1622 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

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 ®nal form 19 July 1999)

ABSTRACT The tidal exchange between the Okhotsk Sea and the North Paci®c Ocean is studied numerically with particular

emphasis on the predominant K1 barotropic component. The calculated harmonic constants of the K1 tide in and around the Okhotsk Sea agree well with those obtained from extensive tide gauge observations. The features

of the simulated tidal ®elds 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 with a maximum amplitude of over 1.5 m sϪ1 in the Kuril Straits. The structures of tide-induced mean ¯ows in most passages of the straits are characterized by ``bidirectional currents'' (in which the mean ¯ow exhibits a reversal in direction across the passages). This feature is clearly indicated in NOAA infrared imagery. The mean transport shows signi®cant net exchange of water via several straits in the Kuril Islands. A transport of about 5.0 Sv (1 6 3 Ϫ1 Sv ϵ 10 m s ) toward the North Paci®c 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 recti®cation over variable bottom topography, whereas in deep passages such as Bussol Strait, propagating trapped waves along the islands are essential for generating the bidirectional mean currents. Particle tracking clearly demonstrates these features. The tidal current is therefore thought to play a major role in water exchange processes between the Okhotsk Sea and the North Paci®c.

1. Introduction from the Kuril Straits and that the con¯uence of the East Kamchatka Current and the discharge from the Okhotsk The Okhotsk Sea (Fig. 1) is separated from the north- Sea forms both the Oyashio current, which ¯ows along western Paci®c Ocean by the Kuril Islands and the sills the Kuril Islands as part of the western boundary current in the straits, almost all of which are shallower than 600 of the subarctic gyre, and the Subarctic Current to the m except for the Bussol (ϳ2200 m) and Kruzenshterna east, thus indicating that the Okhotsk Sea is the most (ϳ1500 m) Straits. However, the transport process be- likely source of low salinity water in the North Paci®c tween the Okhotsk Sea and the North Paci®c Ocean (WuÈst 1930; Favorite et al. 1976; Talley 1991). Kitani plays an important role not only in the local environment (1973) showed that in the northern Okhotsk Sea, the but also in determining the water properties of the North freezing of fresh surface waters can form cold saline Paci®c. The North Paci®c is the source of most of the waters as dense as 27.05 ␴␪, which still have lower water in the Okhotsk Sea. This in¯ow is thought to take salinity than the ambient waters at the same density. By place mainly through the northern part of the Kuril relating an analysis of historical hydrographic data to Straits, whose neighborhood remains ice free even in Kitani's (1973) result, Talley (1991) proposed that the the most severe winters (Reid 1965; Kawasaki and Kono North Paci®c at mid depth is ventilated through sea ice 1994). formation in the innermost part of the Okhotsk Sea and The Okhotsk Sea, on the other hand, is thought to local vertical mixing in the Kuril Straits. From potential have a signi®cant impact upon the North Paci®c. Pre- vorticity maps, Talley (1993) and Yasuda et al. (1996) vious studies in the northwest Paci®c found that a plume commented that the Okhotsk Sea supplies low salinity of low salinity water at 27.0 ␴ extended to the south ␪ water to the North Paci®c Intermediate Water (NPIW) characterized by a salinity minimum centered at 26.8

␴␪. These conclusions were also con®rmed by recent Corresponding author address: Dr. Tomohiro Nakamura, Depart- studies. Warner et al. (1996) showed that the Okhotsk ment of Geophysics, Kyoto University, Kyoto 606 8502, Japan. Sea is an important location for the ventilation of the E-mail: [email protected] intermediate water of the North Paci®c based on chlo-

