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Tidal Exchange through the Kuril Straits
TOMOHIRO NAKAMURA, TOSHIYUKI AWAJI, TAKAKI HATAYAMA, AND KAZUNORI AKITOMO
Department of Geophysics, Kyoto University, Kyoto, Japan

TAKATOSHI TAKIZAWA
Japan Marine Science and Technology Center, Yokosuka, Japan(Manuscript received 11 August 1998, in final form 19 July 1999)
ABSTRACTThe tidal exchange between the Okhotsk Sea and the North Pacific Ocean is studied numerically with particularemphasis on the predominant K1 barotropic component. The calculated harmonic constants of the K1 tide in andaround the Okhotsk Sea agree well with those obtained from extensive tide gauge observations. The featuresof the simulated tidal fields are similar to those reported in the literature. Since the K1 tide is subinertial in the
Okhotsk Sea, topographically trapped waves are effectively generated, contributing to strong tidal currents witha maximum amplitude of over 1.5 m s21 in the Kuril Straits. The structures of tide-induced mean flows in most
passages of the straits are characterized by ‘‘bidirectional currents’’ (in which the mean flow exhibits a reversal
in direction across the passages). This feature is clearly indicated in NOAA infrared imagery. The mean transportshows significant net exchange of water via several straits in the Kuril Islands. A transport of about 5.0 Sv (1
Sv [ 10 6 m 3 s21 ) toward the North Pacific is produced by the K1 tide, primarily through the Bussol, Kruzenshterna,and Chetverty Straits. Analysis reveals that the bidirectional mean currents at shallow passages are produced
through the well-known process of tidal rectification over variable bottom topography, whereas in deep passages
such as Bussol Strait, propagating trapped waves along the islands are essential for generating the bidirectionalmean currents. Particle tracking clearly demonstrates these features. The tidal current is therefore thought toplay a major role in water exchange processes between the Okhotsk Sea and the North Pacific.

1. Introduction
The Okhotsk Sea (Fig. 1) is separated from the northwestern Pacific Ocean by the Kuril Islands and the sills
in the straits, almost all of which are shallower than 600
m except for the Bussol (;2200 m) and Kruzenshterna(;1500 m) Straits. However, the transport process between the Okhotsk Sea and the North Pacific Ocean
plays an important role not only in the local environment
but also in determining the water properties of the North
Pacific. The North Pacific is the source of most of thewater in the Okhotsk Sea. This inflow is thought to takeplace mainly through the northern part of the Kuril
Straits, whose neighborhood remains ice free even in
the most severe winters (Reid 1965; Kawasaki and Kono
1994).
The Okhotsk Sea, on the other hand, is thought tohave a significant impact upon the North Pacific. Previous studies in the northwest Pacific found that a plumeof low salinity water at 27.0 s u extended to the south

Corresponding author address: Dr. Tomohiro Nakamura, Department of Geophysics, Kyoto University, Kyoto 606 8502, Japan.
E-mail: nakamura@kugi.kyoto-u.ac.jp

q 2000 American Meteorological Society

from the Kuril Straits and that the confluence of the East
Kamchatka Current and the discharge from the Okhotsk
Sea forms both the Oyashio current, which flows along
the Kuril Islands as part of the western boundary currentof the subarctic gyre, and the Subarctic Current to theeast, thus indicating that the Okhotsk Sea is the most
likely source of low salinity water in the North Pacific(Wüst 1930; Favorite et al. 1976; Talley 1991). Kitani(1973) showed that in the northern Okhotsk Sea, thefreezing of fresh surface waters can form cold saline
waters as dense as 27.05 s u , which still have lower
salinity than the ambient waters at the same density. By
relating an analysis of historical hydrographic data to
Kitani’s (1973) result, Talley (1991) proposed that theNorth Pacific at mid depth is ventilated through sea ice
formation in the innermost part of the Okhotsk Sea andlocal vertical mixing in the Kuril Straits. From potential
vorticity maps, Talley (1993) and Yasuda et al. (1996)
commented that the Okhotsk Sea supplies low salinity
water to the North Pacific Intermediate Water (NPIW)
characterized by a salinity minimum centered at 26.8
s u . These conclusions were also confirmed by recent
studies. Warner et al. (1996) showed that the Okhotsk
Sea is an important location for the ventilation of theintermediate water of the North Pacific based on chlo-JULY 2000

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FIG. 1. Model domain and topography. Contours are at 500, 1000, 3000, and 5000 m. Symbols denote tide gauge locations for theInternational Hydrographic Office (IHO) tidal harmonic constants edited by the Canadian Department of Fisheries and Oceans.

rofluorocarbons (CFCs) observations. Yasuda (1997)
showed the presence of a pycnostad (i.e., a region of
low potential vorticity) at 26.8 s u in the Okhotsk Sea
and concluded that the low potential vorticity waterflowing out into the North Pacific determines even thedensity of the NPIW. Thus, a clarification of the exchange processes through the Kuril Straits is indispensable for a better understanding of water mass formation in the North Pacific (such as the NPIW).
Past studies regarded the current in the Okhotsk Sea
as part of the cyclonic subarctic circulation, which predominantly flows into the Okhotsk Sea through Kruzenshterna Strait and out through Bussol Strait. However,recent observational studies suggest that there is great
difficulty in explaining this in/outflow in terms of geostrophic balance. One reason for this is that the overallsurface dynamic height is higher in the Okhotsk Sea
than in the northwestern North Pacific (Kawasaki andKono 1992). Another reason is that due to the weakstratification, the Oyashio extends to such depths thatit tends to flow along the continental shelf slope along
the Kuril Islands (2000;3000 m deep) and is most likely unable to pass over the shallow sills in the Kuril

Straits. In fact, Stabeno et al. (1994) reported that only
1 of the 14 buoys that were transported along the Kuril
Islands entered the Okhotsk Sea. This indicates that the
Oyashio does not directly flow into and out of the
Okhotsk Sea. Moreover, Leonov (1960) and Moroshkin(1966) mentioned that bidirectional currents occur inmost passages. This picture is clearly seen in the NOAA12 advanced very high-resolution radiometer imagery(Fig. 2). Such current structure cannot be explained bylarge-scale wind-driven geostrophic flow.
These observational results strongly suggest the importance of nongeostrophic components. In fact, tidal
currents, especially diurnal, are dominant in and aroundthe Kuril Straits (e.g., Thomson et al. 1996), and their
speeds reach a few knots. According to previous studies
on tidal exchange (e.g., Huthnance 1973; Zimmerman
1978; Awaji et al. 1980; Robinson 1981), such strong
tidal currents are expected to induce significant meantransport, even if there are sills in the straits. Moreover,tide-induced mean currents allow us to explain the bidirectional structure of the (local) mean currents in thepassages.
Suzuki and Kanari (1986) performed a simulation of1624

