JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, C09S07, doi:10.1029/2003JC001850, 2004

Tidally induced diapycnal mixing in the Kuril Straits and its
role in water transformation and transport:
A three-dimensional nonhydrostatic model experiment
Tomohiro Nakamura1 and Toshiyuki Awaji2
Department of Geophysics, Graduate School of Science, Kyoto University, Kyoto, Japan
Received 11 March 2003; revised 12 November 2003; accepted 20 January 2004; published 1 July 2004.

[1] Baroclinic processes generated by the K1 tidal flow around the Kuril Straits and theirrole in the linkage between the Okhotsk Sea and the North Pacific are investigated using athree-dimensional nonhydrostatic model. Large-amplitude unsteady lee waves are
generated around sill tops all along the Kuril Island Chain and induce significant density
inversions from the sea surface down to the 27.6 sq density layer. Along with thiswave breaking, a large flow of energy takes place from the swift tidal flow regions to greater
depths as a result of the clockwise propagation of both the topographically trappedwaves around the islands and the remaining unsteady lee waves. Such wave generation andenergy exchange eventually cause intense diapycnal mixing over the shallow topographic
features and near the bottom, leading to a maximum diapycnal diffusivity of over
103 cm2 s1. Even in the deep Bussol’ Strait, which is thought to be the main exit of the
Okhotsk Sea water, considerable mixing (corresponding to diapycnal diffusivity valuesof between 10  50 cm2 s1) occurs. Vigorous mixing in the shallow regions produces low
potential vorticity (PV) water in the upper layer and high PV water below. Accordingly, PV
fronts are formed along the island chain and sustain instabilities that in turn releasebaroclinic eddies with low core PV values. These features are indicated in recent satellite
imagery and in situ observations, suggesting that the tide is the controlling factor in theformation of fronts observed in the Kuril Straits. Tidally induced mean transport across thestraits is estimated to reach 26 Sv (1 Sv = 106 m3 s1), which is much larger than in thebarotropic case. However, most of the exchanged water tends to circulate around theislands due to the effect of bottom topography, whereas eddies pinched off from thetidal fronts carry the exchanged water offshore. The amount of eddy-driven offshoretransport away from the islands reaches 14 Sv, with roughly half being directed to the North
Pacific. This significant offshore transport spreads the effect of the diapycnal mixing
taking place in the straits over wider areas of the North Pacific and the Okhotsk Sea. For
example, the PV values generated in the eddies differ by 30–40% from the ambient wateron average, whereas sea surface salinity within the eddies is 0.1 psu higher than thesurroundings, corresponding to the density increase of 0.08 sq. Thus the eddy transport
provides significant PV and salinity fluxes to both the North Pacific and the Okhotsk Sea.
Hence we infer that a combination of tidally driven processes taking place at thepassages leads to the formation of eddies that play a central role in water transport andtransformation and are an essential aspect of the physical interplay between the Okhotsk
INDEX TERMS: 4520 Oceanography: Physical: Eddies and mesoscale
Sea and the North Pacific.
processes; 4544 Oceanography: Physical: Internal and inertial waves; 4219 Oceanography: General:
Continental shelf processes; 4255 Oceanography: General: Numerical modeling; KEYWORDS: Kuril Straits,internal wave, diapycnal mixing, tidal front, eddy-induced transport, tidal rectification
Citation: Nakamura, T., and T. Awaji (2004), Tidally induced diapycnal mixing in the Kuril Straits and its role in watertransformation and transport: A three-dimensional nonhydrostatic model experiment, J. Geophys. Res., 109, C09S07,
doi:10.1029/2003JC001850.
1
Now at Integrated Modeling Program, Frontier Research System for
Global Change, Yokohama, Japan.
2
Also at Integrated Modeling Program, Frontier Research System for
Global Change, Yokohama, Japan.

Copyright 2004 by the American Geophysical Union.
0148-0227/04/2003JC001850$09.00

1. Introduction[2] The Okhotsk Sea (Figure 1) is separated from thenorthwestern 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 the Kruzenshterna

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Figure 1. (top) Model topography. (bottom) Locations of the 3-D model domain (solid line) and thebarotropic model domain (dashed line). The sites of tide gauge observations used in the comparison are
shown by green asterisks in the bottom panel.
(1500 m) Straits. It is considered that the transport andmixing processes taking place between the Okhotsk Sea andthe North Pacific via the Kuril Straits play an important role
not only in the local environment but also in determining
the water properties of the North Pacific [e.g., Kitani, 1973].
In turn, the North Pacific is the source of most of the waterin the Okhotsk Sea [e.g., Watanabe and Wakatsuchi, 1998].
[3] Previous studies found that a plume of low-salinity
water at 27.0 sq extended to the south from the Kuril Straits
and that the confluence of the East Kamchatka Current andthe discharge from the Okhotsk Sea forms both the Oyashio
current, which flows along the Kuril Islands as part of thewestern boundary current of the subarctic gyre, andthe Subarctic Current to the east, thus indicating that the
Okhotsk Sea is the most likely source of low-salinity waterin the North Pacific [Wüst, 1930; Favorite et al., 1976].
Associating an analysis of historical hydrographic data with
Kitani’s [1973] result, Talley [1991] proposed that the North
Pacific at mid-depth is ventilated through sea ice formationin the innermost part of the Okhotsk Sea and through local
vertical mixing in the Kuril Straits. From potential vorticity(PV) maps, Talley [1993] and Yasuda et al. [1996]
commented that the Okhotsk Sea supplies low-salinity
water to the North Pacific Intermediate Water (NPIW).
More exactly, the Okhotsk Sea Mode Water (OSMW),
which is characterized by low potential vorticity around26.8 sq, is considered to be the major source of the NPIW
[Talley, 1991; Yasuda, 1997; Kono, 1998; Watanabe andWakatsuchi, 1998]. Since the NPIW spreads out over mostof the subtropical gyre [Talley, 1993] and has the capacity to

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store large amounts of greenhouse gases such as CO2[Tsunogai et al., 1993; Yamanaka and Tajika, 1996], it isnecessary to study the water transport and transformation
processes taking place in the Kuril Straits.
[4] Recent observational results identified the importanceof tidal processes at the Kurils in sustaining the interconnection between the Okhotsk Sea and the North Pacific. In
fact, tidal currents, and especially their diurnal components,
are very swift and predominant in and around the Kuril
Straits [e.g., Thomson et al., 1997] (see also Russian reports
cited by Talley and Nagata [1995]). The maximum speed
reaches 2 to 4 m s1 in the relatively shallow straits (100 
500 m depth). According to previous studies on tidal
rectification [e.g., Huthnance, 1973; Awaji et al., 1980;
Robinson, 1981; Ridderinkhof, 1989; Chen and Beardsley,
1995], such strong tidal currents induce significant meantransport, though the tidal flow itself is oscillatory. Moreover, observational studies in the northwest Pacific underlined the difficulty of explaining the in/outflow through the
Kuril Straits in terms of geostrophic balance, because
overall surface dynamic height is higher in the Okhotsk
Sea than in the northwestern North Pacific [Kawasaki and
Kono, 1992; Isoguchi et al., 1997].
[5] Considering these facts, Nakamura et al. [2000a](hereinafter NA00a) performed a numerical simulation of
the barotropic tidal field in the Okhotsk Sea and showed thatthe diurnal K1 tide induces very swift tidal currents in the
Kuril Straits, as is observed. Since the K1 tide is subinertial
around this high latitude (47N), topographically trappedwaves (TTWs) are effectively generated and amplified
while circulating around the islands, a result expected on
the basis of earlier theoretical studies [Chapman, 1989;
Haidvogel et al., 1993; Kowalik and Proshutinsky, 1995].
The work of NA00a indicated that the combined effect ofvorticity transport by TTWs and vorticity advection by
an oscillating tidal flow produces significant residual currents even in deep passages regardless of the weakness of
the local tidal flow. The structures of the simulated tidally
induced mean flows are similar to those reported in observations [Leonov, 1960], and the net transport toward
the North Pacific due to the K1 tide alone is estimated tobe 5 Sv at least and more than 10 Sv from five major
constituents.
[6] As for the transformation of water properties, recent
detailed observations in the Kuril Straits have clearly
revealed the presence of a deep, vertically uniform temperature distribution caused by a strong diapycnal mixing
which leads to a horizontal discontinuity in the temperature
distribution along the Kuril Islands [Kawasaki and Kono,
1994; Gladyshev, 1995; Kawasaki, 1996]. With a vertically
two-dimensional (2-D) nonhydrostatic model, Nakamura etal. [2000b] (hereinafter NA00b) showed the importance oftidal mixing in the observed modification of water in the
Kuril Straits. As swift K1 tidal currents flow over sills in the
Kuril Straits, unsteady lee waves are generated and growinto large-amplitude internal waves with a maximum displacement of 100 m. Though discussion of oceanicinternal gravity waves generated by a tidal flow has usuallyfocused on internal tides at the tidal frequency, the K1
internal tides cannot exist as inertial gravity waves since
the K1 tide is subinertial in the Kuril Straits. Instead,
unsteady lee waves can adopt this role and are more