᭧ 2000 American Meteorological Society JULY 2000 NAKAMURA ET AL. 1623

FIG. 1. Model domain and topography. Contours are at 500, 1000, 3000, and 5000 m. Symbols denote tide gauge locations for the International Hydrographic Of®ce (IHO) tidal harmonic constants edited by the Canadian Department of Fisheries and Oceans. ro¯uorocarbons (CFCs) observations. Yasuda (1997) Straits. In fact, Stabeno et al. (1994) reported that only showed the presence of a pycnostad (i.e., a region of 1 of the 14 buoys that were transported along the Kuril low potential vorticity) at 26.8 ␴␪ in the Okhotsk Sea Islands entered the Okhotsk Sea. This indicates that the and concluded that the low potential vorticity water Oyashio does not directly ¯ow into and out of the ¯owing out into the North Paci®c determines even the Okhotsk Sea. Moreover, Leonov (1960) and Moroshkin density of the NPIW. Thus, a clari®cation of the ex- (1966) mentioned that bidirectional currents occur in change processes through the Kuril Straits is indis- most passages. This picture is clearly seen in the NOAA- pensable for a better understanding of water mass for- 12 advanced very high-resolution radiometer imagery mation in the North Paci®c (such as the NPIW). (Fig. 2). Such current structure cannot be explained by Past studies regarded the current in the Okhotsk Sea large-scale wind-driven geostrophic ¯ow. as part of the cyclonic subarctic circulation, which pre- These observational results strongly suggest the im- dominantly ¯ows into the Okhotsk Sea through Kruz- portance of nongeostrophic components. In fact, tidal enshterna Strait and out through Bussol Strait. However, currents, especially diurnal, are dominant in and around recent observational studies suggest that there is great the Kuril Straits (e.g., Thomson et al. 1996), and their dif®culty in explaining this in/out¯ow in terms of geo- speeds reach a few knots. According to previous studies strophic balance. One reason for this is that the overall on tidal exchange (e.g., Huthnance 1973; Zimmerman surface dynamic height is higher in the Okhotsk Sea 1978; Awaji et al. 1980; Robinson 1981), such strong than in the northwestern North Paci®c (Kawasaki and tidal currents are expected to induce signi®cant mean Kono 1992). Another reason is that due to the weak transport, even if there are sills in the straits. Moreover, strati®cation, the Oyashio extends to such depths that tide-induced mean currents allow us to explain the bi- it tends to ¯ow along the continental shelf slope along directional structure of the (local) mean currents in the the Kuril Islands (2000ϳ3000 m deep) and is most like- passages. ly unable to pass over the shallow sills in the Kuril Suzuki and Kanari (1986) performed a simulation of 1624 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

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 ®eld in the Okhotsk Sea and showed that in diurnal tides are considerably smaller than the diurnal the Okhotsk Sea, 1) the K1 tide is dominant, M 2 is sec- tides in current speed, we describe the M2 tide only. ond, and the O1 component the third largest in elevation Section 2 of this paper describes the numerical model. amplitude; 2) diurnal tides propagate from east to west Section 3 is devoted to a description of the character- and have two amphidromic like points near the Soya istics of the calculated K1 and M2 tidal ®elds and their and Nemuro Straits; and 3) the semidiurnal tides are comparison with tide gauge observations. In section 4, propagating waves with two amphidromic points. tidal exchange is estimated from the Eulerian point of Though they provided many interesting results, the tidal view and the mechanism causing the transport is in- currents around the straits were not reproduced in suf- vestigated in section 5. The results are discussed in sec- ®ciently detailed structure or accuracy since Suzuki and tion 6 and are summarized in section 7. Kanari (1986) did not aim at estimating the transport through the Kuril Straits. 2. Model Thus, as a ®rst step toward understanding the trans- port process and estimating its magnitude, we have in- The model region shown in Fig. 1 covers the entire vestigated numerically the characteristics of the baro- Okhotsk Sea and part of the North Paci®c. The open tropic tides and tidal currents around the Okhotsk Sea. boundaries are set away from the Okhotsk Sea in order Investigation of barotropic tides may be a meaningful to reproduce tidal wave propagation from the North Pa- ®rst step since strati®cation in and around the Okhotsk ci®c, which is one of the major forcing factors for the Sea is weak. We have then estimated the mean transport tidal motion around the Okhotsk Sea, and to prevent the through the Kuril Straits and identi®ed the mechanism in¯uence of arti®cial disturbances generated at the open of tidal exchange. In this paper, though numerical sim- boundaries on the tidal ®eld around the Kuril Straits. ulations for the K1, O1, P1, M2, and S 2 tides have been Since past studies on tidal current dynamics suggest that successfully performed, we discuss our result with a tidal currents near straits (including the Kuril Straits) particular focus on the predominant component, the bar- are greatly in¯uenced by topographic features, we re- otropic K1 tide. The dynamics of other diurnal tides are solved the topography of the model region in greater almost the same as that of the K1 tide. Because semi- detail. Using the DBDB5 topographic data (National JULY 2000 NAKAMURA ET AL. 1625