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FIG. 2. Infrared image of the Kuril Straits taken from the NOAA-12 satellite on 21 September 1994. (Figure courtesy of Prof. S. Saitoh)

the tidal field in the Okhotsk Sea and showed that in
the Okhotsk Sea, 1) the K1 tide is dominant, M 2 is second, and the O1 component the third largest in elevation
amplitude; 2) diurnal tides propagate from east to west
and have two amphidromic like points near the Soyaand Nemuro Straits; and 3) the semidiurnal tides arepropagating waves with two amphidromic points.
Though they provided many interesting results, the tidal
currents around the straits were not reproduced in sufficiently detailed structure or accuracy since Suzuki andKanari (1986) did not aim at estimating the transport
through the Kuril Straits.
Thus, as a first step toward understanding the transport process and estimating its magnitude, we have investigated numerically the characteristics of the barotropic tides and tidal currents around the Okhotsk Sea.
Investigation of barotropic tides may be a meaningful
first step since stratification in and around the Okhotsk
Sea is weak. We have then estimated the mean transport
through the Kuril Straits and identified the mechanismof tidal exchange. In this paper, though numerical simulations for the K1 , O1 , P1 , M 2 , and S 2 tides have beensuccessfully performed, we discuss our result with aparticular focus on the predominant component, the barotropic K1 tide. The dynamics of other diurnal tides arealmost the same as that of the K1 tide. Because semi-

diurnal tides are considerably smaller than the diurnal
tides in current speed, we describe the M 2 tide only.
Section 2 of this paper describes the numerical model.
Section 3 is devoted to a description of the characteristics of the calculated K1 and M 2 tidal fields and theircomparison with tide gauge observations. In section 4,
tidal exchange is estimated from the Eulerian point ofview and the mechanism causing the transport is investigated in section 5. The results are discussed in section 6 and are summarized in section 7.
2. ModelThe model region shown in Fig. 1 covers the entire
Okhotsk Sea and part of the North Pacific. The open
boundaries are set away from the Okhotsk Sea in orderto reproduce tidal wave propagation from the North Pacific, which is one of the major forcing factors for the
tidal motion around the Okhotsk Sea, and to prevent the
influence of artificial disturbances generated at the open
boundaries on the tidal field around the Kuril Straits.
Since past studies on tidal current dynamics suggest thattidal currents near straits (including the Kuril Straits)
are greatly influenced by topographic features, we resolved the topography of the model region in greater
detail. Using the DBDB5 topographic data (National

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FIG. 3. Calculated coamplitude lines of tidal elevation for (a) the K1 tide and (b) the M 2 tide. The contour interval
is 10 cm.

FIG. 4. Calculated cophase lines of tidal elevation for (a) the K1 tide and (b) the M 2 tide. The contour intervals
are 1 lunar hour.

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FIG. 5. The correlation coefficients between model results and observed harmonic constants for(a) the K1 tide, (b) the M 2 tide, and (c) the K1 tide (for the Kuril Straits only).

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Geophysical Data Center, Boulder, Colorado), the model
domain is divided into 5 km 3 5 km grids.
The numerical model is the same as that used by
Hatayama et al. (1996), with the familiar barotropic tidal
equations given as]u
1 (u · =)u 1 f k 3 u 5 2g=(a 0h 2 b0 z )]t
1 A H¹ 2 u 2]h
1 = · [(H 1 h)u] 5 0,
]t

ku|u|
,
H1h

(1)
(2)

where (x, y) are eastward and northward coordinates; tis time; h(x, y, t) is the surface elevation, z(x, y, t) is theequilibrium tide describe below; u(x, y, t) is the horizontal velocity vector; H is the depth; f 5 f 0 1 by (b5 2.28 3 10213 cm21 s21 ) is the Coriolis parameter; gis the gravity acceleration; k is the bottom friction coefficient; and A H is the horizontal eddy viscosity coefficient. It should be noted that the scheme used in thismodel conserves both mass and enstrophy, as recommended by Huthnance (1981), in order to prevent spurious contributions to the torque balance, which determines the residual current strength.
The parameters a 0 and b 0 account for the effect of
the tidal potentials, earth tide, and loading tide. Here
we set a 0 5 0.900, b 0 5 0.690 for the K1 component
according to Schwiderski (1980). Although the TOPEX/POSEIDON Satellite Tidal Committee recommends
somewhat difference values of a 0 5 0.940 and b 0 5
0.736, the former values give better agreement with theobservations.
The equilibrium tide z is expressed asz 5 K sin2f cos(st 1 l )(3)for diurnal andz 5 K cos 2 f cos(st 1 2l )(4)

for semidiurnal tides, where K and s are the amplitudeand frequency taken from Schwiderski (1980), and l
and f are longitude and latitude, respectively. The astronomical arguments are neglected since tidal fields arecalculated for each tidal component.
The bottom stress is added via a quadratic law withk 5 0.0026. This formulation makes it possible for thebottom stress to generate relative vorticity around thestraits as described in section 4 (the dependency on thisfriction scheme will be discussed in section 7). In thedetermination of the horizontal eddy viscosity coefficient A H , we used the formulation by Schwiderski(1980) in which A H depends linearly on the horizontal
and vertical mixing lengths as

A H (x, y) 5 a h DLH(x, y),(5)where DL is the grid length (constant in this model) anda h the reduced eddy coefficient determined to be 7.5 31026 (s21 ) by trial and error to achieve the best agreement with observations. This value gives A H 5 7.5 3
10 5 cm 2 s21 at 2000-m depth.
The boundary conditions are set as follows. A noslip condition is imposed at the land boundaries. At the
open boundaries, the tidal elevation is specified using
the results of Schwiderski (1979, 1981) with the exceptions of the Soya and Tartar Straits, where it is given
from tide gauge observations near the open boundaries.
Thus, the model is forced by these boundary oscillationsin addition to the effects of the tide generating potential,
the earth tide, and the ocean loading tide. To reduce
artificial disturbances at open boundaries due to wave
reflection, Orlanski’s (1976) radiation condition for velocity is used together with the sponge zone condition
within 5 grid points from the open boundaries whereA H is amplified linearly.
The initial conditions are zero currents and a flat sea
surface. We performed 24 cycles of the integration foreach tidal component, by which time the model ocean
reached an almost steady oscillation and the final cycleof simulation is used for the analysis described below.
3. Tidal fields in the Okhotsk Sea
The harmonic constants (sea-level amplitude andphase) are calculated at every grid point, and the spatial
distributions of the coamplitude and cophase lines forK1 and M 2 tides are shown in Figs. 3 and 4, respectively.
These distributions are qualitatively consistent with previous studies (Ogura 1923; Suzuki and Kanari 1986;
Mazzega and Bérge 1994). To estimate water exchange
quantitatively, a more stringent check on our model result is required. Thus we made a comparison with theInternational Hydrographic Office (IHO) tidal harmonic
constants, the locations of which are shown in Fig. 1.
For the predominant K1 tide component, the correlation coefficients between the calculated and the observed harmonic constants are high (0.904 for phaseand 0.976 for amplitude) in the whole region (Fig. 5a).
Although the amplitudes at a few sites are overestimatedcompared with the observational values, the points withthe largest discrepancies are around the northern coastof the Okhotsk Sea and the overestimate is insignificant
in other regions. The correlation coefficients for data in
the Kuril Straits only are somewhat lower (0.814 forphase and 0.907 for amplitude in Fig. 5c) than those forthe whole region, but still remain high.
Further, we estimate the root mean square (rms) errorof the calculated K1 tide over the entire region from theexpression

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RMS 5

1
N

O [E
N

1
T

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]

