scheme
for temperature and salinity. Both temperature and salinity fields are specified on open boundaries using
monthly climatology data (Levitus and Boyer 1994;
Levitus et al. 1994). The internal-mode velocities onopen boundaries are assumed to vanish.
Variables on all lateral boundaries of the high-resolution regional model are determined by values interpolated bilinearly from the low-resolution basin model(Guo et al. 2003). Vertical boundary variables for thehigh-resolution model with 45 sigma levels are createdfrom the low-resolution model with 21 sigma levels by
linear interpolation. The radiation condition considering
the sea surface height of the lower-resolution model isadopted on external mode velocities to keep calculation
stable. Daily mean variables of the low-resolution model
are stored on a disk for the purpose of one-way nesting.
The bottom topography near the boundary of the highresolution model is the same as that of the low-resolution model to allow a smooth connection of both models by linear interpolation of sigma coordinate variables.
Sea ice formation and river runoff are not includedin these simulations. Since nudging to the monthly climatology of temperature and salinity in the Okhotsk
Sea improves watermass properties in the mixed water

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FIG. 3. Mean sea surface height of the model from 1992 to 1998.
Contour interval is 0.1 m.

region north of the Kuroshio Extension (H. Mitsudera
2000, personal communication), we followed their recipe in both the Okhotsk Sea and the Bering Sea. This
procedure may be regarded as a kind of parameterization
for sea ice and lateral freshwater effects. The sea surface
temperature is nudged to the observed temperature witha restoring time scale of 7 days in both regions.
The model is driven by wind stresses and heat andsalt fluxes. The wind stress field is calculated on a weekly basis from ERS-1 and -2 (European Remote Sensing
Satellite) scatterometer data with a 18 3 18 resolution.
The Reynolds and Smith (1994) sea surface temperaturefield used in the simulation is blended from ship, buoy,
and bias-corrected satellite data with a 18 3 18 resolution
also on a weekly basis. The surface heat flux is applied
using the Haney-type formula (Haney 1971); the coefficient used in the retroaction term is 35 W m 22 K 21 .
Salinity at the surface is restored to the monthly mean
climatology (Levitus et al. 1994) with a time scale of
30 days.
The present simulation is conducted with two steps:
an initial spinup experiment and an experiment with
forcing from 1992 to 1998. In the spinup experiment,
the two models are started from a state of rest withannual-mean temperature and salinity derived from the1⁄ 48 3 1⁄48 climatology data (Boyer and Levitus 1997).
The spinup period is 20 years for the coarse-resolution
model and 12 years for the fine-resolution model. They
are forced by monthly mean climatological wind stresses derived from ERS-1 and -2 wind data and monthly
mean climatological heat flux (Da Silva et al. 1994)
modified with the monthly mean SST data. The simulation used for the present analysis is started from thefinal year of the spinup experiment using the weekly
mean wind stress and the monthly mean climatologicalheat flux modified with the weakly mean SST data from
1 January 1992 to 31 December 1998.

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FIG. 4. Mean streamfunction of the model from 1992 to 1998.
Contour interval is 10 Sv.

3. The model resultsa. Mean state of the Kuroshio
Figure 3 shows the mean sea surface height field fromthe high-resolution model during the simulation period
from 1992 to 1998. The model reproduces the Kuroshio–Kuroshio Extension system well with a reasonable
separation latitude at around 358N. In addition, the anticyclonic recirculation gyre is resolved on the southernside of the Kuroshio, which is comparable to the observed recirculation (e.g., Hasunuma and Yoshida1978). We also note that the model climatology of theKuroshio path south of Japan is the nearshore nonlarge
meander path.
The streamfunction averaged for the period from1992 through 1998 is shown in Fig. 4. The volumetransport of the Kuroshio across the PN line in the East
China Sea (see Fig. 1) and that for the Ryukyu Current
east of the Nansei Islands are about 25 and 15 Sv (Sv[ 10 6 m 3 s 21 ), respectively, which are comparable toobservations (Kawabe 1995; Zhu et al. 2003). Therefore, the present model resolves successfully the two
upstream branches of the Kuroshio. However, the eastward volume transport across the ASUKA line south ofJapan (Fig. 1) reaches 79 Sv, which is much larger thanthe mean value of 57 Sv observed from 1992 to 1997
by Imawaki et al. (2001). The volume transport associated with the Kuroshio Countercurrent is about 39 Sv
in the model while the corresponding volume transport
south of Shikoku is only 15 Sv in the observation.
b. Variability of the surface geostrophic current
In order to examine ocean variability near the surface,the eddy kinetic energy (EKE) field derived from satellite altimetry data such as Ocean Topography Experiment (TOPEX)/Poseidon (T/P) is quite useful. Becauseof their global coverage, satellite data effectively capture the spatial pattern of eddy activity (Stammer 1997).