FIG. 3. Calculated coamplitude lines of tidal elevation for (a) the K1 tide and (b) the M2 tide. The contour interval is 10 cm.

FIG. 4. Calculated cophase lines of tidal elevation for (a) the K1 tide and (b) the M2 tide. The contour intervals are 1 lunar hour. 1626 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

FIG. 5. The correlation coef®cients between model results and observed harmonic constants for

(a) the K1 tide, (b) the M2 tide, and (c) the K1 tide (for the Kuril Straits only). JULY 2000 NAKAMURA ET AL. 1627

Geophysical Data Center, Boulder, Colorado), the model AH(x, y) ϭ ah⌬LH(x, y), (5) domain is divided into 5 km ϫ 5 km grids. where ⌬L is the grid length (constant in this model) and The numerical model is the same as that used by a the reduced eddy coef®cient determined to be 7.5 ϫ Hatayama et al. (1996), with the familiar barotropic tidal h 10Ϫ6 (sϪ1) by trial and error to achieve the best agree- equations given as ment with observations. This value gives AH ϭ 7.5 ϫ .u 105 cm2 sϪ1 at 2000-m depthץ (␩Ϫ ␤␨␣)u ϩ f k ϫ u ϭϪg١(١ ´ ϩ (u -t 00 The boundary conditions are set as follows. A noץ slip condition is imposed at the land boundaries. At the ␬u|u| open boundaries, the tidal elevation is speci®ed using (ϩ A ٌ2u Ϫ , (1 H H ϩ ␩ the results of Schwiderski (1979, 1981) with the ex- ceptions of the Soya and Tartar Straits, where it is given ␩ץ .H ϩ ␩)u] ϭ 0, (2) from tide gauge observations near the open boundaries)]´ ١ ϩ t Thus, the model is forced by these boundary oscillationsץ in addition to the effects of the tide generating potential, where (x, y) are eastward and northward coordinates; t the earth tide, and the ocean loading tide. To reduce is time; (x, y, t) is the surface elevation, (x, y, t) is the ␩ ␨ arti®cial disturbances at open boundaries due to wave equilibrium tide describe below; u(x, y, t) is the hori- re¯ection, Orlanski's (1976) radiation condition for ve- zontal velocity vector; H is the depth; f ϭ f ϩ ␤y (␤ 0 locity is used together with the sponge zone condition 2.28 10Ϫ13 cmϪ1 sϪ1) is the Coriolis parameter; g ϭ ϫ within 5 grid points from the open boundaries where is the gravity acceleration; is the bottom friction co- ␬ A is ampli®ed linearly. ef®cient; and A is the horizontal eddy viscosity coef- H H The initial conditions are zero currents and a ¯at sea ®cient. It should be noted that the scheme used in this surface. We performed 24 cycles of the integration for model conserves both mass and enstrophy, as recom- each tidal component, by which time the model ocean mended by Huthnance (1981), in order to prevent spu- reached an almost steady oscillation and the ®nal cycle rious contributions to the torque balance, which deter- of simulation is used for the analysis described below. mines the residual current strength.