1/2

T

{A M cos(s t 2 PM ) 2 A O cos(s t 2 PO )}2 dt

0where N is the total number of tide gauge observations,
T is the tidal periods, s the frequency, A and P theamplitude and phase, respectively, and the suffixes M
and O denote the calculated and observed harmonic
constants, respectively. The calculated rms error is 8.06
cm over the whole region and 6.75 cm in the Kuril
Straits.
Owing to the lack of current measurements, we cancompare the model results with observation only in elevation data. Although it is not safe to assume that goodcorrelation with elevation data implies good model estimates of currents, we believe that, at least qualitatively,
the features of current field are well reproduced. In aquantitative sense, the current field is probably underestimated as will be discussed in section 7.
For the M 2 tide, the correlation coefficients (Fig. 5b)
are also high (0.825 for amplitude and 0.929 for phase).
The calculated rms error is 12.39 cm, since the amplitude is slightly overestimated. Most of the sites withsignificant discrepancies in amplitude are located in
Shantarsky and Shelikova Bays in the northern Okhotsk
Sea, where complicated coastlines are not sufficiently
resolved. When the data at such sites are removed, therms error becomes 9.5 cm. Thus it can be said that thecalculated M 2 tidal field is similar to that observed.
The K1 tide is the largest component in elevation amplitude in the eastern Okhotsk Sea. From Fig. 4a, it canbe seen that the K1 tidal field in the Okhotsk Sea ismostly determined by the tidal wave coming from theNorth Pacific, which enters the Okhotsk Sea mainly
through the northeastern part of the Kuril Straits. Thesewaves progress directly in a roughly westward direction
and along the coast in a cyclonic fashion, and an amphidromic-like point appears on the east coast of Sakhalin. Around the Kuril Straits, cophase lines are complicated because of wave trapping along the islands. The
elevation amplitude is large at the northeastern part ofthe straits and, in general, increases with decreasing
depth toward the northern part of the Okhotsk Sea, witha local maximum of about 0.8 m near the Kushevarova
Bank. In Shelikhova Bay, located in the northeast of the
Okhotsk Sea, the amplitude reaches a maximum valueof 4.2 m as a result of resonance. The natural period of
Shelikhova Bay 21 h and its cooscillating amplification
factor is about 5 according to Suzuki and Kanari (1986).
The amplitude in most of the interior of the bay, then,comes to 5 m with a modeled amplitude of about 1 m
at the mouth of the bay. The actual value agrees wellwith the model value, considering that cooscillation
does not take place in Penzhinskaya Bay, the interior,(6)part of Shelikhova Bay, in our model. We can also recognize a local minimum near Cape Yelizavety (north of
Sakhalin) and relatively higher amplitude along thecoasts (to the west of Kamchatka, the east of Sakhalin,
and the coast of Okhotsk), which is caused by waves
propagating as shelf waves along the coasts as suggested
by Odamaki (1994).
The elevation amplitude of the M 2 tide (Fig. 3b) iscomparable to that of the K1 tide and is even larger
around the northwestern coast of the Okhotsk Sea. The
M 2 tide in the Okhotsk Sea is also largely determinedby the incoming tidal wave from the North Pacific (Fig.
4b). After passing through the Kuril Straits, this wave
propagates roughly northward as a freely propagating
wave, producing two amphidromic points: one in Shelikova Bay and the other near Cape Yelizavety. The M 2
tidal wave partly cooscillates in the northwest and northeast bays, where the elevation amplitude is large (cooscillation in the innermost regions of Shelikova Bay results in a maximum amplitude of 3.6 m.
To study the features of the tidal currents in the
Okhotsk Sea, we calculated the ellipse parameters (major and minor semiaxes and angle of inclination) shownin Fig. 6, using the oscillatory component of the calculated velocities. The K1 tide has the greatest current
speed. The currents are strong and their tidal ellipses
are circular around topographic feature, such as the Kuril Straits and the Kashebarova Bank. For example, thepeak velocity in the northern part of the Kuril Straits
attains about 1.6 m s21 , though the maximum value isachieved within the cooscillating Shelikhova Bay. Thesefeatures are associated considerably with the fact thatthe period of the K1 tide (23.93 h) is longer than theinertial period around the Kuril Straits (15.7–17.0 h).
Subinertial tidal currents generate subinertial waves
trapped at islands and/or submarine banks (e.g., Chapman 1989). The topographically trapped waves are subjected to continuous forcing and are enhanced until
damping by friction or viscosity becomes important.
The resulting amplification of trapped waves is mosteffective when the resonance occurs but is significant
over a wide range of frequency if the tidal frequency
is subinertial (e.g., Haidvogel et al. 1993).
The presence of such topographically trapped waves
is clearly seen in the time series of the along-isobathcomponent of velocity around the Kuril Straits (Fig. 7).
In particular, clockwise propagation of positive anomalies around Simusir Island, the Urup Strait and Etorof
Island, and a bank east of the Kruzenshterna Strait canbe easily distinguished. Thus, the K1 tidal field aroundJULY 2000

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FIG. 6. Calculated tidal ellipses for (a) the K1 tide and (b) the M 2 tide at every 16 points. The magnitude of velocity
is indicated in each figure.

the Kuril Straits is composed of both large-scale K1 tidal
waves coming from the North Pacific and topographically trapped waves. The latter amplifies the currents
and makes tidal ellipses circular around the Kuril Straits.
Therefore the K1 tide is expected to cause significant
tide-induced mean flow around the straits, which will
be discussed in section 4. The along-isobath componentof velocities associated with topographic waves is nearlyin geostrophic balance since these waves are characteristic of shelf waves and topographic Rossby waves (andKelvin waves). This may imply that the time-average
currents are also roughly geostrophic.
Moderately strong currents near the coasts, where theelevation amplitude is also appreciably larger than thatof the surroundings (in Fig. 3a), are thought to be causedby the presence of shelf waves due to the subinertial
tidal frequency. Such shelf waves are identified fromobservations along the Hokkaido coast (Odamaki 1994)
and from numerical simulation along the Sakhalin coast(Suzuki and Kanari 1986).
The M 2 tide (Fig. 6b) is substantially smaller in current speed than the K1 tide, despite the fact that theelevation amplitude is comparable. In contrast to the K1
tidal currents, the maximum value of the M 2 tidal currents around the Kuril Straits reaches only 0.6 m s21
although the currents are strong within the cooscillatingbays in the interior of the Okhotsk Sea. Since the maximum frequencies of barotropic topographic Rossby
waves is less than the inertial frequency, topographicallytrapped waves cannot be generated by superinertial M 2
tides. Indeed, the tidal ellipses are not circular aroundthe Kuril Straits and the Kashebarova Bank. Thus, amplification hardly occurs and the M 2 currents are weakin the Kuril Straits, indicating that the mean currents
induced by the M 2 tide are probably not significant.
4. Eulerian mean currents and estimates of tidal
exchange through the Kuril Straits
Figure 8 shows the depth-averaged velocity vectorsof the Eulerian time-averaged currents over a cycle. For
the K1 tide, significant mean currents near the Kuril
Islands can be seen. These currents become especiallylarge in the northern part of the Kuril Straits, where themaximum velocity exceeds 0.7 m s21 , and have in- andoutflow components, suggesting that the tidal currents
can cause significant long-term exchange through the
Kuril Straits. Another interesting feature is the meancurrent along the coast (with land on the right). Thesemean currents are almost in geostrophic balance, as expected in section 3. On the contrary, the mean currents
around the Kuril Straits induced by the M 2 tide are muchsmaller than those from the K1 tide (Fig. 8b).
For closer examination and estimation of the tidal
exchange, we calculated the streamfunction of the mean
volume transport C, defined as

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FIG. 7. Temporal change of along-isobath components of velocity around the Kuril Straits with an interval of 0.25 tidal cycle for theK1 tide. In these panels, clockwise propagation of the disturbance around Simusir Island (the Urup Strait) is indicated by A (B). The contour
intervals are 7.5 cm s21 . The current in the non shaded areas (the thicker shaded areas) flows with the shallower water on its right (left),
and the current speeds in the thinner shaded areas are less than 7.5 cm s 21 .