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likely to grow by superposition than internal tides, sothat enhanced diapycnal mixing to levels of diapycnal
diffusivity 10– 1000 cm2 s1 can eventually be reached[Nakamura et al., 2000b; Nakamura and Awaji, 2001]. Suchvigorous mixing takes place at the exit of the subducted
OSMW and the entrance of the North Pacific water. Thus,
from a dynamical viewpoint, these facts imply the supply ofpotential vorticity from the lateral boundary (i.e., the Kuril
Island Chain) to both the North Pacific and the Okhotsk
Sea, which could then affect the circulation of the adjacent
Kuril Basin in the Okhotsk Sea and the subarctic gyre of theNorth Pacific according to the ventilated thermocline
theory [Pedlosky, 1996]. Therefore, further investigation of
the 3-D process of transport and diapycnal mixing at the
Kurils with particular emphasis on the K1 tide is required.
[7] In this study, we use a 3-D nonhydrostatic model.
This model can reproduce shear instability and/or convective processes, which are important in vertical mixing
induced by waves [Scinocca and Peltier, 1994]. Moreover,propagation of internal gravity waves and TTWs can beadequately simulated as well as currents in both along- andacross-sill directions, thus enabling us to estimate the 3-Dprocesses of tidally induced transport and diapycnal mixing
reasonably and investigate the subsequent evolution of tidal
fronts around the Kuril Island Chain. This knowledge will
be helpful for clarifying the physics responsible for the
linkage between the Okhotsk Sea and the North Pacific.
[8] The rest of the paper is organized as follows. The
numerical model is described in section 2, and the results arepresented in section 3. Section 4 presents an energy analysis,
whereas diapycnal mixing is estimated in section 5.
The offshore transport of the modified water by frontal
eddies is estimated in section 6, and the roles of the eddytransport and tide-induced mean flow in the linkage between
the Okhotsk Sea and the North Pacific are discussed in
section 7. Our conclusions are summarized and discussed in
section 8.

2. Model2.1. Model Domain[9] The model topography (Figure 1) is set from the
DBDB5 topographic data (U.S. National GeophysicalData Center). The model domain covers most of thestraits in the Kuril Island Chain so as to involve thetwo deep passages, the Bussol’ and Kruzenshterna Straits,
through which the major water flows are considered totake place, and to reproduce the propagation of TTWs
and the tidally induced mean circulation around islands
and/or sills. The two open boundaries along the island
chain are set away from the straits to allow the evolutionof eddies arising from tidal fronts. The model domain andits x and y axes are rotated anticlockwise by 45. For
computational efficiency, the model maximum depth is set
as 6000 m so that the very deep region in the Kuril
Trench is considered flat. Grid sizes are horizontally
about 700 m and vertically 30 m (with the grid point
dimensions of 1212  602  202).
2.2. Nonhydrostatic 3-D Model[10] In order to simulate the baroclinic process inducedby tides and the associated vertical mixing, we use a 3-D

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nonhydrostatic model. This model is also suitable forrepresenting the dispersion relation of internal gravity
waves more accurately. Intense vertical mixing in andaround the straits will bring about tidal fronts in the offshore
region due to the difference in stratification, which evolve to
produce pinched-off eddies by the frontal instability. Therefore we took into account the effect of a planetary-vorticity
gradient by adopting the b-plane approximation. The model
has been constructed using that of Tanaka and Akitomo[2001] as a basis, but with the following governing equations and settings:@u1rþ ðu þ UÞ  ru þ f k  u ¼  rp  gk þ nH r2H u
@t
r0
r0
@2u
þ nZ 2 ;
@z
ð1Þ
@C
@2C
þ r  ½ðu þ UÞC ¼ kH r2H C þ kZ 2 ;
@t
@z

ð2Þ

r ¼ rðq; S; pÞ;ð3Þ

r  u ¼ 0;

ð4Þ

where u = (u, v, w) are ‘‘internal mode velocities’’ in the (x,y, z) directions, respectively; U = (U, V, W) is a barotropic
tidal flow; k is a unit vector along the z axis; p is pressure; r
is density variation; and C represents potential temperature q
or salinity S. The equation of state is that recommended by
UNESCO [Jackett and McDougall, 1995]. A pressure
equation in the nonhydrostatic system is written in
Appendix A.
[11] A barotropic tidal flow U is calculated separatelyfrom a barotropic tide model and is given in the advection
terms that work as the main forcing (i.e., ‘‘surface leadassumption’’). This separation allows us to greatly reduce
the spin-up time and to circumvent difficulties in exact
modeling of a free surface ocean for the nonhydrostatic
equations [e.g., Marshall et al., 1997a], and thus it is aconvenient way to gain insight into important mechanisms
before exploring a more accurate simulation. The detailed
discussion on this assumption is given in section 8. Strictly
speaking, the component u contains all the responses to thespecified barotropic flow, but it is called here the ‘‘internal
mode velocity,’’ for convenience. Note that energy conversion through the Reynolds stress can cause feedback to thebarotropic tide, but it is neglected for dynamical consistency
with the surface lead assumption. Its effect is alreadyincluded in the barotropic model in a crude manner as aresult of using the bottom stress term and horizontal
viscosity (more detailed discussion appears in section 8).
[12] The parameters are defined as follows: f = f0 + b0Y
is the Coriolis parameter around 46.5N ( f0 ’ 1.055 
104 s1, b0 ’ 1.57  1013 cm1 s1, and Y is the distancein the meridional direction; see Figure 1); r0 is the reference
density; g is the gravity acceleration; and n and k are thecoefficients of eddy viscosity and eddy diffusivity, respectively, where the subscripts H and Z represent the horizontal
and vertical directions.

C09S07[13] To reduce numerical diffusion associated withlarge vertical displacements by internal waves, the QUICK
scheme [Leonard, 1979] is used in the vertical direction.
The values of the eddy diffusivities are 0.1 cm2 s1vertically and 104 cm2 s1 horizontally, and those ofviscosities are 1 cm2 s1 and 105 cm2 s1, respectively.
These values are chosen from parameter-sweeping tests
so as to be of the same order of those estimated fromthe calculated field, which will be shown in section 5.
[ 14 ] A no-slip condition is imposed at the bottom
boundary. A sponge zone is adopted near the open boundaries to prevent artificial wave reflection, where the viscosities and the horizontal diffusivities are gradually increased.
In addition, u, q, and S are gradually restored to their initialvalues near to the open boundaries, which, in effect, has theaction of an artificial buoyancy flux and thereby maintains
stratification in the interior.
2.3. Initial Conditions[15] The initial potential temperature and salinity fields
are set to be horizontally uniform with the vertical profiles
shown in Figure 2 (green lines) using the data set of the
U.S. National Oceanographic Data Center. In doing so, asummer time climatology in the Kuril Basin is used fromthe surface to 1500 m depth in order to examine themodification process of the Okhotsk Sea water entering
the North Pacific. A summer time climatology of the East
Kamchatka Current Water (EKCW) is used below 3000 m
because the Kuril Basin (3200 m depth) is shallower
than the deep part of the Pacific region, and because it is
the origin of the water in this region [Reid, 1965]. To
avoid a vertical gap in density around 3000 m depth, theinitial vertical profiles of q and S are gradually changed
from the climatology of the Kuril Basin to that of the
EKCW between 1500 m and 3000 m depth. Note that atthese depths the difference in stratification between thetwo climatology profiles is small (Figure 2). As stratification in summer becomes strong, a significant amount of
the energy contained in internal waves could be trapped ina ‘‘surface’’ layer, which may reach down to 100 m
depth. The initial internal mode velocity is set to be zero,and thus only the barotropic tidal flow is taken into
account for the initial velocity field.
2.4. Barotropic Tidal Flow[16] In this experiment, we direct our attention to the K1
tide alone since the K1 current is largest around the Kuril
Island Chain [e.g., Thomson et al., 1997; Nakamura et al.,2000a]. The barotropic tide model used here is the same asthat of NA00a and is based on work by Schwiderski [1980].
The horizontal resolution, however, is taken to be the sameas in this 3-D model and hence is about 7 times finer thanthat used by NA00a. In addition, the model domain of thebarotropic tide is wider than that of the present 3-D model inorder to reduce spurious disturbances at the open boundariesof the 3-D model as much as possible (Figure 1). The basic
features of the calculated barotropic field are essentiallythe same, but with increasing horizontal resolution, theaccuracy improves.
[17] For example, using the International Hydrographic
Office tidal harmonic constants at 43 sites, as shown in

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Figure 2. Initial vertical profiles of (left) potential temperature and (right) salinity are shown by green
lines. The blue and red lines are those of summer time climatology in the Kuril Basin of the Okhotsk Sea
and the East Kamchatka Current, respectively.
Figure 1, we calculate the root mean square (RMS) misfit ofelevation as per NA00a. The RMS misfit is 6.37 cm, while
the mean observed amplitude is 30.3 cm. The correlation
coefficients between the calculated and the observed harmonic constants are 0.73 for phase and 0.76 for amplitude.
These values are reasonably good despite the complex
topography, so that the simulation is considered to berealistic.
[18] The simulated K1 barotropic flow is very rapid inshallow regions and hence strong wave generation is
expected to occur (Figure 3). This is particularly so inthe vicinity of topographic features such as sills and banks,
where the maximum speed exceeds 2 m s1. In the
Bussol’ Strait, the flow speed ranges from 0.13 m s1 in
the deepest part to 0.5 m s1 over the western sill. These
values are similar to the values of 0.3 – 0.4 m s1 derived
from satellite-tracked drifters [Ohshima et al., 2002].
Around the Friz (Etorofu) Strait, the simulated speed
varies from 0.3 to 1 m s1, in good agreement with theestimation from satellite-tracked drifters by Thomson et al.
[1997] and Rabinovich and Thomson [2001]. As for theshallow straits, where only Russian observations have so