The parameters ␣ 0 and ␤ 0 account for the effect of the tidal potentials, earth tide, and loading tide. Here 3. Tidal ®elds in the Okhotsk Sea we set ␣ 0 ϭ 0.900, ␤ 0 ϭ 0.690 for the K1 component The harmonic constants (sea-level amplitude and according to Schwiderski (1980). Although the TOPEX/ phase) are calculated at every grid point, and the spatial POSEIDON Satellite Tidal Committee recommends distributions of the coamplitude and cophase lines for somewhat difference values of ␣ 0 ϭ 0.940 and ␤ 0 ϭ K1 and M2 tides are shown in Figs. 3 and 4, respectively. 0.736, the former values give better agreement with the These distributions are qualitatively consistent with pre- observations. vious studies (Ogura 1923; Suzuki and Kanari 1986; The equilibrium tide ␨ is expressed as Mazzega and BeÂrge 1994). To estimate water exchange ␨ ϭ K sin2␾ cos(␴t ϩ ␭) (3) quantitatively, a more stringent check on our model re- sult is required. Thus we made a comparison with the for diurnal and International Hydrographic Of®ce (IHO) tidal harmonic ␨ ϭ K cos2␾ cos(␴t ϩ 2␭) (4) constants, the locations of which are shown in Fig. 1. For the predominant K1 tide component, the corre- for semidiurnal tides, where K and ␴ are the amplitude lation coef®cients between the calculated and the ob- and frequency taken from Schwiderski (1980), and ␭ served harmonic constants are high (0.904 for phase and ␾ are longitude and latitude, respectively. The as- and 0.976 for amplitude) in the whole region (Fig. 5a). tronomical arguments are neglected since tidal ®elds are Although the amplitudes at a few sites are overestimated calculated for each tidal component. compared with the observational values, the points with The bottom stress is added via a quadratic law with the largest discrepancies are around the northern coast ␬ ϭ 0.0026. This formulation makes it possible for the of the Okhotsk Sea and the overestimate is insigni®cant bottom stress to generate relative vorticity around the in other regions. The correlation coef®cients for data in straits as described in section 4 (the dependency on this the Kuril Straits only are somewhat lower (0.814 for friction scheme will be discussed in section 7). In the phase and 0.907 for amplitude in Fig. 5c) than those for determination of the horizontal eddy viscosity coef®- the whole region, but still remain high. cient AH, we used the formulation by Schwiderski Further, we estimate the root mean square (rms) error (1980) in which AH depends linearly on the horizontal of the calculated K1 tide over the entire region from the and vertical mixing lengths as expression 1628 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

1/2 11N T RMS ϭ {A cos(␴t Ϫ P ) Ϫ A cos(␴t Ϫ P )}2 dt , (6) NT͸ ͵ MMOO []0

where N is the total number of tide gauge observations, part of Shelikhova Bay, in our model. We can also rec- T is the tidal periods, ␴ the frequency, A and P the ognize a local minimum near Cape Yelizavety (north of amplitude and phase, respectively, and the suf®xes M Sakhalin) and relatively higher amplitude along the and O denote the calculated and observed harmonic coasts (to the west of Kamchatka, the east of Sakhalin, constants, respectively. The calculated rms error is 8.06 and the coast of Okhotsk), which is caused by waves cm over the whole region and 6.75 cm in the Kuril propagating as shelf waves along the coasts as suggested Straits. by Odamaki (1994).