1(u, y ) 5 2

2

1 ]C 1 ]C,,
H ]y H ]x(7)with the zero point taken at the Kamchatka Peninsula.
The result for the K1 tide is shown in Fig. 9. In general,the mean currents are almost parallel to the isobaths andform clockwise mean currents around the islands, leading to bidirectional mean currents in most passages andstrong clockwise along-sill (or along-island) mean currents. In particular, a bidirectional flow is pronounced
in the Bussol and Kruzenshterna Straits that are relatively wide and deep, while the along-sill currents arestrong between the two straits. There is an intense clockwise circulation over the bank to the southeast of Shashikotan Island and an anticlockwise circulation over the
Kuril Basin along the isobath.
Taking the bidirectional current structure into ac-

count, we estimated the total transport for all the straits
with this mean current field. For the K1 tide (Fig. 10),
we can easily see that most of the exchange occurs at
Bussol Strait and the northeastern part of the Kuril
Straits, and that little transport occurs through the southwestern part where depths are shallow and large islands
are present. In terms of magnitude, the net transport ofabout 5.0 Sv from the Okhotsk Sea to the North Pacificoccurs mainly through the Bussol (2.4 Sv), Kruzenshterna (0.8 Sv) and Chetverty (0.8 Sv) Straits. Inflow
transport is largest (1.45 Sv) through Bussol Strait followed by 1.2 Sv through Kruzenshterna Strait. Watertransported through the straits is carried to the southwest
on the Pacific side and to the northeast on the Okhotskside along the islands by along-sill mean flow. Whenneglecting the bidirectional flow (i.e., estimating thetransport per strait) the total transport comes to 2.2 Sv.

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FIG. 8. Eulerian mean currents induced by (a) the K1 tide and (b) the M 2 tide. The mean currents in regions
without arrows are less than 0.5 cm s21 .

This indicates that in order to estimate the total transportobservationally, sufficient current meters need to be deployed to detect the bidirectional current structure.
Transport estimates made with the O1 , P1 , M 2 , andS 2 tides are 3.5 Sv, 1.0 Sv, 0.3 Sv, and 0.1 Sv, respectively, showing that transport induced by diurnal tides
is much greater than that by the semidiurnal tides. With
the maximum tidal speeds of 160, 110, 85, 65, and 25
cm s21 for the K1 , O1 , P1 , M 2 , and S 2 tides in the Kuril
Straits, respectively, the ratios of transports among thediurnal components are almost proportional to their flow
speeds. This is also the case for the semidiurnal components but does not hold between diurnal and semidiurnal tides. The transport by diurnal tides is considerably larger than that expected from the ratio of diurnal
to semidiurnal current speeds. For example, the K1 transport is about 17 times as large as the M 2 transport whereas the K1 flow speed is only about 2.5 times that of M 2 .
Thus, whether tides are subinertial or not is anticipatedto have a large effect on the difference in mean transport
between the diurnal and semidiurnal tides.
5. Formation mechanism of bidirectional meancurrents in the Kuril Straits
a. Vorticity analysis
FIG. 9. Mean transport stream function for the K1 tide, which is
set to be zero at the Kamchatka Peninsula. The contour units are 0.4
Sv and values in shaded areas are positive.

In order to investigate the formation mechanism of
the mean flow, we first make an analysis of vorticity

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FIG. 10. The estimate of the mean transport through the Kuril Straits induced by the K1 tide.
Upward and downward arrows represent inflow and outflow, respectively.

focusing on the K1 case, because the K1 component dominates the mean transport and because the formation
mechanism may be helpful in clarifying the cause forthe difference in mean transport between the diurnaland semidiurnal tides. The vertical component of vorticity v is defined as the depth-averaged relative vorticity

v5

]y
]u
2 .
]x
]y

(8)

Figure 11 shows the Eulerian mean relative vorticity
over a cycle around the Kuril Straits. According to previous studies of tidal rectification (e.g., Robinson 1981),
the mean vorticity generally acquires negative values
on the sill top and positive values at the base of the sill,
which, in turn, produce a clockwise mean current along
the sill since mean currents are almost zero far awayfrom the sill. Such a pattern is clearly seen in shallow
straits (200;600 m depth). A close look at Fig. 11
shows that as the sill gets higher in the vicinity of theislands, the magnitude of the negative mean vorticity
on the top of the sill becomes larger. Supposing massconservation of the along-sill mean currents, such vorticity changes in shallow straits lead to clockwise mean
circulation on island scales, thus creating bidirectionalmean currents in shallow straits as is shown schematically in Fig. 12a.
In deep straits, on the other hand, the mean vorticity
distribution on the sill top has positive values near theislands (except for thin viscous boundary layers closer
to islands). This vorticity pattern differs greatly fromthat in shallow straits in spite of the presence of similarbidirectional currents (Fig. 11). To investigate this problem, we direct our attention to Bussol Strait, where the

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FIG. 11. The Eulerian mean relative vorticity over one cycle around the Kuril Straits for the K1 tide. The contour interval
is 1 3 1025 s21 . Values in nonshaded areas and the thicker shaded areas are positive and negative, respectively, and theabsolute values in the thinner shaded areas are less than 1 3 1026 s21 .

sill is very deep, bidirectional currents are dominant,and hence most of the outflow from the Okhotsk Sea
occurs. The vorticity distributions around the strait are
as follows. (i) A positive mean vorticity is located in
the western part of Bussol Strait (near the shallow Urup
Strait). (ii) In the central part of Bussol Strait, a negative
mean vorticity is present over the deep sill. (In contrast
to shallow sills, the positive mean vorticity at the footof the sill is too small to be distinguished and has little
influence.) (iii) A positive mean vorticity is located in
the eastern part of Bussol Strait. The mean vorticity
distribution (i) produces strong clockwise mean currents, flowing out with a transport of 1.4 Sv throughthe western part of Bussol Strait to the southwest along
the Kuril Island Chain. The distributions (ii) and (iii)merge to produce a mean outflow of 1.0 Sv to the southeast from the middle of Bussol Strait [intermediate to
the distributions (ii) and (iii)]. The distribution (iii) produces a strong mean inflow of 1.45 Sv along Simusir
Island (east of Bussol Strait). It is worth mentioning thatthe mean vorticity values in Bussol Strait are so smallthat a slow mean flow is produced, though the deep
strait (over 2000 m) makes the overall mean transport
significant. In this way, the mean vorticity produces
bidirectional mean currents and a slow centered-outflow
in Bussol Strait, as is shown schematically in Fig. 12b.
To examine the cause for the different vorticity distribution between deep and shallow straits, we first diagnose the temporal evolution of the vorticity balance

in a similar way to Ridderinkhof (1989), because ourinterest is in the generation mechanism of bidirectional
current structures in the Kuril Straits. Taking the curlof the momentum equation (1) yields the vorticity equation asDv
5 2 f = · u 2 v= · u
(a)
(b)
Dt
1 ku 32

1=|u|
1
1 ku 3 |u|=
H1h
H1h

k |u|
v
H1h

1 A H¹ 2v ,
(e)

2

(c)