Figure 3. Major (red) and minor (blue) axes of the calculated barotropic K1 tidal flow. Horizontally
averaged values over every 20  20 grid points are shown. Depth contours at 500, 1000, 2000, and4000 m are overplotted.
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Figure 4. Eulerian mean transport stream function for thebarotropic K1 tide, which is set to be zero at Hokkaido
Island. Values in shaded areas are negative. The contour
interval is 1 Sv (contours of 0 Sv are excluded).
far been permitted, the Luchin report from Talley andNagata [1995] commented on the presence of very strong
currents of 5 to 7 knots. Generally speaking, the agreement
obtained between the simulated and observed parameters

C09S07support the view that our numerical simulation for the K1
tidal current field is realistic.
[19] As mentioned by NA00a, significant TTWs arereadily excited as the subinertial K1 tidal waves comingfrom the North Pacific encounter the large-amplitude sills in
the Kuril Straits. TTWs intensify the K1 current, leading to
the generation of a remarkable tidally induced mean flow
(Figure 4) through the ‘‘extended tidal rectification’’ proposed by NA00a. In Figure 4, a ‘‘bi-directional’’ residual
flow structure is clearly present in the straits in addition to
circulation around shallow topographic features like islands
and sills as reported by Moroshkin [1966] and NA00a. Some
eddy-like features also appear in this fine-resolution case.

3. Features of the Simulated Field
3.1. Tidal Fronts and Eddies[20] Figure 5a shows the model sea surface temperature
after 25 periods (after an interval of time corresponding to
25 periods). Low temperature anomalies are produced along
the island chain, which indicate the formation of tempera-

Figure 5. (a) Temperature at the model sea surface (15 m depth) after 25 periods. Green areas indicate
lands. White circles indicate eddy-like structures also seen in a satellite-derived sea surface temperature
imagery (Figure 6). (b) Planetary part of potential vorticity (f/r0  dsq/dz  103) after 25 periods at
30 m depth. In Figure 5b, red color areas indicate density inversion.
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Figure 6. Satellite-derived sea surface temperature(MCSST/AVHRR) over the northern part of the Kuril
Straits from the NOAA-12 satellite (orbit 17429; time
2231 – 2233 GMT; 21 September 1994). White circles
indicate eddy-like structures similar to features in the model
SST (Figure 5). Note that the model domain is inclined by45. (Figure courtesy of S. Saitoh)ture fronts and eddies. The patterns and size of eddies are
generally similar to those seen in an infrared imagery(Figure 6). In particular, the eddy-like structures marked
by white circles take place at almost the corresponding
locations and bear a resemblance. Such temperature fronts
are known to exist almost throughout the year, althoughcooling in winter makes it a warm anomaly [Kitani, 1973].
These facts strongly suggest that tidally induced baroclinic
processes are responsible for the observed fronts and eddies.
[21] Since the formation of tidal fronts are associatedwith vertical mixing and/or stirring [e.g., Simpson et al.,C09S07

1978; Nakamura et al., 2000b], we next examine the@rjplanetary component of potential vorticity, rf @zp¼00(PPV), which is a useful indicator of water mass transformation by diapycnal mixing. Though fronts can be also
identified by potential energy anomaly, since we set theinitial stratification to be horizontally uniform, the change
in PPV implies the presence of available potential energy.
A vertical distribution of potential density and PPV after
25 periods over a sill in the northeastern part at x =575 km (Figure 7) indicates that water mass transformation occurs over the sill from the sea surface to theintermediate layer. Low PPV water is produced over thesill though it shifts somewhat to the right from the sill
due to advection. Several previous observations confirmed
the presence of such vertically uniform water masses in
the northeastern part of the Kurils [Gladyshev, 1995;
Kawasaki, 1996] as well as in the Bussol’ Strait [e.g.,
Kitani, 1973; Kawasaki and Kono, 1994]. Beneath thislow PPV component, high PPV water is produced around27.1 sq, mainly because of entrainment of the water into theabove layer (thus layer thickness decreases). A similar
situation occurs above the low PPV water, though it is notclearly appreciable. Figure 7 also shows the presence ofdensity inversions (denoted by red) between the surface andintermediate layers (say, 26.9 sq to 27.3 sq), thus indicatingthat water mass transformation is still going on. Such PPVchange indicates that the temperature fronts are caused bytidal mixing, considering the fact that the initial condition ishorizontally uniform.
[22] The formation of PPV fronts is due to the fact thatthe vertical mixing taking place in and around the sills or
islands is stronger than that in the surrounding deep regions.
The fronts, in turn, spawn various instabilities such as
baroclinic instability and associated eddies [e.g., Qiu etal., 1988; Boss and Thompson, 1999; Pedlosky, 1987].
Figure 5b shows that the sea surface PPV map after
25 periods clearly corresponds to the modeled temperature
distribution. The tidally induced PPV fronts evolve byforming and releasing baroclinic eddies. These eddies
should contain low PPV water in their cores, and thus
anticyclonic eddies are easier to produce. A very recent
hydrographic observation in the Kuril Basin, which was

Figure 7. Vertical section of planetary part of potential vorticity (f/r0  dsq/dz  103: tone) andpotential density (sq: contour) after 25 periods. The section crosses a typical sill in the northeastern part of
the Kuril Island Chain (x = 575 km). Red color areas indicate density inversion.
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C09S07carried out by a Hokkaido University group, clearly captured such a pinched-off eddy originating from the Kuril
Straits (M. Itoh, personal communication). This indicatesthat eddies convey vertically well-mixed water locatedaround the straits toward the offshore region. We will
return to this aspect in section 6.
[23] According to NA00b, unsteady lee waves generated
over sills at the Kurils are more likely to induce intense
vertical mixing. Thus we next examine wave processes inorder to shed light on the mechanism responsible for watermass transformation in the Kuril Straits.
3.2. Generation of Unsteady Lee Waves[24] Figure 8 shows the initial response of isopycnal
surfaces and vertical velocities over the sill located in thenortheastern part to the barotropic K1 flow. This crosssection corresponds to that of the PPV discussed above,
and an internal wave response is easy to identify because thesill is relatively wide.
[25] Figure 8a shows that as a barotropic across-sillcurrent flows rightward, an internal wave-like structure is
generated on the lee side of the sill. The co-phase lines lean
toward the upstream side, thus indicating that the wave is an
unsteady lee wave. In fact, the subinertial K1 internal tidecannot exist as inertial gravity waves. Even for a simple
higher harmonics like K2, such waves should propagate inboth upstream and downstream directions, in contrast to theresult simulated here.
[26] The intrinsic frequency of internal waves is estimatedfrom the simple dispersion relation,s2i ¼

N 2 ðlv =lh Þ2 þ f 2
1 þ ðlv =lh Þ2;ð5Þ

where lv/lh is the ratio of vertical and horizontal
wavelengths, si is an intrinsic frequency, and N is abuoyancy frequency. When we use the approximation of22l2h  kc /4p (where kc is the horizontal wave number in
the across-sill direction), the frequency estimated from thefigure (Table 1) roughly agrees with the theoretically
predicted frequency of unsteady lee waves: According toNA00b, the intrinsic frequency of tidally generated internal
waves is, in general, given as
kc vc  sK1 ;ð6Þ

where vc is the across-sill current speed and sK1 is the K1
tidal frequency. Though unsteady lee waves can be excitedwhen jkcvc/sK1j  1 in their definition, the behavior of the
waves becomes similar to that of unsteady lee waves when
jkcvc/sK1j > 2 as in this case [Nakamura and Awaji, 2001].
For this reason, in the following discussion, we use the

Figure 8. Initial evolution of potential density (sq:contour) and vertical velocity (w + W: tone) in a y-z section
across a sill (the same one in Figure 7). Contour interval is
0.1 sq. Arrows in the sill region represent the direction of
the across-sill barotropic flow. Green lines denote the waves
whose intrinsic frequencies are estimated in Table 1.
Table 1. Estimate of Intrinsic Frequencya
Period

2p/kc

lv/lh

v

Dispersion Relation

Unsteady Lee Wave

1/8
1/4

6 (±0.5) km
4.5 (±0.5) km

0.17 (±0.02)
0.14 (±0.02)

31 (±5) cm/s
19 (±5) cm/s

4.8 (±0.8)  104 s1
4.0 (±0.8)  104 s1

4.0 (±0.8)  104 s1
3.4 (±1.0)  104 s1aValues of 2p/kc and lv/lh are estimated from Figure 8. The buoyancy frequency used is the vertical average from 150 m to 1000 m at the initial time (2.8(±0.2)  103 s1) and the across-sill velocities used are the barotropic flows 1/16 period before the corresponding times. The theoretically predictedfrequency of an unsteady lee wave shown is that of the fast mixed tidal – lee wave component only [Nakamura and Awaji, 2001]. A range of possible errors
in estimating each value is indicated in brackets.