Owing to the lack of current measurements, we can The elevation amplitude of the M2 tide (Fig. 3b) is compare the model results with observation only in el- comparable to that of the K1 tide and is even larger evation data. Although it is not safe to assume that good around the northwestern coast of the Okhotsk Sea. The correlation with elevation data implies good model es- M2 tide in the Okhotsk Sea is also largely determined timates of currents, we believe that, at least qualitatively, by the incoming tidal wave from the North Paci®c (Fig. the features of current ®eld are well reproduced. In a 4b). After passing through the Kuril Straits, this wave quantitative sense, the current ®eld is probably under- propagates roughly northward as a freely propagating estimated as will be discussed in section 7. wave, producing two amphidromic points: one in She-

For the M2 tide, the correlation coef®cients (Fig. 5b) likova Bay and the other near Cape Yelizavety. The M2 are also high (0.825 for amplitude and 0.929 for phase). tidal wave partly cooscillates in the northwest and north- The calculated rms error is 12.39 cm, since the ampli- east bays, where the elevation amplitude is large (coos- tude is slightly overestimated. Most of the sites with cillation in the innermost regions of Shelikova Bay re- signi®cant discrepancies in amplitude are located in sults in a maximum amplitude of 3.6 m. Shantarsky and Shelikova Bays in the northern Okhotsk To study the features of the tidal currents in the Sea, where complicated coastlines are not suf®ciently Okhotsk Sea, we calculated the ellipse parameters (ma- resolved. When the data at such sites are removed, the jor and minor semiaxes and angle of inclination) shown rms error becomes 9.5 cm. Thus it can be said that the in Fig. 6, using the oscillatory component of the cal- calculated M 2 tidal ®eld is similar to that observed. culated velocities. The K1 tide has the greatest current

The K1 tide is the largest component in elevation am- speed. The currents are strong and their tidal ellipses plitude in the eastern Okhotsk Sea. From Fig. 4a, it can are circular around topographic feature, such as the Ku- be seen that the K1 tidal ®eld in the Okhotsk Sea is ril Straits and the Kashebarova Bank. For example, the mostly determined by the tidal wave coming from the peak velocity in the northern part of the Kuril Straits North Paci®c, which enters the Okhotsk Sea mainly attains about 1.6 m sϪ1, though the maximum value is through the northeastern part of the Kuril Straits. These achieved within the cooscillating Shelikhova Bay. These waves progress directly in a roughly westward direction features are associated considerably with the fact that and along the coast in a cyclonic fashion, and an am- the period of the K1 tide (23.93 h) is longer than the phidromic-like point appears on the east coast of Sa- inertial period around the Kuril Straits (15.7±17.0 h). khalin. Around the Kuril Straits, cophase lines are com- Subinertial tidal currents generate subinertial waves plicated because of wave trapping along the islands. The trapped at islands and/or submarine banks (e.g., Chap- elevation amplitude is large at the northeastern part of man 1989). The topographically trapped waves are sub- the straits and, in general, increases with decreasing jected to continuous forcing and are enhanced until depth toward the northern part of the Okhotsk Sea, with damping by friction or viscosity becomes important. a local maximum of about 0.8 m near the Kushevarova The resulting ampli®cation of trapped waves is most Bank. In Shelikhova Bay, located in the northeast of the effective when the resonance occurs but is signi®cant Okhotsk Sea, the amplitude reaches a maximum value over a wide range of frequency if the tidal frequency of 4.2 m as a result of resonance. The natural period of is subinertial (e.g., Haidvogel et al. 1993). Shelikhova Bay 21 h and its cooscillating ampli®cation The presence of such topographically trapped waves factor is about 5 according to Suzuki and Kanari (1986). is clearly seen in the time series of the along-isobath The amplitude in most of the interior of the bay, then, component of velocity around the Kuril Straits (Fig. 7). comes to 5 m with a modeled amplitude of about 1 m In particular, clockwise propagation of positive anom- at the mouth of the bay. The actual value agrees well alies around Simusir Island, the Urup Strait and Etorof with the model value, considering that cooscillation Island, and a bank east of the Kruzenshterna Strait can does not take place in Penzhinskaya Bay, the interior be easily distinguished. Thus, the K1 tidal ®eld around JULY 2000 NAKAMURA ET AL. 1629

FIG. 6. Calculated tidal ellipses for (a) the K1 tide and (b) the M2 tide at every 16 points. The magnitude of velocity is indicated in each ®gure.