(9)

(d)

where D/Dt represents the time variation in the Lagrangian frame and the b term and the terms arisingfrom the spatial variation of horizontal eddy viscosity
are neglected because of their smallness. The sum ofterms on the rhs of Eq. (9) represents the mechanisms
generating and damping vorticity. Terms (a) and (b)generate vorticity by stretching or squeezing of a watercolumn through the conservation of potential vorticity.
For term (a), the vorticity generated by stretching(squeezing) acquires positive (negative) values. Term(c) represents vorticity generation due to velocity shear(for a quadratic friction law) and the horizontal gradientof water depth transverse to the direction of the tidal

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VOLUME 30

thought to be similar in both shallow and deep straits,
despite that their vorticity distributions differ. This implies the presence of a different physical process fromthe previous tidal rectification theory (e.g., Robinson1981) for the formation of the mean circulation in deep
straits. Previously, vorticity (nonaveraged) was generated by tidal currents over variable topography and redistributed by advection, eventually forming a time-averaged vorticity distribution with positive (negative) located on the shallower (deeper) side when stretching/squeezing terms are dominant in the vorticity equation.
This is certainly the case for the present shallow straits
but is not the case for the deep straits. The most likely
candidate for generating the mean circulation in deep
straits is the effect of topographically trapped waves,discussed below.
b. Generation mechanism of bidirectional meancurrents in deep straits

FIG. 12. Schematic illustrations of mean currents associated withthe mean vorticity distribution in (a) shallow straits (200;600-m
depth) and (b) deep straits (the case of the Bussol Strait).

flow. Term (d) represents the damping part of bottom
friction. Term (e) causes a damping of vorticity throughthe horizontal eddy viscosity.
Though the vorticity balance is examined during atidal cycle, we show the spatial distributions of eachterm on the rhs of Eq. (9) only when the outflow speed
is a maximum in Bussol Strait (Fig. 13). The featuresdescribed below are essentially similar for the other tidal
phases. In general, as in the previous studies, the stretching/squeezing term (a) from the Coriolis effect is mosteffective in vorticity generation while the other stretching/squeezing term (b) is less so, with the exception thatterm (b) is quite significant in regions of strong relative
vorticity such as over the bank to the southeast of Shashikotan Island. The vorticity generation due to bottom
friction is much smaller than that due to these terms
except in spatially small shallow regions (depth less than
100 m) such as in the vicinity of Onnekotan Island,
where water exchange between the Okhotsk Sea and theNorth Pacific is not significant. The damping of vorticity
is caused primarily by bottom friction, and the effect ofhorizontal eddy viscosity is negligible when comparedto that of bottom friction. Thus, the vorticity sources
for generating the bidirectional current structure are

To identify a possible role for topographically trappedwaves (TTW) in the vorticity balance, we first look at
the temporal change of vorticity around the deep Bussol
Strait (Fig. 14). On the northern side of the shallow
Urup Strait (west of Bussol Strait), a significant portionof positive vorticity (nonshaded in Fig. 14) generated
at flood tide (after 0 h; Fig. 14a) propagates clockwise
and enters the deep Bussol Strait (Figs. 14b–c), while
negative vorticity (thicker) at ebb tide (Fig. 14e) scarcely moves (Figs. 14f–h). Similar propagation is seen to
the north of Simusir Island (east of Bussol Strait). Fromthese results, one may speculate that the difference inpropagation of positive and negative vorticity anomalies
may create positive mean vorticity in the southwesternand northeastern parts of Bussol Strait, which is capableof producing bidirectional mean currents as illustrated
in Fig. 12b.
In previous studies on subinertial tidal currents (e.g.,
Chapman 1981; Kowalik and Proshutinsky 1995), these
vorticity anomalies propagating along isobaths are attributed to TTWs. In fact, the frequency of these anomalies is estimated as 0.5 3 1024 (rad s21 ), using a linear
dispersion relation of TTW on a constant slope a withmean depth H,s 5 2f1

21

2 , (10)a1 a2
f2
k k2 1 l 2 1
1
2
H
4H
gH

where s is the frequency, k is the wavenumber in thealong-isobath direction and l in the across-isobath direction. These values are taken from the figure (H ;700 m, a ; 0.1, 2p /k ; 40 km, 2p /l ; 40 km). The
estimated frequency roughly agrees with the K1 frequency (0.7 3 1024 rad s21 ), implying that these anomalies are TTWs generated by the incoming K1 tidal wave.
Although most previous studies on tidal exchange have
paid little attention to the role played by TTWs, theabove facts strongly suggest that the propagation of vor-

JULY 2000

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NAKAMURA ET AL.

FIG. 13. The distributions of the generation and damping
terms in the vorticity Eq. (9) for the K1 tide, when theoutflow speed is maximum around the Bussol Strait: thepanels (a)–(e) correspond to the terms (a)–(e) in Eq. (9),respectively. The contour intervals are 1 3 1029 s22 forthe terms (a)–(d) and 1 3 10210 s22 for the term (e). Values
in nonshaded areas and the thicker shaded areas are positive and negative, respectively, and the absolute values
in the thinner shaded areas are less than one tenth of theminimum contour value.

ticity anomaly as TTWs may be effective in the vorticity
balance around the Kuril Islands for subinertial tides
such as the K1 tide. Focusing on this point, we investigate the generation mechanism of mean vorticity in
the Kuril Straits.
We begin with the following vorticity equation,]v
1 u · =v 5 2 f = · u 1 damping,
]t

(11)

where only the dominant vorticity-generation term (a)in Eq. (9) at the Kurils is taken into account for simplicity. Note that, though the b term permits the presence of barotropic Rossby waves, this term can be neglected in comparison with topographic variation in the
Kuril Straits. This is because the topography influence

dominates b when |=H|/H . b / f 0 (e.g., LeBlond andMysak 1978), which is roughly estimated as the inequality 1027 k 1029 .
Since the propagation of TTWs such as topographic
Rossby waves relates to vorticity change in space andtime, we separate the velocity field according to Holton(1979) as follows. The Helmholtz theorem states thatany velocity field V can be divided into a nondivergent
part V c plus an irrotational part Virr such thatV 5 V c 1 Virr ,(12)where = · V c 5 0 and = 3 Virr 5 0. If the velocity
field is two dimensional and is denoted by V 5 (U, V),
the nondivergent part can be expressed in terms of thestreamfunction c defined by

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JOURNAL OF PHYSICAL OCEANOGRAPHY

1(U c , V c ) 5 2

2

]c ]c
,
.
]y ]x

(13)

While previous studies focus mainly on the advectionof vorticity in the across-isobath direction, TTWs propagate along the isobaths. Taking this fact into account,
we take the coordinate x (y) to represent the northeast(northwest) direction, which is almost along (across) thesills in the Kuril Island Chain. Accordingly, H x K H yand the component U basically represents the alongisobath velocity component and V the across-isobathcomponent. The across-isobath velocity V generates a
net across-isobath advection of vorticity through thewell-known mechanism of tidal rectification over variable topography, thus producing mean along-isobath
currents (e.g., Robinson 1981). The vorticity can also
be advected in the along-isobath direction by the velocity component U.
The stretching/squeezing of water columns by the
motion of the free surface can be neglected whenf 2 L 2 /gH K 1, where L is the horizontal length scaletaken as the lesser of the topographic length scale or
wavelength (e.g., LeBlond and Mysak 1978). In the K1
case, L is less than several tens of kilometers, giving adivergence parameter f 2 L 2 /gH of the order of 1022 .
Thus a rigid lid approximation is a reasonable simplification. Hence, the continuity equation (2) yields
H= · u 5 2=H · u.