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In the present study, we use the National Aeronautics
and Space Administration Goddard Space Flight Center
Ocean Pathfinder collinear dataset for the T/P altimeter
mission over the period between September 1992 andDecember 1998.
The EKE is calculated from the along-track gradientin the sea surface height anomaly, assuming the geostrophic approximation. Before this calculation, themodel sea surface height anomaly is interpolated on thesatellite track. Then the EKE along the satellite track isinterpolated to half-degree regular grids using an optimal interpolation method.
Figure 5a shows that the satellite-derived EKE ishigher than 0.03 m 2 s 22 in the western subtropical region
between 158 and 408N. In particular, the North Equatorial Current and the Kuroshio–Kuroshio Extension
show values higher than 0.08 m 2 s 22 . The flow fieldsouth of Japan also shows high EKE, which reflects thepath variation of the Kuroshio. As shown in Fig. 5b,
the present high-resolution model successfully reproduces those satellite-derived features. The maximum
EKE in the Kuroshio–Kuroshio Extension region is larger than 0.3 m 2 s 22 in the model, which is comparable
to the observation. The high EKE in the Kuroshio region
is attributed not only to mesoscale eddy activity but also
to the path migration of the Kuroshio (Mizuno andWhite 1983). The present model succeeds in representing such variability as well. The realistic EKE distribution in the model mainly results from the high horizontal resolution (Guo et al. 2003). However, the model
does not reproduce well the observed EKE in the central
part of the subtropical gyre. This may reflect the deficiency of resolving midocean eddies in the low-resolution model.
c. Mesoscale eddy activity south of Japan
Ebuchi and Hanawa (2000) have reported significant
mesoscale eddy activity with a time scale of 40–200
days south of Japan (278–308N, 1358–1558E) using theT/P data. In a subsequent paper, they have suggested
that coalescence of the mesoscale eddy with the mainstream may trigger the path variation of the Kuroshio(Ebuchi and Hanawa 2003).
In order to compare statistical properties of the eddy
activity with observations, we plot the power spectra ofsea surface height anomaly calculated using the T/P data
and the model output (Fig. 6). Although the model fails
to simulate the eddy activity with time scales of 40–
200 days south of Japan (278–308N, 1358–1558E), it
successfully simulates the eddy activity in a slightly
more northern region (298–328N, 1358–1558E). The horizontal scale evaluated from the filtered sea surface
height anomaly in the latter region is 500 km, which iscomparable with the observation. The westward phasespeed estimated from the model result is 5.5 cm s 21 ,which is almost the same as the observed value of 5.4
cm s 21 . The vertical sections for simulated eddies over

FIG. 5. Mean eddy kinetic energy (m 2 s 22 ) calculated from sea
surface height anomaly (Sep 1992–Dec 1998): (a) TOPEX/Poseidon
altimetry and (b) model result.

the Izu–Ogasawara Ridge are shown in Fig. 7. The eddy
has a diameter of about 400 km and a maximum swirling
speed of about 60 cm s 21 and extends to a depth of1000 m. Displacement of the 158C isotherm reaches
about 200 m at the center. All of these properties correspond well to observations (Ebuchi and Hanawa 2000;
Mitsudera et al. 2001).

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FIG. 6. Power spectra of sea surface height anomaly. (a) TOPEX/Poseidon data averaged in theregion (278–308N, 1358–1558E), (b) the model result averaged in the region (278–308N, 1358–1558E),(c) TOPEX/Poseidon data averaged in the region (298–328N, 1358–1558E), and (d) the model result
averaged in the region (298–328N, 1358–1558E). An error bar indicating 95% confidence level isshown in each panel.

d. Path variations of the Kuroshio
Three different types of the Kuroshio path south ofJapan are simulated in the present model, which uses
forcing from January 1992 to December 1998. Two correspond to the nearshore nonlarge meander and the offshore nonlarge meander, following the definition of Kawabe (1985). The other path is similar to the large meander. The mean path during the simulation period corresponds to the nearshore nonlarge meander path (Fig.
3).
It is well known that the change of the Kuroshio path
is associated with sea level changes along the southerncoast of Japan. According to tide gauge data, the sea
level difference between Kushimoto and Uragami (seeFig. 1 for locations) during the large meander state is
negative (about 210 mm) and less variable than during
the nonlarge meander state (Kawabe 1995). As shownin Fig. 8a, this feature is reproduced well in the present
model. The modeled Kuroshio path from November
1993 to July 1994 and from January 1998 to May 1998
is similar to the large meander path. The sea level dif-ference between Kushimoto and Uragami is negativeand less variable during these periods as in the observations, even though the duration is much shorter thanis observed. The actual large meander path persists fora period from a few years to a decade. On the other
hand, the real Kuroshio shows only transitions between
the offshore and nearshore nonlarge meander paths during the simulation period (Ebuchi and Hanawa 2003).
Kawabe (1985) showed that the sea level at Hachijojima (see Fig. 1 for location) is useful for distinguishing the offshore nonlarge meander from the nearshore
nonlarge meander. When the sea level at Hachijojima
is high, the main axis of the Kuroshio is close to theJapan coast. On the other hand, when the sea level at
Hachijojima is low, the Kuroshio is away from the coastof Honshu. The time series of the model sea level at
Hachijojima indicates the existence of two basic states.
The nearshore nonlarge meander is characterized by sea
level ranging from 0 to 400 mm and the offshore nonlarge meander is for the range from 2700 to 2300 mm(see arrows in Fig. 8b). Thus the model appears to re-OCTOBER 2004