the Kuril Straits is composed of both large-scale K1 tidal trapped waves cannot be generated by superinertial M 2 waves coming from the North Paci®c and topographi- tides. Indeed, the tidal ellipses are not circular around cally trapped waves. The latter ampli®es the currents the Kuril Straits and the Kashebarova Bank. Thus, am- and makes tidal ellipses circular around the Kuril Straits. pli®cation hardly occurs and the M 2 currents are weak Therefore the K1 tide is expected to cause signi®cant in the Kuril Straits, indicating that the mean currents tide-induced mean ¯ow around the straits, which will induced by the M 2 tide are probably not signi®cant. be discussed in section 4. The along-isobath component of velocities associated with topographic waves is nearly in geostrophic balance since these waves are character- 4. Eulerian mean currents and estimates of tidal istic of shelf waves and topographic Rossby waves (and exchange through the Kuril Straits Kelvin waves). This may imply that the time-average currents are also roughly geostrophic. Figure 8 shows the depth-averaged velocity vectors Moderately strong currents near the coasts, where the of the Eulerian time-averaged currents over a cycle. For elevation amplitude is also appreciably larger than that the K1 tide, signi®cant mean currents near the Kuril of the surroundings (in Fig. 3a), are thought to be caused Islands can be seen. These currents become especially by the presence of shelf waves due to the subinertial large in the northern part of the Kuril Straits, where the tidal frequency. Such shelf waves are identi®ed from maximum velocity exceeds 0.7 m sϪ1, and have in- and observations along the Hokkaido coast (Odamaki 1994) out¯ow components, suggesting that the tidal currents and from numerical simulation along the Sakhalin coast (Suzuki and Kanari 1986). can cause signi®cant long-term exchange through the Kuril Straits. Another interesting feature is the mean The M2 tide (Fig. 6b) is substantially smaller in cur- rent speed than the K tide, despite the fact that the current along the coast (with land on the right). These 1 mean currents are almost in geostrophic balance, as ex- elevation amplitude is comparable. In contrast to the K1 pected in section 3. On the contrary, the mean currents tidal currents, the maximum value of the M 2 tidal cur- Ϫ1 rents around the Kuril Straits reaches only 0.6 m s around the Kuril Straits induced by the M 2 tide are much although the currents are strong within the cooscillating smaller than those from the K1 tide (Fig. 8b). bays in the interior of the Okhotsk Sea. Since the max- For closer examination and estimation of the tidal imum frequencies of barotropic topographic Rossby exchange, we calculated the streamfunction of the mean waves is less than the inertial frequency, topographically volume transport ⌿, de®ned as 1630 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

FIG. 7. Temporal change of along-isobath components of velocity around the Kuril Straits with an interval of 0.25 tidal cycle for the

K1 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 sϪ1. The current in the non shaded areas (the thicker shaded areas) ¯ows with the shallower water on its right (left), and the current speeds in the thinner shaded areas are less than 7.5 cm sϪ1.

⌿ count, we estimated the total transport for all the straitsץ ⌿ 1ץ 1 (u, ␷ ) ϭϪ , , (7) with this mean current ®eld. For the K1 tide (Fig. 10), x we can easily see that most of the exchange occurs atץyHץ ΂΃H with the zero point taken at the Kamchatka Peninsula. Bussol Strait and the northeastern part of the Kuril