(14)

Using the notation for V given in Eq. (12), the rhs of
Eq. (14) is written as
2=H · V 5 2=H · (V c 1 Virr ).

(15)

Note that under the present approximation, V represents the divergent component when neglecting the contribution of sea surface elevation to the volume transport.
Substitution of Eqs. (12)–(15) into Eq. (11) yields
irr1]t 1 V · =2v 2 H 12H ]y 1 H ]x 2
]

]c

f

x

5

f
=H · V irr 1 damping.
H]c

VOLUME 30

from topographic rectification of the K1 current over thesill. Another conspicuous feature in Fig. 15 is the generation of significant vorticity anomalies in both positive
and negative senses on the down- and upstream sidesof the sill, respectively. The vorticity anomalies largely
propagate along the isobaths [for example, northeastward (southwestward) propagation of the positive (negative) vorticity anomaly in Figs. 15a,b]. This propagation could be associated with TTWs because the propagation of TTWs is caused by the difference in themagnitude of vorticity in the along-isobath direction(e.g., Longuet-Higgins 1965) and swifter currents within
the strait do, in fact, produce stronger vorticity than inother regions. In the latter half cycle, almost all of thesefeatures can be seen but their phase is reversed. However, the propagation of vorticity anomalies is in thesame direction as in the previous half cycle.
Considering that an incident K1 wave has very small
vorticity in deep regions (one or two orders of magnitude less than in the straits; Figs. 14 and 15) and thatvorticity change is caused almost solely by the changeof f/H, the component V c in a slope region may be
dominated by the contribution from the vorticity generated by the stretching/squeezing effect. To conveniently identify the role of TTWs in the vorticity balancearound the Kuril Islands, we define the velocity comc
ponent associated with TTWs (VTTW) as that representing the propagation of the vorticity anomalies. The relevance of this will be discussed later. The remainderc(Vrec) is hereafter called the rectified temporal current
in parallel with previous tidal rectification studies (e.g.,
Robinson 1981), although it is in general difficult toseparate the velocity components associated with TTWs
from the rectified temporal currents because both are
topographically produced.
Taking the above facts into account, we therefore separate the nondivergent velocity component V c ascc
V c 5 VTTW
1 Vrec.

(17)

These are expressed in terms of the streamfunctions as

y

(16)

To examine the vorticity balance in the vicinity of theKuril Straits in detail, we look at the temporal changesof both velocity and vorticity in the shallow Urup Strait
during one cycle as an example (Fig. 15). As the northwestward K1 current flowing into the Okhotsk Sea runs
over the sill, it is clear that a strong northeastward current appears over the sill after 0.25 cycle (Fig. 15b) due
to the occurrence of the along-isobath current arising

1 ]y , ]x 2,]c ]cV 5 12
,
,
]y
]x 2

c
VTTW
5 2

c
rec

]c TTW ]c TTW

rec

rec

(18)

where cTTW and crec are the streamfunctions for the
TTWs and the rectified current.
We assume that the wave solution for the streamfunction cTTW associated with TTWs is given ascTTW 5 ĉTTW e i(kx1ly2st) ,(19)→

FIG. 14. The time series of vorticity anomalies around Bussol Strait after (a) 0.0, (b) 0.125, (c) 0.25, (d) 0.375, (e) 0.5, (f ) 0.625, (g)0.75, and (h) 0.875 cycle. The contour interval is 1 3 1025 s21 . Values in non shaded areas and the thicker shaded areas are positive andnegative, respectively, and the absolute values in the thinner shaded areas are less than 0.5 3 1025 s21 .

JULY 2000

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JOURNAL OF PHYSICAL OCEANOGRAPHY

where k and l are the wavenumbers in the x and y directions, respectively. Using Eqs. (17)–(19), the second
term on the lhs of Eq. (16) becomesffc
2 (2Hx il 1 Hy ik)c TTW 2 =H · (V c 2 VTTW)
H
H
5 (cx ik 1 cy il)(2k 2 2 l 2 )c TTW 2fc=H · Vrec
Hfc=H · Vrec.
H

5 c · =v wave 2(20)

Here, vwave is the vorticity component associated withcTTW such thatc
= 3 VTTW
5 ¹ 2 cTTW 5 vwave .

(21)

The quantity c 5 (c x , c y ) in Eq. (20) represents the phasespeed of the vorticity anomalies and is given by
cx 5

Hy

f
,
k 1l H2

Hx f
cy 5 2 2.
k 1 l2 H

2(22)Interestingly, this is the same form as the phase velocity
of a nondivergent linear topographic Rossby wave (e.g.,
Cushman-Roisin 1994). Since H x K H y , the propagationof the vorticity vwave is dominated by the component c x .
Substitution of Eq. (20) into Eq. (16) yields

1]t 1 (V 1 c) · =2v
]

5

wave

1

1]t 1 V · =2(v 2 v )]fc=H · (V irr 1 Vrec
) 1 damping.
H

wave

(23)

Equation (23) shows that the interaction between the
net across-sill (across-isobath) current and the topographyfc=H · (V irr 1 Vrec)
H
generates two vorticity components that are governedby different dynamics. Note that as in previous studies,c
Vrec
is dominated by the along-isobath component and,hence, the effect of the current associated with the K1
tidal waves (;Virr ) coming from the North Pacific dominates the vorticity generation in the Kuril Straits. The
vorticity component (v 2 vwave ) is transported only by
advection and causes the well-known process of tidal
rectification (e.g., Chen and Beardsley 1995). In contrast, the transport of the vorticity anomaly vwave is driven not only through advection by the currents (U, V)
but also by the propagation of TTWs with phase speedc. This means that there are additional vorticity changes
caused by the propagation of TTWs at all locations
along the wave paths. Accordingly, TTWs are able toaffect the mean vorticity field at locations (e.g., the deep
Bussol Strait) well away from the generation region(e.g., the shallow Urup Strait). This effect has important
implications but is absent unless both subinertial tides