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Figure 9. Horizontal sections of total vertical velocity in the fourth period at 390 m depth, whichapproximately corresponds to that of the OSMW (and thus NPIW) core. Green areas indicate land grids at
this depth.
name unsteady lee waves in a broader sense than theoriginal definition for convenience.
[27] After 1/4 period (Figure 8b), the across-sill flow
turns to the left and another unsteady lee wave is generated
over the left side of the sill top. The unsteady lee wave
produced by rightward flow in the previous period begins topropagate to the left as the across-sill flow weakens andreverses its direction. After 3/8 period, superposition of a
propagating unsteady lee wave and a newly generated
unsteady lee wave evolves into a large-amplitude wave
with a displacement of about 200 m (Figure 8c). Suchamplification eventually causes significant wave breaking,which then leads to strong diapycnal mixing even though
the barotropic flow is not so strong here (the amplitude isabout 60 cm s1).
[28] These features are qualitatively similar to those in thevertically 2-D case (NA00b). However, the responses
around islands and/or banks are more complicated due to
3-D wave processes such as waves propagating from othersills and their reflection at islands and to more complex
features in the flow field. In addition, in the case of a strong
barotropic tidal flow passing over a sill, strongly nonlinear
phenomena like bores and intense bottom currents accompanying strong vertical shear can occur and give rise toconsiderable mixing across the wider density range from
26 sq to 27.6 sq (not shown). In this way, water masses aretransformed in and around the Kuril Straits. More detailed
estimates will be presented in section 5.
3.3. Horizontal Distribution of Unsteady Lee Waves[29] A signature from internal waves is easily visible invertical velocity. Figure 9 shows the horizontal distribution ofvertical velocity simulated for the fourth period at 390 m
depth, roughly corresponding to the core density layer of
NPIW. Many large-amplitude waves are present in Figure 9
and can be identified as inertial gravity waves from theirspreading pattern and speed. The generation mechanism ofthese waves is inferred to be unsteady lee wave (and/or mixed
tidal lee wave) excitation from the same reasons as discussed
in the previous section. In short, large-amplitude unsteadylee waves are produced all along the Kuril Island Chain.
[30] Though these waves interfere with each other allover the domain, a surface of constant phase must indicate ageneration region. A close examination reveals that largeamplitude internal waves originate mainly from (1) the banklocated in the northeastern Pacific region (around x =700 km and y = 150 km), (2) the Urup Strait, and (3) sills
in the northeastern part of the island chain. These regions
are characterized by low PPV and temperature anomalies in
Figure 5. Therefore it is inferred that one of the main causes
of intense vertical mixing in the Kuril Straits results fromthe generation of large-amplitude unsteady lee waves.

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Figure 10. (a) Same as Figure 9 but for the north of the Urup Strait after 3.875 period. (b) An observed
internal wave train identified in the visible band channels of a LANDSAT-4 image gathered on 13 August
1994. (Figure courtesy of John Matthews). The circles indicate the waves in the corresponding region.
[31] Another interesting feature in the model result isthat a propagating wave train is observed north of the
Urup Strait as marked in Figure 10. Some evidence of acorresponding effect in nature is present in a LANDSAT-4
image (Figure 10) gathered on 13 August 1984 (themechanism through which ocean internal waves become
visible on radar and/or visible-band images is discussed,
for example, by Apel et al. [1975] and Alpers [1985]).
Here the 30-m spatial resolution offered by the visible
band channels enables a soliton-like wave train propagatingin the almost same direction at the same location to beprovisionally identified. The difference in wave number is
attributed to a limited model resolution, which weakens thedisintegration process of large-amplitude internal waves.
Though we cannot state with certainty that this wave-likefeature is generated by a subinertial diurnal tide because of
the limited data availability, the close similarities outlined
here support the possibility of generation by the strong
Kuril Islands tides.
[32] Some of these waves travel long distances andgradually decay. For example, large-amplitude waves propagate from the Urup Strait to the Bussol’ Strait. Also, waves
propagating from the bank in the Pacific region (x = 700 km
and y = 150 km) reach Urup Island. Considerable energy
transport by these waves could supplies energy for mixing
along the pathways, even in deep passages.
3.4. Topographically Trapped Waves[33] In addition to the unsteady lee waves describedabove, a tidal flow over a slope can excite internal tides
at the corresponding tidal frequency. Since the K1 tide issubinertial in the Kuril Straits, K1 internal tides are topographically trapped, whereas unsteady lee waves (andmixed tidal lee waves) can exist as inertial gravity waves,
as summarized in Table 2. For the effective detection of
TTWs, we consider along-isobath velocity data at the model
sea surface (Figure 11). In general, TTWs exhibit theirsignal strongly in along-isobath velocity, and the surface
is not a node in the vertical direction. Subinertial TTWs arerotational (except for Kelvin waves), and hence the rotary
spectral is often used for detection [e.g., Hsieh, 1982;
Cummins et al., 2000]. Here, however, relative vorticity
parameter is not so good because the dominant contribution
comes from inertial gravity waves.
[34] Figure 11 shows clockwise propagation of bothbaroclinic and barotropic components around topographic
features. Examples are indicated using red and blackarrows for positive anomalies of the baroclinic andbarotropic components, respectively (a positive alongisobath flow is defined as the flow with the shallower
water on the right). A careful look at these arrows points
to a difference in phase speed and thus in phase between
these two components. This confirms that baroclinic
signals are not merely forced motions and are associatedwith baroclinic TTWs. Similar wave propagation isdetected in recent observations [Rabinovich and Thomson,2001]. Note that positive anomalies are stronger thannegative ones in most places. This fact suggests thatclockwise mean flows around islands are produced by
TTWs as discussed by NA00a, though both barotropic
and baroclinic components are involved in this case. For
this reason, the mean flows produce the ‘‘bi-directional’’

Table 2. Properties of Tidally Generated Internal Wavesa
Wave type
Intrinsic frequency
When stide < fPropagation

kU0/stide  1

kU0/stide  1

kU0/stide  1

unsteady lee waves
kU(t)internal gravity waves (IGW)
capable of crossing isobaths

mixed tidal lee waves
kU(t) ± stide
IGW and/or TTW
cross and/or along a slope

internal tides
±stidetopographically trapped waves (TTW)(clockwise) along a slopeaHere stide is the tidal frequency, k is horizontal wavenumber (or curvature of the topography), and U0 is flow speed amplitude. For
details, please see Nakamura and Awaji [2001].

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Figure 11. Along-isobath velocity of the internal mode (color) and the barotropic (contours)
components in the fourth period at the model sea surface (15 m depth). Positive is defined as the
direction with the shallower water on the right. Contours for the barotropic component are drawn at
20 cm s1 (thick line) and 10 cm s1 (thin line).
current structure within the straits leading to effective
tidal exchange as shown in section 7.

CAPE ¼xyt[35] As described in the previous section, subinertial K1
internal tides take the form of TTWs and propagate along
the slope, whereas unsteady lee waves behaving as inertial
gravity waves in nature can propagate across the slope.
Horizontal propagation of these two kinds of waves could
be accompanied by energy transport from energetic wavegeneration regions (i.e., shallow sills) to deep regions. In
particular, when generated in the shallow Urup Strait ofswift barotropic flow, both types of wave can convey
considerable energy to the adjacent deep Bussol’ Strait
where weak barotropic forcing is present. This possibility
is examined below.
4.1. Energy Equation[36] The equation used in an energy analysis is@E
þ CAPE ¼ r  ½ ðu þ UÞE þ up þ rj0p¼0 gW þ D;
@t

ð7Þ

where
E ¼ KE þ APE;

ð8Þ

1
KE ¼ r0 u  u;
2

ð9Þ

02

1 g2 rjp¼0;
2 r N 2 jxyt
0

p¼0

ð10Þ

ð11Þ

p¼0

4. Energy Analysis

APE ¼


APE ðw þ W Þ d  2 xyt   0
N jp¼0 þ r  rj0p¼0 gw;
xyt
dz
N 2j

N 2 jp¼0 ¼ 
g d  xyt
rjp¼0 ð zÞ :
r0 dz

ð12Þ

xyt

Here rjp¼0 (z) is a horizontal average of the time-averaged
potential density over a cycle and rj0p=0 is the deviation fromit. Total energy, E, is the sum of kinetic energy of theinternal mode, KE, and the available potential energy, APE,
defined following Gill [1982]. Basically, energy is supplied
from the barotropic tidal flow to APE through theconversion term rj0p=0gW. The term CAPE, arising from thexytvertical variation of N 2 jp¼0 and the compressibility, can beinterpreted as a correction term. A detailed discussion ismade in Appendix B. The right-hand side of equation (7)consists of the convergence of energy flux arising from theadvection and the work by pressure, together with the local
energy supply and a dissipation term D.
4.2. Energy Flux and Supply[37] Figure 12 shows the depth-integrated energy flux
vectors and potential energy supply. To focus on thehorizontal energy transport during one tidal period, thesedata are temporally averaged over the fourth period. It
should be noted that around this time, the wave spin-up
process is largely at an end as seen in Figures 9 and 11.
[38] The potential energy supply from barotropic flow isquite large around the bank and sills in the northeast region
and around the Urup Strait. These are areas where largeamplitude unsteady lee waves are generated, as indicated in