The result for the K1 tide is shown in Fig. 9. In general, Straits, and that little transport occurs through the south- the mean currents are almost parallel to the isobaths and western part where depths are shallow and large islands form clockwise mean currents around the islands, lead- are present. In terms of magnitude, the net transport of ing to bidirectional mean currents in most passages and about 5.0 Sv from the Okhotsk Sea to the North Paci®c strong clockwise along-sill (or along-island) mean cur- occurs mainly through the Bussol (2.4 Sv), Kruzen- rents. In particular, a bidirectional ¯ow is pronounced shterna (0.8 Sv) and Chetverty (0.8 Sv) Straits. In¯ow in the Bussol and Kruzenshterna Straits that are rela- transport is largest (1.45 Sv) through Bussol Strait fol- tively wide and deep, while the along-sill currents are lowed by 1.2 Sv through Kruzenshterna Strait. Water strong between the two straits. There is an intense clock- transported through the straits is carried to the southwest wise circulation over the bank to the southeast of Shash- on the Paci®c side and to the northeast on the Okhotsk ikotan Island and an anticlockwise circulation over the side along the islands by along-sill mean ¯ow. When Kuril Basin along the isobath. neglecting the bidirectional ¯ow (i.e., estimating the Taking the bidirectional current structure into ac- transport per strait) the total transport comes to 2.2 Sv. JULY 2000 NAKAMURA ET AL. 1631

FIG. 8. Eulerian mean currents induced by (a) the K1 tide and (b) the M2 tide. The mean currents in regions without arrows are less than 0.5 cm sϪ1.

This indicates that in order to estimate the total transport observationally, suf®cient current meters need to be de- ployed to detect the bidirectional current structure.

Transport estimates made with the O1, P1, M 2, and S 2 tides are 3.5 Sv, 1.0 Sv, 0.3 Sv, and 0.1 Sv, respec- tively, 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 Ϫ1 cm s for the K1, O1, P1, M 2, and S 2 tides in the Kuril Straits, respectively, the ratios of transports among the diurnal components are almost proportional to their ¯ow speeds. This is also the case for the semidiurnal com- ponents but does not hold between diurnal and semi- diurnal tides. The transport by diurnal tides is consid- erably larger than that expected from the ratio of diurnal

to semidiurnal current speeds. For example, the K1 trans- port is about 17 times as large as the M 2 transport where- as the K1 ¯ow speed is only about 2.5 times that of M 2. Thus, whether tides are subinertial or not is anticipated to have a large effect on the difference in mean transport between the diurnal and semidiurnal tides.

5. Formation mechanism of bidirectional mean currents 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 In order to investigate the formation mechanism of Sv and values in shaded areas are positive. the mean ¯ow, we ®rst make an analysis of vorticity 1632 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

FIG. 10. The estimate of the mean transport through the Kuril Straits induced by the K1 tide. Upward and downward arrows represent in¯ow and out¯ow, respectively.

focusing on the K1 case, because the K1 component dom- from the sill. Such a pattern is clearly seen in shallow inates the mean transport and because the formation straits (200ϳ600 m depth). A close look at Fig. 11 mechanism may be helpful in clarifying the cause for shows that as the sill gets higher in the vicinity of the the difference in mean transport between the diurnal islands, the magnitude of the negative mean vorticity and semidiurnal tides. The vertical component of vor- on the top of the sill becomes larger. Supposing mass ticity ␻ is de®ned as the depth-averaged relative vor- conservation of the along-sill mean currents, such vor- ticity ticity changes in shallow straits lead to clockwise mean u circulation on island scales, thus creating bidirectionalץ ␷ץ ␻ ϭϪ. (8) mean currents in shallow straits as is shown schemat- .y ically in Fig. 12aץ xץ Figure 11 shows the Eulerian mean relative vorticity In deep straits, on the other hand, the mean vorticity over a cycle around the Kuril Straits. According to pre- distribution on the sill top has positive values near the vious studies of tidal recti®cation (e.g., Robinson 1981), islands (except for thin viscous boundary layers closer the mean vorticity generally acquires negative values to islands). This vorticity pattern differs greatly from on the sill top and positive values at the base of the sill, that in shallow straits in spite of the presence of similar which, in turn, produce a clockwise mean current along bidirectional currents (Fig. 11). To investigate this prob- the sill since mean currents are almost zero far away lem, we direct our attention to Bussol Strait, where the JULY 2000 NAKAMURA ET AL. 1633

FIG. 11. The Eulerian mean relative vorticity over one cycle around the Kuril Straits for the K1 tide. The contour interval is 1 ϫ 10Ϫ5 sϪ1. 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 1 ϫ 10Ϫ6 sϪ1.