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FIG. 7. Depth–latitude sections at 1398E. (a) Temperature and (b) eastward velocity of a simulated
anticyclonic eddy on 7 Sep 1992. (c) Temperature and (d) eastward velocity of a simulated cycloniceddy on 17 Sep 1994. Contour interval of temperature is 18C and that of velocity is 0.2 m s 21 .

produce both nonlarge meander paths during the simulation period. We note that a low sea level state at
Hachijojima in the model appears to correspond to thestate of negative sea level difference between Kushimoto and Uragami. This feature is inconsistent withobservation; the typical large meander shows high sea
level state at Hachijojima (Kawabe 1985).
In summary, the model reasonably reproduces bothof the two nonlarge meander states, but its ability toreproduce the large meander state needs improvement
because the duration is too short in comparison withobservations. The low sea level state at Hachijojima,
which has been frequently observed in the decay phaseof the large meander (Kawabe 1995), may be associatedwith the short duration of the large meander in the pres-ent model. Nevertheless, the existence of the brief large
meander states in the model is worthy of further investigation; the present model appears to capture almost all
key elements in the Kuroshio path dynamics.
4. Roles of mesoscale eddies on the Kuroshio pathvariations
a. Offshore nonlarge meander
The sea level at Hachijojima exhibits a low state fora short period of about 1 month three times from February 1993 to August 1993 (see arrows in Fig. 8b).
These short-term variations correspond to the offshore
nonlarge meander as mentioned in the previous section.
We analyze the process here in detail.

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al. 2001; Ebuchi and Hanawa 2003). The anticycloniceddy associated with this offshore nonlarge meander
evolves by absorbing small eddies near the Izu–Ogasawara Ridge and finally separates from the Kuroshio.
Then the whole process is repeated two more times (e.g.,
Fig. 9d).
b. Large meander

FIG. 8. (a) Time series of model sea level difference between Kushimoto and Uragami. Lines with arrows denote the large meander
period. (b) Time series of model sea level at Hachijojima. Both data
are averaged over 10 days, and the reference value is the mean forthe period from Jan 1992 to Dec 1998. The arrows denote the onsetof the offshore nonlarge meander path.

As shown in Fig. 9a, small anticyclonic eddies arefound along the offshore side of the Kuroshio from theLuzon Island to the Kuroshio recirculation region insummer 1992. Anticyclonic eddies passing through theTokara Strait influence the Kuroshio path there and induce subsequent small meanders farther downstream
southeast of Kyushu. Ichikawa (2001) has discussed thephenomenon using the T/P, ERS-1, and ERS-2 altimetrydata. The small anticyclonic eddies propagating downstream are absorbed by a large anticyclonic eddy locatednear the Izu–Ogasawara Ridge. The large eddy thenpropagates westward and collides with the Kuroshio eastof Kyushu about 3 months after the eddy formation (Fig.
9b). The Kuroshio is intensified in this way and thenmeanders east of the Kii Peninsula in February of 1993
(Fig. 9c). This eddy–Kuroshio interaction process issimilar to a real event observed in 1998 (Mitsudera et

The Kuroshio followed the large meander path after
three episodes of interaction with an anticyclonic eddy
during the state of the offshore nonlarge meander as
described in section 4a. The large meander thus generated is associated with negative sea level difference
between Kushimoto and Uragami from November 1993
to July 1994 (Fig. 8a). The anticyclonic eddy, indicatedby the arrow in Fig. 10a, starts moving westward. Thenthe eddy collides with the Kuroshio (Fig. 10b) and isadvected back eastward by the current. Associated withthis process, the large meander grows southeast of theKii Peninsula (Figs. 10b–d). This large meander isstrengthened by absorbing a cyclonic eddy east of the
Izu–Ogasawara Ridge and then sheds a strong eddy, that
is, a cyclonic ring. This results in a nearshore nonlarge
meander path (not shown).
The second large meander occurs suddenly in January
1998 (Fig. 11). The weak cyclonic eddy south of Shikoku is first captured by the Kuroshio, as indicated by
the arrow in Fig. 11a. The meander southeast of the Kii
Peninsula grows just after that, as shown in Figs.
11b–d. The second large meander also absorbs the cyclonic eddy east of the Izu–Ogasawara Ridge, and thenmoves toward the east of the Izu–Ogasawara Ridge andreturns to the nonlarge meander (not shown).
In order to analyze the meander growth, the verticalvelocity at 400-m depth and the abyssal flow at 4000m depth are shown for the two large-meander cases andfor one nonlarge meander case (Fig. 12). Large anomalous downward velocity is found in the east half of themeander trough, whereas anomalous upward velocity isfound in the west half. Abyssal anticyclonic circulation
exists below the upper downwelling region. Cyclonic
circulation occurs at middepth (2000–3000 m) below
the upwelling region (not shown). These features are
consistent with the dynamical constraint of potential
vorticity conservation. The large meander path (Figs.
12a,b) is associated with the strengthened abyssal anticyclonic circulation around Koshu Seamount andshows a contrast to the offshore nonlarge meander path
(Fig. 12c), as previously simulated by Hurlburt et al.
(1996) and Endoh and Hibiya (2001).
Figure 13 shows the kinetic energy at 4000-m depth
averaged in 31.58–32.58N, 1328–1378E. There are fourpeaks (.0.4 3 10 24 m 2 s 22 ) during the simulation period. Three of them correspond to the large meander
paths and are indicated by arrows. The fourth peak, in
October 1994, is due to passage of the cyclonic eddy
through the analysis region. The offshore nonlarge me-OCTOBER 2004