VOLUME 30

and the variation in the along-isobath direction are considered.
To easily assess whether or not the treatment of TTWs
in this study [Eqs. (17)–(19)] is reasonable, we make acomparison between the intrinsic phase speed c x estimated from Eq. (22) and that appearing in the model
results, for example, around Urup Strait as shown in
Fig. 15. Equation (22) for the intrinsic phase speed c xof vwave in the along-isobath direction yields approximately 60.3 m s21 on the northern (southern) side of
the sill using the values estimated earlier. On the other
hand, in Figs. 15a,b, the apparent speed of the positive(negative) vorticity anomaly corresponding to A (B) in
the along-sill direction is estimated to be about 11.0 m
s21 (20.1 m s21 ). According to Eq. (23), the intrinsic
phase speed c x of these anomalies is given by subtracting
the along-isobath current speed U from the apparent
speeds of the vorticity anomalies. Since the corresponding speed U calculated in the model is about 10.6 m
s21 (10.2 m s21 ) for the positive (negative) anomaly,so the intrinsic phase speed c x of the modeled positive(negative) anomaly seen in Fig. 15 is estimated approximately as 10.4 m s21 (20.3 m s21 ), in good agreement (approximately 80%) with the value of c x of thevorticity anomaly corresponding to vwave from Eq. (22).
Note that both anomalies move with the shallower sideon the right in a similar sense to TTWs. This provides
some support for the treatment of TTWs in this study.
Based on the above consideration, the formation of
the bidirectional mean current in deep straits such as
Bussol Strait can be interpreted as follows. In the Northern Hemisphere, the intrinsic phase velocity c of TTWs
is in the along-isobath direction with shallower regions
on the right. When the K1 tidal current moving toward
the Okhotsk Sea flows over a sill such as that in theshallow Urup Strait adjacent to the deep Bussol Strait,
the along-sill (along-isobath) current U is generated on
the sill slope and flows like a rectified temporal current
with a positive (negative) value of topographically generated vorticity to the north (south), as seen in Fig. 15b.
At this moment, on the positive vorticity side to thenorth of the sill top, the along-sill current (U) is in thesame direction as the intrinsic phase velocity (c x ) of the
TTWs with positive vorticity anomaly, as is shown schematically in Fig. 16b. In contrast, on the negative vorticity side to the south of the sill top, the along-sillcurrent (U) is in the opposite direction to the propagation of TTWs of negative vorticity anomaly. When
the K1 tidal current reverses, a similar situation occurs
but the positive (negative) vorticity side is to the south(north) of the sill. Consequently, the TTWs with positive
vorticity anomaly appearing on the downstream side of
the sill move faster than those with negative vorticity
on the upstream side of the sill due to the difference inthe direction between the phase velocity (c x ) and thealong-sill current (U) during the ebb and flood tides as
seen in Fig. 15. This means, in a sense, that the magnitude of the positive vorticity flux created by TTWs inJULY 2000

NAKAMURA ET AL.

the along-isobath direction is larger than that of thenegative vorticity flux over a tidal cycle, and eventuallyleads to the presence of a net flux of positive vorticity
in a clockwise sense around the islands as schematicallyillustrated in Fig. 16c.
In shallow straits, since TTWs hardly cross the shallow sills, the above process has little effect on the formation of mean vorticity. In contrast, in deep and widestraits such as the Bussol and Kruzenshterna Straits,mean vorticity generation through the classical tidal rectification process is small but the TTWs coming fromthe adjacent shallow straits such as Urup Strait can crossthe deep sills, thus producing positive mean vorticity.
This leads to the formation of a bidirectional mean current structure around both ends of the deep sills. In
addition, weak negative mean vorticity generated bylarge-scale tidal currents in the central part of the straits
remains unaffected by TTWs. These processes may produce the mean vorticity distribution illustrated in Fig.
12b.
Rough estimates of the transport associated with the
TTWs for the K1 tide is about 50% of the total transport,
assuming that the transport by the bidirectional currents
in the Bussol (the outflow from the central part is excluded) and Kruzenshterna Straits are due to TTWs.
Thus, TTWs play an important role in producing effective water exchange through the Kuril Straits in themodel, by generating strong bidirectional mean currents
in deep and wide straits. However, this mechanism has
little effect on tidal exchange for the case of superinertial
tides (e.g., the M 2 tide) because they are inefficient generators of TTWs as seen in section 3. This is a possible
explanation for the fact that subinertial diurnal tides
cause more efficient water exchange through the Kuril
Straits than superinertial semidiurnal tides, as estimatedin section 4.
6. Discussion
Although we used a quadratic friction form in thisstudy, a different scheme for bottom friction may leadto different results in coastal embayments (shallower
than some tens of meters) according to past studies.
However, bottom friction is not strong enough to change
the calculated current field in the Kuril Straits qualitatively because most straits are deeper than several hundred meters. In fact, the term balance of the vorticity
equation (Fig. 13) shows that the bottom friction terms
are more than one order of magnitude less than thedominant stretching/squeezing terms in the Kuril Straits,
except in very shallow and narrow regions (some tensof meters deep). Thus, the essential results obtained here
are largely valid, with the proviso that the strength ofmean currents is somewhat changeable for the choiceof the friction law. For example, Huthnance (1981) indicated by analytical study that the magnitude of a meancurrent produced by the quadratic friction form is 2/3
times that by linear friction and the current structures1639

are qualitatively the same. However, when undertaking
the modeling problem in shallow embayments in coastal
region, some improvements to this model will be necessary.
We performed another experiment for the K1 tide inwhich grid sizes were reduced to 2.5 km 3 2.5 km since
the resolution of topographically trapped waves (awavelength or about 40 km) is not sufficient. The resultshows better agreement with observations of elevationand the rms error reduces by 1 cm. The qualitative features of the calculated mean current field is common inboth cases although the amount of water exchange
through the straits becomes 9.5 Sv (Fig. 17). Despite
the substantial increase in mean transport, the increaseof maximum current and mean current speeds in the
Kuril Straits are about 20% (1.6 to 1.9 m s21 ) and 30%(0.7 to 0.9 m s21 ), respectively. The current structureof a topographically trapped wave (e.g., in Urup Strait)
is reproduced more clearly (not shown). These are probably due to the better resolution of current structure,
vorticity generation in a slope region and thus topographically trapped waves. The better resolution may
result in greater water exchange.
In section 5b, we neglected the v term (b) (i.e.,
2v= · u) in the formulation of the generation of bidirectional mean currents in deep straits. Here, we briefly
discuss the effect of this on the generation of bidirectional mean currents in deep straits based on Eq. (23),which is the final formula for the analysis. When term(b) is taken into consideration, the intrinsic phase velocity c and the forcing term on the rhs of Eq. (23) arealtered through the change of f to f 1 v. As for thephase velocity, Eq. (22) implies that the along-isobath
phase speed (c x ) of TTWs on the positive (negative)
vorticity side increases (decreases) in the northern hemisphere. For example, when the magnitude of v is assumed to be 0.2 3 1024 (a typical value in the present
shallow straits), the speed increases (decreases) by about
20% on the positive (negative) vorticity side. This acts
to enhance the net positive vorticity flux from shallow
straits to deep straits, which is described in section 5b.
Similarly, the change in the forcing term strengthens(weakens) the generation of positive (negative) vorticity. Thus, the net effect becomes significant as relative
vorticity v increases, modifying the net positive vorticity flux to deep straits from that expected from Eq.
(23). However, once relative vorticity is transported
away from shallow straits into deeper regions by TTWs,
the subsequent transport and the resulting mean vorticity
formation could be qualitatively similar to that explained in section 5b because relative vorticity in the
deep regions is expected to be very small.
We investigated the basic features and the generation
mechanism of mean transport for each component.
However, it is desirable to run the model with several
tidal components simultaneously in order to make an
actual quantitative estimate of tidal exchange. According to Kowalik and Polyakov (1998), the K1 and O1

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VOLUME 30

FIG. 15. Isolines of vorticity and the K1 tidal current vectors around the shallow Urup Strait after (a) 0.0, (b) 0.25, (c) 0.5, and (d) 0.75
cycle. The contour interval is 1 3 1025 s21 and the dashed lines denote negative values of vorticity. The arrow A: positive vorticity; thearrow B: negative vorticity. Shaded area is shallower than 1200 m.

tides are the major constituents around the Kuril Islands,
which interact nonlinearly, producing mainly a fortnightly tide (the linear fortnightly modulation is enhanced) and an M 2 tide although the dominant component remains the K1 tidal current. Such nonlinear interactions between the components might cause difference in calculated transport. It remains a subject for
future investigation.
Owing to the lack of current measurements, the reliability of the calculated current field is difficult to assess. We compare the model results with observation
only in elevation data. Accordingly, although the results
suggest that tidal exchange is a possible mechanism ofwater exchange through the Kuril Straits, we await fu-

ture current measurements for comparison and improvement of our estimates of tidal exchange. Nevertheless,bidirectional mean currents in the Straits, through whichthese tidal exchanges are effectively produced, are consistent with the current structure observed in infrared
images taken by NOAA-12 and mentioned in the earlier
work by Moroshkin (1966) and Leonov (1960). To emphasize this point, we have tracked numerous labeled
particles in the calculated velocity field following earlier
works (e.g., Miyama et al. 1995). Focusing on Bussol
Strait, where most of the discharge is considered tooccur, we performed 10 cycles of tracking from the ebb
tide (Fig. 18). The calculated flow pattern of the Okhotsk
Sea water (represented by blue particles in Fig. 18) has

JULY 2000

NAKAMURA ET AL.