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Figure 12. Energy flux vectors superposed on the distribution of potential energy supply from thebarotropic tidal flow, which are vertically integrated and temporally averaged in the fourth period.
Arrows are plotted at every 10 grid points and represent the horizontal average over 10  10 grids.
Contours are also drawn at intervals of 10  103 erg cm2 s1.
the preceding section. This fact therefore confirms that alarge amount of energy is transported from these wave
generation regions. Figure 12 implies that the energy
transport can be primarily attributed to both an acrossisobath energy flow carried by inertial gravity waves andto a clockwise along-isobath transport carried by TTWs.
Interestingly, the across-isobath flux also moves in a clockwise sense. This is mainly because unsteady lee waves
generated by a clockwise barotropic flow propagate in aclockwise sense and hence draw spiral trajectories. Therefore the wave energy flux from the Urup Strait to the
Bussol’ Strait is intensified. This takes place in the westernpart of the strait, with a similar process developing in theeast.
[39] The term balances of equation (7) in the fourth
period in the Bussol’ and Urup Straits are shown in
Table 3. It is clear that energy influx from outside regions
dominates in the deep Bussol’ Strait (even after it islargely canceled by outflux). This is made mainly throughthe work done by the pressure term and therefore comesfrom the energy transport by waves. Since dissipation acts
on both waves and the mean state, the dissipation term
also becomes dominant when temporally averaged. This
therefore implies that incoming waves lose their energy inthis region to small-scale turbulent motions leading todiapycnal mixing.
[40] On the other hand, the local energy supply from thebarotropic tide is even smaller than the energy increase

rate (@E/@t + CAPE). This also indicates the importance ofthe net energy influx by waves propagating from adjacentshallow sills. Though this small fraction of energy input,
which is now used to increase the local energy, will be
consumed by dissipation and/or outflux after the energy
increases to a saturation level, the main balance is notaffected qualitatively.
[41] In contrast, the energy balance in the shallow Urup
Strait shows that energy derived from the barotropic flow is
distributed out to the adjacent deep regions. Though thepresence of large-amplitude waves makes the correction
term somewhat large, it is not a dominant term.

5. Diapycnal Mixing
5.1. Method[42] To estimate the intensity of vertical mixing associated with the wave generation and energy transport processes,
we calculate diapycnal diffusivity coefficients, Kr, using thedata in the fourth period. In doing so, since the periods of
unsteady lee waves are much different from the tidal period,
the diffusivity coefficients will be overestimated whencalculated on the basis of the Fickian formulation (i.e.,
Kz = r0 w0 /(@r/@z), where ðÞ and 0 denote a temporal averageover one tidal period and its deviation, respectively). In fact,
the calculated values (not shown) were about 10 times
larger than those shown later, though the overall pattern
was similar.

Table 3. Energy Budget in the Fourth Perioda
Strait15

Bussol’ (10 )Urup (1016)@KE/@t@APE/@t

CAPEr  [(u + U)E]r  (up)rjp=00gW

Dissipation

0.92
0.01

1.26
0.03

0.82 + 0.14
1.21 + 0.03

0.88
1.09

4.60
2.58

1.41
5.78

5.39
0.85

a

Values shown are volume-integrated and time-averaged values for the fourth period. The integration regions are (x = 430 km, 460 km, and y =190 km, 230 km) for the deep ‘‘Bussol’ Strait’’ and (x = 360 km, 390 km and y = 210 km, 270 km) for the shallow ‘‘Urup Strait.’’ The unit iserg cm3 s1. The dissipation is calculated as the residual of the other terms. The values of the correction term are shown for both the first and second
terms in equation (11).

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Figure 13. Temporally averaged diapycnal diffusivity coefficients (cm2 s1) estimated from thecalculated fields in the fourth period. Contours are drawn at 50 cm2 s1. (a) An example of y-z sections
across a moderately high sill (the same one in Figure 7). (b) The Bussol’ Strait section shown along theIsland Chain, but the vertical axis is potential density. (c) Average along isobaths taken on isopycnal
surfaces. Vertical and horizontal axes are sq and isobaths, respectively. (d) Average along isobaths but on
the horizontal surfaces. The abscissa represents the area integrated from the shallower side, and ordinate
is depth. The depth at the bottom of the averaged values (the top of the black area) corresponds to thedepth of the isobath along which the average is taken.
[43] Thus we estimate the diffusivity using the following
scaling proposed by Gregg [1989]. Since the method isbased on the internal wave dynamics and observations, itallows us to estimate the diapycnal diffusivity more accurately in the presence of waves of various frequencies.
Although Polzin et al. [1995] indicated that Gregg’s[1989] parameterization can result in underestimates ofenergy and thus its dissipation rate, , in a high energy
region and hence proposed a more sophisticated scaling, it
is difficult to apply their method to our model results
because of the huge data size.
[44] Owing to our limited grid size, a 30-m shear is usedinstead of the 10-m shear of Gregg [1989] for the estimationof  and dynamical mixing coefficient, Kr as
 ¼ 7  1010

4N 2 S30;
2
4
N0 SGM

ð13Þ


:
N2

ð14Þ

Kr ¼ 0:25

5.2. Diapycnal Diffusivity Coefficient[45] The estimated Kr is temporally averaged over the 4th
period. Figure 13a shows the distribution in the verticalcross section of the northeastern island chain, where significant mixing corresponding to values of Kr > 50 cm2 s1can be seen over a relatively wide area. The maximum value

exceeds 1000 cm2 s1 over shallow sills. The distribution
pattern and magnitude are similar to those of the vertically
2-D case (NA00b) and are in agreement with the results ofsection 3. Therefore significant diapycnal mixing in thisregion is attributed to unsteady lee waves. On the contrary,
Figure 13b shows the Kr map across the deep Bussol’ Strait
where wave energy generation is much weaker than in theabove region. On this map, sq is used as a vertical axis to
identify the density layers of active diapycnal mixing. It isapparent that considerable mixing (Kr > 10 cm2 s1) takes
place as expected from the results of the energy analysis.
This is consistent with the recently observed distributions ofcarbon isotopes [Aramaki et al., 2001] as well as
temperature and salinity [Kawasaki and Kono, 1994]. As
discussed earlier, this arises from the along-isobath transportof significant wave energy from adjacent shallow sills. It
should be noted that the density layer of the neighboring
OSMW and NPIW core (26.8 sq) is subject to this mixing.
Therefore the outflowing Okhotsk Sea water is expected tobe modified by tidal mixing to an extent determined by thetravel time of passage through the Strait.
[46] The above features relating to the intensity of diapycnal mixing are expected to be general in the Kuril Island
Chain. This can be seen in Figure 14, where areas ofsignificant diapycnal mixing at each isopycnal layer in thewhole model domain are represented. The figure confirmsthat intense diapycnal mixing distributes in shallow straits,around islands, and over the bank where tidal flow is swift.

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Figure 14. Same as Figure 13b, but for horizontal distribution in four isopycnal layers. Green areas
denote land grid points at the corresponding density range.
Hence energetic unsteady lee waves are generated in theseregions, whereas the mixing weakens with depth except
near the bottom. In addition, Kr values averaged at eachpotential density for water columns of the same water depth
in the whole model domain are presented in Figure 13c.
These figures are consistent with the high oxygen anomaly
in the Kuril Straits observed from the surface to around2200 m, which is a signature of locally enhanced ventilation[Yasuoka, 1968; Talley, 1991; Freeland et al., 1998].
Observed chlorofluorocarbons (CFCs) concentrations also
indicate the importance of diapycnal mixing in forming the
Okhotsk Sea water below 27.2 sq [Wong et al., 1998]. Thus,
diapycnal mixing induced by unsteady lee waves and TTWs
is the most likely cause of the observed intense verticalmixing at the Kurils, and the estimated values for eachisopycnal layer will provide information on how much thevertical density distributions of the water masses are
modified in and around the Kuril Straits. For comparison,
the Kr values averaged horizontally at each depth for watercolumns of the same water depth in the whole model
domain are presented in Figure 13d.

6. Eddy Transport of Transformed Water to the
Offshore Region[47] As mentioned in section 3.1, the pinched-off eddies
moving away from tidal fronts have the ability to transport

the transformed water from the straits to offshore regions.
This spreads the effect of tidal mixing around the islands tothe deep basins. In this section, such offshore transport isestimated to assess the impact of tide-induced water modification in and around the straits on the Okhotsk Sea andthe North Pacific.
6.1. Eddy-Induced Transport of Mixed Water[48] To quantify the offshore transport of mixed wateraround the straits (defined here as transport reaching deep
offshore regions), we use PPV to differentiate the mixed
water from the surroundings and calculate its volume indeep regions, defined here as >3000 m, because the deepest
strait of the Kuril Chain is 2200 m while the adjacent
Kuril Basin is around 3200 m deep and because theestimated diapycnal mixing is rather small in regions deeper
than 3000 m except near the bottom (Figure 13). The region
where y > 330 km is also regarded as the deep region to
include the fringe of the Kuril Basin (except for the partnear the Kuril Straits), where the mixing is weak but thedepth <3000 m. The mixed water is identified as having a
PPV value either 20% lower or higher than the ambient
average, approximated here as the isopycnal average in aregion of almost no PPV anomaly (x = 50 km to 200 km, y =30 km to 150 km). Following on from these definitions, thevolume increase of the mixed water in the deep regions is
calculated in order to indicate the offshore transport of the