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FIG. 9. Evolution of sea surface height showing the interaction of the anticyclonic eddy (indicatedby arrows) and the Kuroshio. Contour interval is 0.05 m. Regions greater than 0.6 m are shaded: (a)7 Sep 1992, (b) 6 Dec 1992, (c) 4 Feb 1993, and (d) 13 Aug 1993.

ander (e.g., the peak on 13 August 1993) is associatedwith much smaller kinetic energy. The marked rise in
the abyssal kinetic energy during the onset phase of thelarge meander path suggests vertical kinetic energy
transfer due to baroclinic instability. In section 4c, we
address the energetics of the meander growth.
c. Energetics of the meander growth
To examine how the large meander grows, we haveanalyzed local energetics in a way similar to Masina etal. (1999) and Wells et al. (2000). The results are also
compared with a standard linear stability analysis toclarify mechanisms of the initial growth. Although thesimulated large meanders are short lived as comparedwith the observed phenomena, the present analysis isuseful in understanding the genesis of the large meander.
The local energy transfer from mean kinetic energy
to eddy kinetic energy is expressed as follows (Wells
et al. 2000):[

K 5 2 u9u9

1

2

]

]u
]u
]y
]y
1 u9y 91
1 y 9y 9
,
]x
]y
]x
]y

(1)

where u (y ) is the eastward (northward) mean velocity
and u9(y 9) is the eastward (northward) perturbed velocity. When K is positive, the barotropic energy transfer
may generate disturbances. Similarly, the energy transfer from mean potential energy to eddy kinetic energy
is judged by the following term:

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FIG. 10. As in Fig. 9 except showing the amplification of the Kuroshio meander due to the interaction
with the anticyclonic eddy [indicated by an arrow in (a)]: (a) 9 Feb 1994, (b) 1 Mar 1994, (c) 21
Mar 1994, and (d) 10 Apr 1994.

P 5 2gu9r9(] r /]x) 1 y 9r9(] r /]y),dr b /dz(2)

where g is the gravity acceleration, and r9, r , and r b (z)are the perturbed, mean, and background density fields.
When P is positive, the baroclinic energy transfer may
generate disturbances. A part of P is transformed into
eddy kinetic energy through the buoyancy term, B 52gr9w9 , where w9 is the perturbed vertical velocity.
However, the complicated distribution of vertical velocity due to rough bottom topography prevents us fromobtaining a meaningful view from the plot of B (Wells
et al. 2000).
Figure 14a shows a meridional section at 1368E of
the time-averaged eddy kinetic energy (u9 2 1 y 9 2 )/2during the period when the first meander grows. We findtwo peaks: one is at the Kuroshio core of the nonlarge
meander path (338N) and another is on the offshore sideof the Kuroshio (32.28N). Meridional sections of theconversion terms K at 1368E (Fig. 14b) show two positive K regions (on the onshore side at 33.78N and on
the offshore side at 32.78N) within the upper 300 m.
On the other hand, the maximum of P is found in the
Kuroshio core near 338N (Fig. 14c). This corresponds
to the maximum of the eddy kinetic energy on the onshore side (Fig. 14a). We also note that the positive P
region extends to the main thermocline at 600-m depth.
This suggests that the evolving cyclonic disturbance due
to baroclinic instability may influence the movement of
the Kuroshio core of the nonlarge meander path during
the onset phase of the large meander path. Barotropic
instability appears to be responsible for further growth

OCTOBER 2004

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2213

FIG. 11. As in Fig. 10 except showing the amplification of the Kuroshio meander due to theinteraction with the cyclonic eddy [indicated by an arrow in (a)]: (a) 10 Dec 1997, (b) 9 Jan 1998,(c) 8 Feb 1998, and (d) 10 Mar 1998.

of the meander because the maximum of the eddy kinetic energy on the offshore side at 32.78N (Fig. 14a)
is accompanied only by the maximum in K. The energetics for the other large meander path show similarfeatures (not shown).
Time series of both vertical and horizontal velocity
shear averaged along the Kuroshio main stream showthat the vertical shear of the Kuroshio increases prior
to the onset of the large meander (Fig. 15). This leads
to enhancement of the baroclinicity. The horizontal
shear of the Kuroshio also increases prior to the large
meander path, leading to a favorable condition for barotropic instability. Those preconditions permit the Kuroshio to generate the meander through the interaction
with finite-amplitude disturbances, that is, mesoscaleeddies. Zhu et al. (2001) also observed increase of bothvertical and horizontal shear of the Kuroshio south of
Shikoku prior to the path transition from the nearshore
to the offshore nonlarge meander during the period from1994 to 1995.
We, therefore, analyze the stability of the preconditioned Kuroshio using a two-dimensional inviscid primitive equation model (cf. Xue and Mellor 1993). The
preconditioned velocity profile from 318 to 33.58N at
1368E is used for the analysis. The bottom topography
and the velocity profile are approximated using the analytical functions as described in the appendix. Figure
16 shows the growth rate and the phase speed for theunstable modes corresponding to the above two meanders. The most preferred mode has an e-folding timeof 3.0–3.4 days and wavelength of 240–260 km. The
phase speed for the most unstable wave is 35 km day 21