1641

FIG. 17. Same as Fig. 9 but for the 2.5 km 3 2.5 km grid sizes
case and the contour unit of 0.8 Sv.

FIG. 16. Schematic illustration of the formation mechanism of meanvorticity by topographically trapped waves. (a) Vorticity generationby the stretching/squeezing effect. (b) Generation of a net flux ofpositive vorticity due to the combined effect of advection by thealong-isobath current and the propagation of topographically trappedwaves. (c) Net positive vorticity flux is conveyed by topographicallytrapped waves from a shallow strait to a deep strait where the waves
can cross the sill, producing the mean bidirectional current structure.

a qualitatively similar appearance to that of the infrared
image. The simulation data in Fig. 18 exhibit such features as bidirectional and along-sill mean currents. Discharge from the middle of Bussol Strait is also visible,
part of which joins the coastal side of the Oyashio current flowing offshore.
On the other hand, from geostrophic calculations
based on CTD data, Kawasaki and Kono (1994) indicated that 1) outflows take place from Matsuwa Island
to Kruzenshterna Strait and north of Simusir Island to
Bussol Strait, 2) inflows take place from Nadezhdy
Strait to Ketoy Island, and 3) strong vertical and horizontal mixing is caused at the northern straits and Bussol
Strait by tidal currents, providing 2.9 Sv of Okhotsk
Sea water and 2.5 Sv of mixed water, both of which
join the Oyashio (12.8 Sv). Their results are different
from our results in quantity, but the similarity in exchange and mixing locations with these observations
suggests that their geostrophic calculation contains partof the tide-induced mean currents, which are in geo-

strophic balance. In fact, the presence of bidirectional
currents is also observed by geostrophic calculation in
Amchitka Strait (Reed 1990), which connects the Bering
Sea and the North Pacific and is located north of thecritical latitude for diurnal tides. This indicates the importance of direct current measurements for the estimation of water exchange between the two basins sothat barotropic mean flow induced by subinertial tides
can be precisely taken into account.
7. Summary
Our regional model has successfully reproduced theobserved barotropic K1 tidal field in the Okhotsk Sea,
although the reliability of the calculated current field isdifficult to assess owing to the lack of current measurements. Using the calculated tidal currents, the Eulerian mean outflow from the Okhotsk Sea is estimatedto reach the significant value of 5.0 Sv for the K1 tide,the main part of which is conducted through the Bussol,
Kruzenshterna, and Chetverty Straits. In addition to theK1 tide, the O1 , P1 , M 2 , and S 2 tides induce Eulerianmean exchanges estimated at 3.5, 1.0, 0.3, and 0.1 Sv,
respectively. These tidal exchanges are produced by bidirectional mean currents in the straits, consistent withthe current structure observed in infrared images taken
by NOAA-12 and mentioned in the earlier work by Moroshkin (1966) and Leonov (1960). Therefore, it is suggested that tidal currents play an important role in waterexchange between the Okhotsk Sea and the North Pacific, although confirmation of this prediction and improvements in accuracy await future observations.
We have shown that the mean currents are produced
through the effects of topographically trapped waves as1642

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VOLUME 30

FIG. 18. Particle tracking results around the Kuril Straits, (a) initial position, and (b) after 10 cycles.

well as through well-known tidal rectification. In shallow straits (depth 200;600 m), tidal rectification mainly
due to advection, vorticity generation by the stretching/squeezing effect, and damping by bottom friction produces the strong along-sill and weak bidirectional meancurrents. On the other hand, in deep straits, such as
Bussol strait, a net flux of positive vorticity from theadjacent shallow straits to the deep strait is caused bytopographically trapped waves and produces strong bidirectional mean currents there. This net flux is causedby the fact that the along-isobath currents are in thesame direction as the phase velocity of the topographically trapped waves with positive vorticity and are in
the opposite direction to that with negative vorticity.
The mean currents produced by topographicallytrapped waves have three important properties: First,
the mean currents induced by these waves are in neargeostrophic balance, since these waves are characterized
as a rotational wave. Second, because this mechanism
is responsible for the water exchange through deep
straits, its depth makes the amount of the mean transport
significant. In fact, roughly half of the total exchange
induced by the K1 tide is considered to be caused by

the effect of topographically trapped waves. Last themean exchanges induced by subinertial tides are muchgreater than those expected from the previous theories
for tidal rectification which consider only the case of
superinertial tides because superinertial tides are inefficient at generating topographically trapped waves.
Thus, it is suggested that the energy of subinertial tides
is effectively cascaded upscale to produce bidirectionalmean exchange currents in geostrophic balance, causing
significant water exchange between two basins even if
they are separated by sills.
We have clarified the mechanisms of the horizontal
exchange induced by the tidal currents which dominate
the Kuril Straits region. However, since we use a depthaveraged model, the vertical structure is still unclear.
Many observations indicate strong vertical mixing at
the straits. Based on the vertical distributions of oxygenand density across Bussol Strait, Yasuoka (1967) suggested a surface layer inflow, a sinking outflow in theintermediate layer, and strong inflow over the sill. Tidal
currents may also contribute significantly to verticalmixing and formation of the vertical circulation throughthe generation of internal waves, which are thought toJULY 2000

NAKAMURA ET AL.

have a major influence on water modification, as discussed in the accompanying paper (Nakamura et al.
2000). Therefore, an investigation of the vertical structure of tidal currents around the straits, which includes
the baroclinic effect, may be important for our understanding of the detailed transport processes and watermass transformation.
Besides tidal currents, water exchange and mixing canbe caused by eddies (which often appear along the islands), flow driven by local winds, and advection anddiffusion due to the difference in stratification between
the Okhotsk Sea and the North Pacific. In particular,
although exchange by the western boundary current of
the subarctic gyre itself is of secondary importance as
it flows along the Kuril Island Chain, this current canhave a significant effect when it interacts with oscillating tidal currents. We should combine knowledge of thetidal currents with these effects in the future in order
to identify and quantify the impact of the Okhotsk Sea
upon the North Pacific.
Acknowledgments. We wish to acknowledge Prof. S.
Saitoh (Hokkaido University, Japan) for the kind offer
of NOAA-12 AVHRR imagery. We also thank Dr. J. P.
Matthews and anonymous reviewers for their criticalreading and useful comments. Numerical Calculations
were done on the FACOM M1800 and VP2600 at theData Processing Center of Kyoto University.
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