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mixed water, assuming that diapycnal mixing is not effective in the deep regions. Our estimate does not fully remove
the influence of horizontal diffusion that is inevitably
involved in a numerical model. Note that increase or
decrease of the above threshold values of PPV by 5% does
not make a qualitative difference.
[49] Figure 15 shows the calculated volumes for eachisopycnal layer at five-period intervals. The major offshoretransport of low PPV water to the deep regions is conducted
through layers lighter than 26.65 sq (Figure 15a). At greater
depth, an alternating pattern appears. This shows as a peakof high PPV water around 26.65 sq (Figure 15b), a
significant amount of low PPV water around 26.8 sq, andhigh PPV water in the deep layer. Each peak has its
counterpart in shallow regions (Figures 15c and 15d),
indicating that their formation regions lie in the Kuril
Straits (the shallow region is defined here as a region thatis neither the deep region nor the sponge zone). This is not
the case for the deepest of the high-PPV anomalies that is
produced locally (and is excluded in the following
estimates).
[50] Each pair of low and high peaks is preceded by theformation of a low PPV peak. The reason for this is asfollows. Intense diapycnal mixing over shallow sill tops
(200 m) produces vertically uniform (thus low PPV) waterin the upper layer. As this mixing evolves, high PPV water
is formed beneath it and the density of the peak moves toheavier water. The former (latter) corresponds to the firstpeak of low (high) PPV water. At mid-depths (say 500 m to1500 m), a similar process occurs associated with considerable diapycnal mixing generated around sill tops ofmoderate depth and over sill slopes, thereby producing asecond peak of low PPV water in the intermediate layer anda second high PPV peak below. Note that water modification is still in effect after 25 periods since the diffusion
timescale is longer than in shallower layers because of
weaker diapycnal mixing. In addition, the above patternalso depends somewhat on the vertical profile of PPV
initially set in this experiment. In this case, the lightest
and largest peak of high PPV is enhanced by the presence ofthe low PPV OSMW.
[51] The total offshore volume flux of low and high
PPV waters during 25 periods reaches 5.7 Sv and 8.7 Sv,
respectively, on average, of which 2.6 Sv and 3.9 Sv enter
the open Pacific. These offshore transports are attributed
mainly to eddies arising and moving away from tidal
fronts (at least in this model) since the net offshoretransports by tidally induced residual flow are about 2 Sv
for the Okhotsk Sea and almost nothing for the open North
Pacific, which are similar to those in the barotropic case
(Figure 4). Figure 15 suggested that the volume increment
to the mixed water in the offshore regions is roughly
constant around 25 periods because the eddy transport isstill in effect. This indicates that the offshore transport
is roughly in a steady state and hence that our estimate ismeaningful.
[52] Diapycnal mixing within the vicinity of the Kuril
Islands therefore has a greater impact than previously
thought on the Okhotsk Sea and the North Pacific as aresult of both modification of in/outflowing water properties
and offshore transport of the modified water due to eddies.
This is consistent with a recent analysis of observed oxygen

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Figure 15. Evolution of anomalous PPV water volume inisopycnal layers. (a) Low and (b) high PPV waters in theoffshore area, and (c) low and (d) high PPV waters in theshallow region. Thicker lines indicate later time as indicatedin Figure 15a.

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East Kamchatka Current Water. Nevertheless, the close
similarities to the observations suggest that our results will
not be changed qualitatively.

7. Water Exchange Between the Okhotsk Sea
and the North Pacific[55] To examine the relative importance of the eddydriven transport, in this section we compare it with a varietyof estimates for water exchange through the Kuril Straits.

Figure 16. Temporally averaged inflow (red) and outflow(blue) in the Bussol’ Strait in the fourth period. Inflow
denotes to the Okhotsk Sea from the North Pacific. Contour
interval is 10 cm s1.

7.1. Water Exchange by the K1 Tide[56] Figure 16 shows a map of the time-averaged current
in the vertical cross section of the Bussol’ Strait in the fourth
period. In general, the mean current flows along the slopewith the shallower side on the right and is characterized by ahorizontally alternating structure favorable for enhancing the
net water exchange as in the barotropic case. In the verticalprofile, considerable shear exists. In particular, the current isintensified near the bottom to a significant flow speed of
20 cm s1 or more. These features are qualitatively similar to
the findings of the very recent LADCP measurement program [Katsumata et al., 2004], which resolved the complicated current structure in the strait. Moreover, the observed
mean flow is stronger near the peak of the fortnight springtide compared with that of neap tide. These results suggestthat the tide is its major forcing.
[57] The time-averaged water exchange through the Kuril
Straits in the whole model domain is shown in Figure 17.

isotope distributions that suggests that vertical mixing ismore important than the role of sea ice in the formation of
the intermediate water of the Okhotsk Sea [Yamamoto et al.,2002].
6.2. PPV and Salinity Transport by Eddies[53] In association with the eddy-driven transport, water
bodies exhibiting locally anomalous properties are conveyed steadily offshore. Here we assess the impact onoffshore deep regions focusing on the change in PPV andsea surface salinity. On the basis of the previous section,
PPV values of the eddies differ on average by 30% to 40%
from the background values. Similarly, the salinity of theeddies differs; for example, the model sea surface salinity of
low PPV water is 0.1 psu larger on average than the
background value. This induces an increase in potential
density by 0.08 sq in offshore regions. (Note that thesedifferences are still increasing after 25 periods.) Reid [1973]
and Gladyshev [1995] reported that high sea-surface-salinity
anomalies of 0.1  0.3 psu greater than the surroundings
exist in the Kuril Straits. This implies that tidal mixing in the
Kuril Straits induces a significant upward salt flux into
the surface layer, which can be subsequently transported tothe interior regions of the Okhotsk Sea and the North
Pacific. In addition, the PPV flux will affect the circulationin the interior region according to the ventilated thermocline
theory. With a saline flux into the surface layer, cooling in
winter will produce heavier water and thus enhance
subduction.
[54] The above estimation of PPV and salinity fluxes
could somewhat change if the initial stratification is alteredfrom that exhibited by the Kuril Basin water to that of the

Figure 17. Water exchange through the straits obtained bytemporally averaging currents, shown in terms of volume
flux per unit depth (Sv/m). Thick and thin lines are those of
periods 4 and 26, respectively, and dashed lines are thosecorresponding to the barotropic flow. The values areintegrated in the whole straits in the model, though thenorthernmost and southernmost parts of the straits are notincluded. Note that these straits are very shallow (less than
100 m) so that the transport will be as small as in thebarotropic case considered by Nakamura et al. [2000a].

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The total amount of exchanged water reaches 26 Sv in the
26th period, with roughly half passing through the wide anddeep Bussol’ Strait. This represents a marked increase overthat in the barotropic case of NA00a and is mainly due tointensification of the mean flow by the effect of baroclinic
waves, as the ‘‘extended’’ tidal rectification mechanism
suggests [NA00a]. The effect associated with the tidal fronts
make an additional contribution in the 26th period. (Theincrease in the barotropic component from NA00a’s estimate is due to the finer grid resolution used here.)
7.2. Comparison With Other Estimates and theRoles of Tide- and Eddy-Induced Transports[58] There are three observational estimates of outflow
to the North Pacific using direct current measurements.
From the intensive LADCP measurements mentioned
above, Katsumata et al. [2004] have estimated an outflow
through the Bussol’ Strait to be 8.2  8.8 Sv. Note thathorizontal integration was applied to their estimate ofthese values, and thus the outflow volume would bemuch larger when taking the bi-directional flow structure
into consideration. The outflow for the full island chain
was estimated to be 16.7 Sv by Kurashina et al. [1967],
who combined a variety of ‘‘two current meter,’’ GEK,and geostrophic measurements. This value could be also an
underestimate since their estimate for the Bussol’ Strait is
only 4.8 Sv, even smaller than the estimate by Katsumata
et al. [2004]. An outflow through the Kruzenshterna Strait
was estimated to be small (1.6 Sv) [Katsumata et al.,2001].
[59] In contrast, observational estimates based on tracer
budgets are much smaller than those based on current
measurements. Wong et al. [1998] gave an estimate of
2.7 Sv for the density range of 26.6 to 27.4 sq (roughly
corresponding to 100– 1100 m depth) from q, S, and
CFC budgets in the Okhotsk Sea. By estimation of themixing ratio between the Okhotsk Sea and the East
Kamchatka Current water in the Oyashio Current from q-S
analysis, Yasuda [1997] and Yasuda et al. [2002] calculated
the outflow to be 2  5 Sv for a 26.6 to 27.2 sq density
range (100– 900 m depth) and 4.2 Sv for a 26.6– 27.5 sq
density range (100– 1300 m depth), respectively. Even
taking into account the facts that these estimates do notinclude the contribution of surface and deep layers and that
estimates based on tracer budgets are sensitive to theassumptions used [Kobayashi, 2000], the difference fromthose based on current measurements nevertheless seems
significant.
[60] On the other hand, the present estimate of the tideinduced water exchange via the Kuril Straits is closer to theestimates based on direct current measurements. For example, our simulation experiment forced by the K1 tide alone
explains at least a half of the horizontally integrated outflow
volume from the Bussol’ Strait reported by Katsumata et al.
[2004]. This is confirmed by the fact that the correspondingarea integration of outflow using our simulation result
yields the amount of 4.4 Sv. As for the offshore transport
by eddies, the estimated result in section 6.1 is similar to
those derived from tracer budgets. Thus, our estimates of
the tide- and eddy-induced transports have a gap that issimilar to the significant difference in water exchange
through the straits described above.