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VOLUME 34

FIG. 13. Time series of kinetic energy (m 2 s 22 ) at 4000-m depth
averaged over 31.58–32.58N, 1328–1378E.

and does not show significant dependence on the downstream wavenumber. Characteristics of the most unstable mode are summarized in Table 2. The energetics of
the unstable mode are calculated using the baroclinic
conversion term P, the buoyancy term B, and the barotropic conversion term K. As shown in Table 2, theratios of B and K to P show that baroclinic energy
transfer is mainly responsible for the growth of the unstable wave.
Similar characteristics of the meander simulated by
the OGCM were estimated from the sequences of sea
surface height (Table 3). The simulated meander grows
and moves more slowly than expected from the linear
stability analysis. The wavelength is larger than the theoretical prediction. The finite amplitude of the meander
and the existence of viscosity in the OGCM may be
responsible for these differences. This is because thestructure of the unstable disturbance corresponds wellto that of the simulated disturbance near 338N in the
OGCM (Fig. 17a). The vertical structures for the barotropic conversion term K and the baroclinic conversion
P are also similar to those near 338N in the OGCM
(Figs. 17b,c). The ratio K/P estimated in the onshore
region for the OGCM (Table 3) also indicates that thebaroclinic instability dominates in the onshore side during the initial growth. On the other hand, barotropic
instability is responsible for the growth in the offshore
region (Table 3).
To check the parameter dependence of the above re←
FIG. 12. Snapshots of the smoothed vertical velocity at 400-m
depth: (a) the large meander case on 13 Aug 1993, (b) the large
meander case on 21 Mar 1994, and (c) the offshore nonlarge meandercase on 8 Feb 1998. The shaded region denotes upwelling, and thedashed contour denotes downwelling. Koshu Seamount is indicatedby a closed circle in each panel. Contour interval is 20.03, 20.02,
20.01, 20.005, 0.005, 0.01, 0.02, and 0.03 cm s 21 . The horizontal
velocity at 4000-m depth is also shown by the vectors. To show theKuroshio path, the temperature contour of 138C at 400-m depth isdenoted by the thick line.

OCTOBER 2004

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2215

FIG. 15. Time series of the rms velocity shear of the Kuroshio mainstream in 1348–1388E from 100 to 1000 m. The Kuroshio main stream
is defined as the region in which mean velocity is greater than 0.4
m s 21 . Variations with time scale shorter than 30 days are removed.
(a) Vertical shear, and (b) horizontal shear.

FIG. 14. Depth–latitude sections at 1368E for (a) time-mean eddy
kinetic energy (contour interval is 0.1 m 2 s 22 ), (b) time-mean barotropic conversion (contour interval is 0.5 3 10 26 m 2 s 23 ), and (c)time-mean baroclinic conversion (contour interval is 0.5 3 10 26
m 2 s 23 ). The period of time mean is from 2 Oct 1993 to 10 Jan 1994.
The diamond at the top of (a) indicates mean position of the Kuroshio.

FIG. 16. Growth rate and phase speed for the velocity profiles at
1368E on 12 Oct 1993 (solid line) and 9 Jan 1998 (dashed line). Thicklines denote growth rate, and thin lines denote phase speed.

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VOLUME 34

TABLE 2. Characteristics of the most unstable wave for two velocity
profiles: B/P denotes the ratio of the buoyancy term B to the baroclinic
conversion term P, and K/P denotes the ratio of the barotropic conversion term to the baroclinic conversion term P.

Profile on

Growth rate
(day21)

Phase speed(km day21 )Wavelength
(km)

K/P

B/P

12 Oct 1993
9 Jan 1998

3.4 3 1021
2.9 3 1021

35
35

260
240

0.120
0.077

0.863
0.875

sults, we have analyzed several other profiles obtainedby perturbing parameters defining the velocity profile
by one standard deviation during the simulation period(Fig. 18). It is found that lower current speed smallerU 0 ), lower vertical shear (larger Z s ), shifting the velocity core more toward the coast (smaller y f ), broader
current width (smaller yd1 , yd2 ) and more southward inclination of the velocity core (larger A 0 ) lead to reduction of the growth rate. In particular, shifting the velocity
core toward the coast by 30 km remarkably stabilizes
the current. This is because the bottom slope constrains
the baroclinic energy transfer (De Szoeke 1975). The
offshore position of the model Kuroshio is highly sensitive to the interaction with offshore eddies just before
the meanders occur (not shown). This suggests that theKuroshio can be preconditioned by the eddies throughthe offshore shift of the main axis.
d. Variation of the Kuroshio recirculation
The present analysis of the model results suggeststhat the preconditioned Kuroshio may generate the large
meander path through baroclinic instability triggered byeither an anticyclonic or a cyclonic eddy. According to
Kagimoto and Yamagata (1997), the anticyclonic Kuroshio recirculation is intensified by a merger of anticyclonic eddies. Therefore we discuss roles of the Kuroshio recirculation at the preconditioning phase. To
achieve this, analysis of the vorticity budget is useful.
The vorticity budget is calculated using the following
equation (Ezer and Mellor 1994; Kagimoto and Yamagata 1997):

TABLE 3. Characteristics of the meanders simulated by the OGCM:
K/P in the onshore region denotes the ratio of the barotropic conversion term to the baroclinic conversion term P in 32.58–33.58N,
1358–1368E, and K/P denotes that in 31.08–33.58N, 1358–1368E.
Phase
WaveGrowth rate
speed
lengthMeander(day21) (km day21) (km)Oct 1993
Jan 1998

0.7 3 1021
0.7 3 1021

12
6

600
720

K/P in theonshoreregion

K/P

0.208
0.221

0.655
0.427

FIG. 17. Depth–latitude sections at 1368E for (a) structure of thegrowing disturbances (ũ 2 1 ỹ 2 ), (b) barotropic conversion, and (c)baroclinic conversion.

OCTOBER 2004

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FIG. 18. Dependence of the growth rate on various velocity profiles at 1368E on 12 Oct 1993
for U 0 5 1.4 m s 21 (dashed line), Z s 5 710 m (dashed line with pluses), yf 5 80 km (short dashedline with crosses), y d1 5 49 km (dash–dotted line with asterisks), y d2 5 49 km (dash–dotted linewith open squares), and A 0 5 4.4 (dash–dotted line with closed squares). Thick solid line denotes
the basic growth rate.

[]] ]( y D)
](uD)
2
]t ]x
]y
52

1 ]x 2 ]y 2 2
]A y

]A x

[

]

]( f uD)]( f y D)1]x]y

1 J(Pb , D) 1 curl(t s 2 t b ),(3)

where D is the depth, (u , y ) are the vertical averaged
velocities, (A x , A y ) are the vertically integrated advection plus diffusion terms in the zonal and the meridional
momentum equations, respectively, f is the Coriolis parameter, P b is the bottom pressure, and t s and t b are thewind and the bottom stresses, respectively; J denotes
the Jacobian operator. The term on the left-hand side isthe vorticity tendency term, and the terms on the righthand side are the advection plus diffusion of the vorticity, the planetary geostrophic divergence, the bottompressure torque, and the curl of wind and bottom stresses. The second term on the right-hand side of Eq. (3)is reduced to the planetary beta effect when the timedependence of the surface elevation is negligible (Kagimoto and Yamagata 1997).
Figure 19a shows the time series of vorticity (]y D/]x 2 ]u D/]y) averaged in the Kuroshio recirculation
region (308–338N, 1338–1408E). The area-averaged anticyclonic (i.e., negative) vorticity is significantly intensified just before the occurrence of the large meander.
The anticyclonic vorticity averaged in the area excluding the cyclonic meander region shows a more drastic
variation. The time evolution of all terms in (3) is shownin Fig. 19b. We note that diffusion is negligible in comparison with advection; the wind stress is negligible incomparison with the bottom stress in this region.
During the nonlarge meander period, the negative
beta advection and nonlinear advection terms are almost
balanced with the positive bottom pressure and stresstorques. This suggests that the Kuroshio interacts withthe bottom slope through bottom pressure torque during
the period. The advection intensifies the anticylonic vorticity during the nonlarge meander period; each negative
peak of the advection term corresponds to intrusion of
anticylonic eddies. In particular, the anticyclonic vorticity is supplied by the advection from the summer of1992 to autumn of 1993 in the model.
When the first large meander occurs, the balanceamong terms drastically changes. The beta advection
term changes from a negative value to a positive value
owing to the strong southward flow. The nonlinear advection term and bottom stress torque frequently change
sign owing to large variation of the cyclonic meander
and the anticylonic recirculation. Because of the lackof constant supply, the anticyclonic vorticity in the recirculation region weakens during the large meander
period. The second large meander occurs after the anticyclonic vorticity is again significantly intensified in
the summer of 1997.
The time series of the model Kuroshio volume transport across the PN and ASUKA lines suggests a causeof the intensification of the Kuroshio recirculation (Fig.
20). The volume transport across the PN line increases

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FIG. 19. (a) Time series of mean vorticity of vertically integrated velocities in 308–338N, 1338–
1408E (solid line). Dashed line denotes mean vorticity in the area excluding the Kuroshio meander.
Variations with time scale shorter than 30 days are removed. (b) Time series of torque balance in
308–338N, 1338–1408E. Variations with time scale shorter than 30 days are removed.

VOLUME 34

OCTOBER 2004

MIYAZAWA ET AL.

2219

FIG. 21. Relations between the surface velocity of the Kuroshio(in the Tokara Strait) and the volume transport (across the PN line).
Closed circles correspond to the large meander and crosses correspond to the nonlarge meander. The unit is one standard deviationfrom the mean. The surface velocity in the Tokara Strait is estimatedfrom the sea level difference between Naze and Nishinoomote (1 and
2 in Fig. 1, respectively).