C09S07[61] The above comparisons of the outflow evaluations
suggest that the gap in the observational estimates has aphysical reasoning. Considering the fact that the tideinduced residual flow circulates along isobaths and thatmost of it is therefore trapped around the islands, the gap
is likely to be explained by the joint action of tide-induced
residual transport dominating in the vicinity of islands andthe offshore eddy-driven transport as follows. While alarge amount of water passing through the straits by
tide-induced residual current remains in the vicinity of
the islands for a while, a fraction of the exchanged waterof modified water properties is subsequently transported tothe offshore regions by eddies generated from tidal fronts.
The direct measurements in the straits observe the firstprocess while the budget calculations correspond to thesecond.
[62] There are other processes that should be included in
the above discussion. First of all, the effects of large-scale
wind-driven and thermohaline circulations should be considered. In fact, the presence of significant seasonal and/orinterannual variation in transport through the straits isreported [Kawasaki and Kono, 1992; Yasuda et al., 2000].
This issue has not been well described and is currently
under investigation by several researchers. We note that
there are spring-neap cycles of a semi-annual period such as
those generated by the K1 and P1 tides. Inclusion of theseeffects are necessary for a more accurate estimates oftransport. The variation in the depth of straits also results
in a net outflow of 1 Sv by tide-induced mean flow from thedeepest Bussol’ Strait. This is not counted in the ‘‘offshoretransport’’ in section 6.1 since it flows over a shelf breakthat is shallower than 3000 m, as in the barotropic case,though it is confined to the intermediate layers locatedroughly from 500 m (27.0 sq) to 1500 m (27.5 sq).
Eddies also arise from other mechanisms, such as thoseoriginating from the Kuroshio Extension. In addition, thereis the difficult matter of the relation between Lagrangianand Eulerian transports. For example, tidally induced
residual transport could make a significant contribution
when interacting with eddies. These problems should befurther investigated in the future. Nevertheless, good
similarities with observations have been found in ourmodeling results, in particular regarding the presence of
mixed water produced by strong tidal currents in the straits
and the presence of many eddies [Talley and Nagata, 1995;
Yasuda et al., 2000]. Moreover, long-term observations by
Kono and Kawasaki [1997] pointed to the fact that pure
Okhotsk Sea water hardly reaches offshore of Hokkaido(just downstream of the Kuril Island Chain) and that theEast Kamchatka Current water has already been modified
before the confluence with Okhotsk Sea water from the
Bussol’ Strait. Our model result is able to explain theseobservational facts. As such, the concept that waterexchange through the straits and offshore transport isdominated by a number of separate physical processes will
be useful in better understanding the relation between the
Okhotsk Sea and the North Pacific as well as the impact oftidal processes in the Kuril Straits.
[63] We suspect that both eddy genesis from tidal fronts
and tidally induced residual flow circulating around an
island also work as the major causes of isopycnal mixing
for the Okhotsk Sea water and the East Kamchatka Current

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water. These problems are beyond the present model configuration and are left for future work.

8. Summary and Discussion[64] An experiment using a 3-D nonhydrostatic model
was conducted in order to investigate water transformationand transport processes associated with the K1 tide aroundthe Kuril Straits. These processes are considered to be
central in our understanding of the linkage between the
Okhotsk Sea and the North Pacific via the Kuril Straits. The
results obtained are as follows.
[65] As in the vertically 2-D case, large-amplitude unsteady lee waves are generated around a sill top andpropagate away as the flow reverses. The generation regionsof intense internal waves with a maximum elevation higher
than 200 m correspond to areas where the energy conversion from the barotropic tidal flow to potential energy islarge. Such zones have been identified as (1) the bank on the
Pacific side of the northeastern Kurils, (2) the Urup Strait,and (3) sills in the northeast of the study area. As a result,significant wave breaking occurs from the sea surface toabout the 27.6 sq density layer. Though firm experimental
evidence to support these prediction of wave generation isrequired, some internal-wave-like signatures observed in
LANDSAT-4 TM visible-band imagery provide encouragement that our simulated results are indicative of the realsituation. Over the sill slope, subinertial K1 internal tides are
generated as topographically trapped waves and propagate
clockwise along isobaths. The propagation of these twokinds of waves is accompanied by energy flux from theregions of strong tidal flow to greater depths.
[66] The wave generation and energy flow eventuallycause intense diapycnal mixing over the shallow sills
and bank and near the bottom leading to the maximum
diapycnal diffusivity of over 1000 cm2 s1. These same
locations are also the generation regions of unsteady lee
waves. Interestingly, considerable mixing takes place (10 
50 cm2 s1) even in the deep Bussol’ Strait, which isthought to be the main exit of the Okhotsk Sea water. Thisis mainly due to energy supply carried by the two types ofwave from the adjacent Urup and Simusir Straits whereenergetic wave generation occurs.
[67] The intense mixing transforms water properties inand around the straits and thereby produces an upper layerof well-mixed low potential vorticity (PV) water with alayer of high PV water below. Accordingly, PV fronts areformed around the islands, and these can sustain instabilities
and eventually lead to the formation and release of eddies
with low core PV values. Though a robust comparison withsatellite imagery awaits a more detailed future study, thecalculated distribution of sea surface temperature nevertheless bears an encouraging resemblance to an advanced very
high resolution radiometer (AVHRR) sea surface temperature image gathered on 21 September 1994. The similarities
identified here imply that the tidal mixing process alone is
responsible for frontogenesis and associated eddy formationin the vicinity of the Kuril Islands.
[68] The offshore volume transport away from islands bythese eddies reaches 14.4 Sv on average, with some 6.5 Sv
being carried to the open North Pacific. This amount issimilar to the previous outflow estimates based on tracer

C09S07budgets. On the other hand, water passing through thestraits due to tidal residual flow reaches 26 Sv. Though thisvalue is huge, both the pattern and the amount of exchanged
water are in good agreement with the results of direct
current measurements in the straits. In particular, theresemblance in the Bussol’ Strait with the recent observation by the Hokkaido University group [Katsumata et al.,2004] is striking. These comparisons strongly suggest that
our model results are not unrealistic, and we infer that(1) water exchange through the Kuril Straits is mainly
caused by tides but (2) most of it is trapped and circulates
around the islands as a tidally induced residual flow, and(3) the eddies arising from tidal fronts are mainly responsible for the offshore transport of exchanged water subject
to transformation in the straits. Direct measurements in thestraits observe the first two processes while the tracer
budget analysis corresponds to the last.
[69] Significant offshore eddy transport away from theisland region further implies that the effect of diapycnal
mixing, which dominates at the Kurils, spreads to the
Okhotsk Sea and the North Pacific. In fact, the offshore
eddy transport of the transformed water in the straits
supplies significant PV and salinity fluxes to both the
Okhotsk Sea and the North Pacific. The PV values of sucheddies differ by 30– 40% from the ambient water. The sea
surface salinity is 0.1 psu higher than the ambient water, andthis difference leads to a density increase of 0.08 sq in theoffshore regions. Such fluxes will affect water masses andcirculations in the two basins. Our results imply that thejoint effect of tidally induced transport and transformation
dominating in the straits and subsequent offshore eddytransport are essential aspects of the link between the
Okhotsk Sea and the North Pacific Ocean.
[70] As mentioned in section 2.2, this study adopts a‘‘surface lead assumption’’; that is, a barotropic tide used inour 3-D model experiment is calculated separately from abarotropic tide model and is given as the main forcing forthe baroclinic process. This assumption is accompanied by
the following three approximations.
[71] First of these is a hydrostatic approximation for thebarotropic tide model. This is considered to be permissible
because the barotropic waves we concern have elevation
amplitude of at most 2 m and wavelength of tens tothousands of kilometers (NA00a).
[72] Second, sea surface is approximated to be rigid for abaroclinic component. This leads to the neglect of bothnonlinear interaction between barotropic and baroclinic
components through displacement of the sea surface andthe difference in internal wave reflection at the surface fromthe free surface case. Errors arising from the neglect of thenonlinear interaction through surface displacements are
considered not to be significant since the phase speeds ofbarotropic tides and baroclinic motions are generally muchdifferent from each other so that resonant interaction may
hardly occur. Regarding the difference in the reflection at
the surface, the linear internal wave theory shows that thedifference in reflection between the rigid and free surface
cases is indistinguishable (precisely, within an error of theBoussinesq approximation) under the conditions that thesurface displacement due to an internal wave is sufficiently
smaller than the vertical scale of the wave, and that thewave frequency squared is sufficiently smaller than the