FIG. 20. Time series of the model Kuroshio transport across (a)the PN line relative to 700 m and (b) the ASUKA line upper 1000m from 1992 to 1998. Thin line denotes the filtered estimate (longer
than 1 yr) of the volume transports.

seasonally when the anticyclonic eddies pass throughthe PN line in summer (Kagimoto and Yamagata 1997).
The interannual increase of the Kuroshio volume transport across the PN line during the period from 1993 to
1994 and the period from 1997 to 1998 is also due tothe interannual enhancement of the eddy activity. Since
the anticyclonic eddies intrude into the Kuroshio recirculation region and circulates in the region (see Fig. 9),
the volume transport across the ASUKA line is highlyvariable. The intensification of the anticyclonic Kuroshio recirculation corresponds to the merger of anticyclonic eddies traced back to the region northeast of
Luzon Island (e.g., Fig. 9a). In 1995, the recirculationis reduced by the intrusion of a cyclonic eddy despite
the merger of the anticylonic eddies from the upstream
region.
Both theoretical and observational studies (e.g.,
White and McCreary 1976; Kawabe 1995) suggest that
the Kuroshio path south of Japan is related to variationof the volume transport and the surface velocity at up-

stream locations, for example, the PN line. Figure 21
shows relations among the Kuroshio volume transport,
the surface velocity, and the Kuroshio meander fromthe present model. The large meander is basically associated with large transport and large surface velocity
on an interannual time scale. This is consistent withanother model result, Kagimoto (1999), and supports
the relation obtained from observations (Kawabe 1995).
This typical tendency corresponds to the first meander
from November 1993 to July 1994. However, the large
meander exists even when the transport and surface velocity are near normal. The latter case corresponds tothe second meander from January 1998 to May 1998.
We suggest that the supply of anticyclonic eddies fromthe upstream region as shown by the increase of thevolume transport in 1997 destabilizes the Kuroshio prior
to the second meander (Fig. 20a).
5. Summary and discussion
We have discussed the results from the OGCM experiment for the period from 1992 through 1998 using
the high-resolution nested grid model for the North Pacific. It has turned out that the present model successfully reproduces several important features. Those features are 1) the propagation of anticyclonic eddies andtheir merger with the Kuroshio recirculation in the Shikoku Basin, 2) frequent occurrence of the offshore nonlarge meander owing to the interaction between the Kuroshio and the anticyclonic eddy, 3) the intensificationof the Kuroshio recirculation (identified by the increase

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of volume transports across the ASUKA lines) due tosupply of anticyclonic vorticity prior to the large meander, 4) the large meander triggered by the interaction
between the anticyclonic eddy and the strong Kuroshio
recirculation, 5) the initial growth of the large meander
due to the baroclinic instability, and 6) the demise of
the meander after shedding the cyclonic ring intensified
by the merger of the cyclonic eddy.
A synthesis of these results leads to the following
scenario for the formation of the Kuroshio large meander. At the beginning, anticyclonic eddies are activated near Taiwan or the Philippine coast and advectedby the Kuroshio into the Shikoku Basin. The transport
across the PN line increases by the successive arrivalof those anticyclonic eddies and the anticyclonic Kuroshio recirculation south of Shikoku is intensified by
the merger of those eddies. Then, the Kuroshio large
meander is generated by baroclinic instability triggeredby the interaction with the anticyclonic/cyclonic eddies.
During the meandering period, the meandering cyclonicjet matures by absorbing a cyclonic ring propagatingfrom the Kuroshio Extension and eventually sheds thecyclonic ring. Thus, the large meander state ends. The
above scenario suggests the importance of eddy activities to the Kuroshio meandering and provides a key topredict the ever-mysterious phenomenon of the Kuroshio meander; the eddy activities introduce a favorable
condition for the Kuroshio large meander through intensification of the Kuroshio recirculation.
So far, observational studies have suggested that theKuroshio large meander occurs through generation of asmall meander southeast of Kyushu [so-called trigger
meander according to Solomon (1978)]. The present
model shows that the anticyclonic/cyclonic eddies propagate westward along 298–328N (see Fig. 6d) and interact directly with the Kuroshio south of Shikoku. Since
the actual eddies may interact with the Kuroshio southeast of Kyushu, the concept of the trigger meander might
have captured this possible phenomenon (Endoh andHibiya 2001).
The simulated large meander does not persist longand it changes into the offshore nonlarge meander. The
meander east of the Izu–Ogasawara Ridge and the cyclonic eddy south of the Kuroshio Extension influence
the stability of the large meander in the model (see Figs.
10 and 11). This study suggests that the persistence ofthe Kuroshio large meander is strongly affected by themesoscale eddies generated by flow instabilities. Ichikawa and Imawaki (1994) reported the merger of theKuroshio large meander and the cyclonic eddy originated from the Kuroshio Extension using Geosat data.
They did not clarify how this event influenced the amplitude of the large meander. More intensive observational studies are certainly needed to clarify the interaction of mesoscale eddies with the Kuroshio path variation.
In the present simulation, the Kuroshio large meander
occurs through intensification of the Kuroshio recircu-