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NAKAMURA AND AWAJI: TIDE-INDUCING MIXING AND TRANSPORT AT KURIL

buoyancy frequency squared [e.g., LeBlond and Mysak,1978]. In our numerical experiment (section 3.2), though
there are waves of large amplitude (100 m), their surface
displacement is at most 0.1 m, much smaller than their
vertical wavelength (O(100 m)). Also, the squared frequencies of unsteady lee waves are much smaller than thebuoyancy frequency squared (say, (5/30)2 = 1/36). In fact,many previous studies such as that of Hibiya [1988] andLamb [1994] successfully reproduced internal wave processes using the rigid lid approximation. Thus the result
obtained in this study is considered to be reasonable at least
qualitatively.
[73] Last, the energy dissipation of a barotropic tide overa topographic feature is strengthened primarily through theconversion to baroclinic potential energy. The baroclinic
motions induced by this energy supply then produce theReynolds stress, which causes the secondary conversion of
kinetic energy between the barotropic and baroclinic
motions, and could further strengthen the damping of thebarotropic tides.
[74] In the present numerical approach, however, suchdissipation of a barotropic tide is included as a result ofusing the bottom friction and horizontal eddy viscosity inthe barotropic tide model. Though these are crude parameterizations, a barotropic tide is well reproduced in manystudies by using the above parameterizations, as shown by
Le Provost et al. [1994] for the global ocean and Kowalik
and Polyakov [1998] and NA00a for the Okhotsk Sea andthe Kuril Straits. In addition, the surface elevation and flow
speed of the barotropic tide calculated in this study agree
by and large with those of observations as discussed in
section 2.4.
[75] The secondary energy conversion through the Reynolds stress can cause some feedback to the barotropic tide,but it is neglected for dynamical consistency with thesurface lead assumption in this study. Since this could
modify the calculated field, we estimated the energy conversion through the Reynolds stress (using the result calculated without the Reynolds stress term). This term issignificant over relatively shallow sills, so that the horizontal distribution of the energy input from the Reynolds stressis basically similar to that of the potential energy supply
from the barotropic tide (section 4). The ratio of these twoenergy source terms averaged in the model domain is 0.46
and 0.48 in the fourth and 26th periods, respectively.
Suppose that the fraction of the energy used for local mixing
is nearly the same as in the case without the Reynolds stress,
the above ratio means that the values of diapycnal mixing
coefficient shown in section 5 would increase by 1.5 times.
Therefore the Reynolds stress term should be taken into
account in order to make more precise estimates in the
future. Nevertheless, the distribution of diapycnal mixing
would not change qualitatively. Besides, as the Reynolds
stress will enhance the energy input to the baroclinic
component, the tidally induced processes could be ofgreater importance than in this study.
[76] From the above discussion, the use of the surface
lead assumption and the associated approximations will notchange the conclusions obtained in this study qualitatively.
This is also supported by the encouraging resemblances
between the model results and observations mentioned
earlier.

C09S07[77] The present study is a first step toward clarifying thebaroclinic process in the Kuril Straits and its influence on the
North Pacific and the Okhotsk Sea circulation. Our work is amodeling study of one possible process associated with thepredominant K1 tide. In fact, the process is isolated byidealizing the background states. Thus our process study
should be complemented by observational studies and comprehensive models with more realistic forcing and capable ofinvestigating the roles of wind-driven and thermohaline
circulations on the transport and transformation processes
in and around the Kuril Straits. Thus future modifications to
our numerical model should provide more realistic simulations. The generation of intense unsteady lee waves implies
that an internal wave drag is effective not only for superinertial tides, as considered by Jayne and Laurent [2001],
but also for subinertial tides as an energy dissipation mechanism in deep regions. This is an interesting issue, but its
overall relevance to the energy budget of barotropic tides
should be evaluated on the basis of future observations.
Nevertheless, the many similarities to observations described above strongly support our qualitative conclusions
and confirm/underline the importance of the processes
considered here.

Appendix A: Pressure Equation[78] In general, the pressure field of nonhydrostatic equations for an incompressible fluid can be found by solving a
Poisson equation, which is derived from the divergence ofthe momentum equation. For computational efficiency, we
use an iterative method for the Poisson equation. To
enhance the convergence of the inversion, the pressure isseparated into hydrostatic and nonhydrostatic parts, following Marshall et al. [1997b]. The hydrostatic part (pHY) is
defined so as to satisfy the hydrostatic balance,@pHYr¼  g:@zr0

ðA1Þ

The nonhydrostatic part (pNH) is obtained from thefollowing Poisson equation:
1 2
r pNH ¼ r 
r0



@u
 ðu þ UÞ  ru  f k  u þ nH r2H u@t
@2uþ nZ 2 ;ðA2Þ@z

with a homogeneous Neuman boundary condition (n 
rpNH = 0), where n is a unit vector normal to a boundary.
More detailed discussions are given by Harlow and Welch[1965], Williams [1969], and Marshall et al. [1997b].

Appendix B: Energy Equation[79] The energy equation used in section 4 is derived in
the following way. First, a dot product of r0u with themomentum equation (2) yields an equation for the internal
mode kinetic energy (KE),@þ ðu þ UÞ  r KE þ r  ð upÞ ¼ r0 gw þ Du ;
@t

ðB1Þ

where the term (r0gw) represents the energy conversion
from potential energy (PE) to KE, and Du is the dissipation

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NAKAMURA AND AWAJI: TIDE-INDUCING MIXING AND TRANSPORT AT KURIL

term. In the derivation of the conversion term, the density
variation is expressed as the sum of a horizontal average ðÞxyand its deviation ()0,
rtotal ¼ r0 þ rxy ð z; t Þ þ r0 ð x; y; z; tÞ:ðB2Þ

The dynamically irrelevant part, rxygw, is subtracted. Thislatter term gives rise to the variation of PE due to theinteraction with the outside of the model domain through an
open boundary, but the restoring condition used here works
to keep the domain almost closed, and thus it is negligible inthis case.
[80] Second, in order to easily estimate a dynamically
relevant part of PE, we define APE as in equation (10)following Gill [1982]. Since this definition invokes anapproximation,
r0  

drxy
h;
dz

ðB3Þ

for an isopycnal elevation, h, the density used for thedefinition should be conserved at least approximately. Thus
we use the potential density for APE. An equation ofpotential density is@rjp¼0þ r  ðu þ UÞrjp¼0 ¼ D0r :
@t

ðB4Þ

Here the term D0r represents the diffusion of salinity andpotential temperature and includes the cabbeling effectthough, in this case, the maximum variation in potential
temperature is about 1C except for the surface layer sothat the cabbeling effect is very small. The product ofequation (B4) and gh yields an equation for APE,





@
APE @
@
xy
N 2 jp¼0
þ ðu þ UÞ  r ð APEÞ þþ ðw þ W Þ
xy
2
@t
@t
@z
N jp¼0 xy

rj0p¼0 g @rjp¼0 =@t
 xy

þ
r0
@rj =@zp¼0¼ rj0p¼0 gðw þ W Þ þ Dr ;ðB5Þ

where N2|p=0 is a squared buoyancy frequency calculatedusing potential density and Dr is the diffusion term.
[81] The second and third terms on the left-hand side ofequation (B5) are the correction terms to the first termarising from the approximation (B3). To simplify further,
we replace a horizontal average of potential densityxy
rjp¼0 (z, t) with its temporal average over one tidal cycle
xyt
rjp¼0 (z). Then the correction terms becomeAPEðw þ W Þ @ 2 xyt
N jp¼0 :
xyt
@z
N 2j

ðB6Þ

p¼0

[82] Finally, using equation (B6), the sum of equations (B1)and (B5) gives the energy equation (7),@EAPEðw þ W Þ @ 2 xyt
N jp¼0þ r  ½ ðu þ UÞE þ up þ
xyt
@t
@z
N 2 jp¼0

¼  r0  rj0p¼0 gw þ rj0p¼0 gW þ Du þ Dr :ðB7Þ

In the above, the term rj0p=0gW represents an energy supply
from the barotropic tidal flow (kinetic energy) to APE,

C09S07

which is almost all of the energy source of the model (thesponge zone mainly acts as an energy sink).
[83] Another correction term arises from the use of
potential density in APE. The terms rj0p=0gw and r0gw
represent energy conversions from KE to APE and PE to
KE, respectively. The sum of these two would vanish if weused an general expression of PE instead of the APE, andcan be regarded as a correction to the variation of APE(due to the compressibility). Although use of PE allows us
to circumvent these two correction terms, it makes thedefinition of energy flux vectors due to advection difficult.
We thus use the APE since we are interested in energy
transport.
[84] We choose the averaged density in equation (B3) inorder to avoid a singularity and to enable a robust calculation of APE even in the presence of density inversions.
However, it should be noted that the use of @r/@z instead of
the average reduces the equation (B6) part of the correction
term when there are no density inversions. The reason forthis is that when the averaged buoyancy frequency varies inthe vertical direction, the former method leads to an
overestimate of h for a vertical displacement extending to
the layer with greater buoyancy frequency and vice versa.
[85] Acknowledgments. We greatly appreciate the kind offer of useof the numerical model from K. Tanaka and K. Akitomo. We also wish toacknowledge J. P. Matthews for his critical reading and for the kind offer of
LANDSAT-TM imagery, and S. Saitoh (Hokkaido University, Japan) for
the kind offer of NOAA 12 AVHRR imagery. Thanks are extended toanonymous reviewers for their useful comments and to S. Martin and
K. Ohshima, who are the associate editors of the special section, for theircomments on the figures. Numerical calculations were done on the VPP800
at the Data Processing Center of Kyoto University. T. A. and T. N. arepartly supported by Category 7 of MEXT RR2002 Project for Sustainable
Coexistence of Human, Nature and the Earth. T. N. is also supported by a
JSPS Research Fellowship for Young Scientists.

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T. Awaji, Department of Geophysics, Graduate School of Science, Kyoto
University, Kyoto 606-8502, Japan.
T. Nakamura, Integrated Modeling Program, Frontier Research System
for Global Change, Yokohama 236-0001, Japan. (tnakamura@jamstec.
go.jp)

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