VOLUME 34

lation caused by the interannual variation of the Kuroshio transport across the PN line. The volume transport of the Kuroshio increases through amplification of
the anticyclonic eddies originated in the region near theLuzon Island as indicated by the local maximum of the
EKE there (Fig. 5b; also see Figs. 9a,d). More detailed
analysis of eddy activity near Luzon Island is certainly
necessary. We note that the simulated eddy activity fromthe subtropical front east of the Nansei Islands is weaker
than in the observations (Fig. 5). Since mesoscale eddies
in this region are important to generate the variation of
the Kuroshio volume transport (Ichikawa 2001), improvement of the model performance in this region may
lead to a more realistic simulation of the Kuroshio pathvariation.
Acknowledgments. We appreciate useful discussions
with Drs. H. Hukuda and T. Kagimoto during the courseof the present work. Dr. H. Xue kindly provided us withthe code for the linear stability analysis. We are also
thankful to two referees and, in particular, the editor Dr.
L. D. Talley for their constructive comments on theearlier version of the manuscript. This work is part of
the Japan Coastal Ocean Predictability Experiment(JCOPE) started in October 1997 under the initiative of
the Frontier Research System for Global Change(FRSGC), which is supported jointly by National Space
Development Agency of Japan (NASDA) and Japan
Marine Science and Technology Center (JAMSTEC).
The scientific interaction with the IOC/UNESCO
NEAR-GOOS project supported by Ministry of Education, Culture, Sports, Science and Technology(MEXT) was helpful in completing this work.
APPENDIX
Linear Stability Analysis
Linear instability of the velocity profile of the Kuroshio is investigated using a two-dimensional, inviscid
primitive equation model (cf. Xue and Mellor 1993) toclarify mechanisms of the initial growth of the meander.
The governing equations for the disturbances are
]u
]u
]U
]U
1 ]p
1 U 2 fy 1 y
1w
1
5 0,
]t
]x
]y
]z
r 0 ]x]y]y1 ]p
1 U 1 fu
5 0,]t]x
r 0 ]y
b2

1 ]p
5 0,
r 0 ]z

]u
]y
]w
1
1
5 0,
]x
]y
]z

and

]b
]b
]B
]B
1U 1y
1w
5 0,
]t
]x
]y
]z

(A1)

where u, y , and w represent x, y, and z components

OCTOBER 2004

2221

MIYAZAWA ET AL.

of the perturbation velocity vector; p is the perturbation pressure; and b is the perturbation buoyancy,
b 5 2gr(y, z)/r 0 . A steady current U (y, z) is assumed
to flow parallel to the coast, which is in thermal windbalance; for example, f U z 5 B y , where subscripts
indicate partial derivatives. The boundary conditions
are

y 50

at y 5 0,p, u, y → 0

at y → `,w50

at z 5 0,

w 5 2y (]h/]y)

at z 5 2h(y).

and
(A2)

(A3)

Zs
(m)

yf
(km)

y d1
(km)

yd 2
(km)

A0

12 Oct 1993
9 Jan 1998

1.60
1.38

650
655

110
100

36
34

74
66

3.5
4.3

1z 2 Y 2 ,
z

2
i

1

A 5 A0 1 2

z
,
Hd

and



 y d1 2

yd 5 

(A4)

We assume perturbed disturbances of the formu 5 Re{ũ(y, z ) exp[i(s t 1 lx)]},y 5 Re{iỹ (y, z ) exp[i(s t 1 lx)]},u 5 Re{ṽ (y, z ) exp[i(s t 1 lx)]},andp 5 Re{ip̃(y, z ) exp[i(s t 1 lx)]},(A5)

where l is the downstream wavenumber and s 5 s r 1
is i is the frequency. The above system is solved by thespectral technique. It has turned out that a truncationlevel of 28 is sufficient to obtain a convergent solution.
Interested readers are referred to Xue and Mellor (1993)
for details of the spectral technique.
In the present analysis, the meridional section of Kuroshio from 318 to 33.58N at 1368E is adopted. The
bottom topography including a sharp continental slope
is approximated by the following function (Xue andMellor 1993):

2 (A6)

1y 2 ymh(y) 5 H s 1 (H d 2 H s ) 1 1 tanh,2awhere H s and Hd are the minimum depth and the maximum depth in the domain, respectively. The slope isgiven by a and the maximum slope is realized at y 5
ym . The four parameters (H s , H d , a, y m ) are given by
1110 m, 4600 m, 20 km, and 80 km, respectively; they
are determined by the least squares method from themodel topography. The background velocity profile isgiven by the following formula as in Xue and Mellor(1993):

]

2

z
1
,
zs A ydz(y d 2 2 y d1 ) y d 2 2 y d1
2
,
Hd
Hd

if Yi # 0
if Yi . 0,

 yd 2 ,]h.
]yb 5 Re{ib̃(y, z ) exp[i(s t 1 lx)]},[Yi 5 Yi (y) 5 y 2 y f 1 2Then the vertical velocity is transformed into

1

U0
(m s21 )

s

z
.
h(y)

v 5 w 2 (§ 2 1)yProfile onU(y, z) 5 U0 exp

For later convenience, we introduce a bottom-following
coordinate:§511

TABLE A1. Parameters of two velocity profiles.

(A7)
where U 0 is the maximum velocity of the Kuroshio, yf
is the distance of the location of the surface velocity
maximum from the northern boundary, y d is the widthof the Kuroshio, z s is the velocity decreasing rate against
depth, and A is the southward tilt of the maximum velocity with increasing depth. The above six parameters(U 0 , z s , y f , y d1 , y d2 , A 0 ) are determined by the leastsquares method for the 10-day mean velocity data justbefore the meander occurs. Parameters on 12 October
1993 and 9 January 1998 are summarized in Table A1.
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