sill is very deep, bidirectional currents are dominant, in a similar way to Ridderinkhof (1989), because our and hence most of the out¯ow from the Okhotsk Sea interest is in the generation mechanism of bidirectional occurs. The vorticity distributions around the strait are current structures in the Kuril Straits. Taking the curl as follows. (i) A positive mean vorticity is located in of the momentum equation (1) yields the vorticity equa- the western part of Bussol Strait (near the shallow Urup tion as Strait). (ii) In the central part of Bussol Strait, a negative D␻ u ´ u Ϫ ␻١ ´ ١ mean vorticity is present over the deep sill. (In contrast ϭϪf to shallow sills, the positive mean vorticity at the foot Dt (a) (b) of the sill is too small to be distinguished and has little u|1|١ in¯uence.) (iii) A positive mean vorticity is located in ١|ϩ ␬u ϫϩ␬u ϫ |u the eastern part of Bussol Strait. The mean vorticity H ϩ ␩ ΂΃H ϩ ␩ distribution (i) produces strong clockwise mean cur- (c) rents, ¯owing out with a transport of 1.4 Sv through ␬|u| 2 (the western part of Bussol Strait to the southwest along Ϫ ␻ ϩ AHٌ ␻ , (9 H ϩ ␩ (e) the Kuril Island Chain. The distributions (ii) and (iii) (d) merge to produce a mean out¯ow of 1.0 Sv to the south- east from the middle of Bussol Strait [intermediate to where D/Dt represents the time variation in the La- the distributions (ii) and (iii)]. The distribution (iii) pro- grangian frame and the ␤ term and the terms arising duces a strong mean in¯ow of 1.45 Sv along Simusir from the spatial variation of horizontal eddy viscosity Island (east of Bussol Strait). It is worth mentioning that are neglected because of their smallness. The sum of the mean vorticity values in Bussol Strait are so small terms on the rhs of Eq. (9) represents the mechanisms that a slow mean ¯ow is produced, though the deep generating and damping vorticity. Terms (a) and (b) strait (over 2000 m) makes the overall mean transport generate vorticity by stretching or squeezing of a water signi®cant. In this way, the mean vorticity produces column through the conservation of potential vorticity. bidirectional mean currents and a slow centered-out¯ow For term (a), the vorticity generated by stretching in Bussol Strait, as is shown schematically in Fig. 12b. (squeezing) acquires positive (negative) values. Term To examine the cause for the different vorticity dis- (c) represents vorticity generation due to velocity shear tribution between deep and shallow straits, we ®rst di- (for a quadratic friction law) and the horizontal gradient agnose the temporal evolution of the vorticity balance of water depth transverse to the direction of the tidal 1634 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

thought to be similar in both shallow and deep straits, despite that their vorticity distributions differ. This im- plies the presence of a different physical process from the previous tidal recti®cation theory (e.g., Robinson 1981) for the formation of the mean circulation in deep straits. Previously, vorticity (nonaveraged) was gener- ated by tidal currents over variable topography and re- distributed by advection, eventually forming a time-av- eraged vorticity distribution with positive (negative) lo- cated 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 mean currents in deep straits To identify a possible role for topographically trapped waves (TTW) in the vorticity balance, we ®rst 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 signi®cant portion of positive vorticity (nonshaded in Fig. 14) generated at ¯ood 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) scarce- FIG. 12. Schematic illustrations of mean currents associated with ly moves (Figs. 14f±h). Similar propagation is seen to the mean vorticity distribution in (a) shallow straits (200ϳ600-m depth) and (b) deep straits (the case of the Bussol Strait). the north of Simusir Island (east of Bussol Strait). From these results, one may speculate that the difference in propagation of positive and negative vorticity anomalies may create positive mean vorticity in the southwestern ¯ow. Term (d) represents the damping part of bottom and northeastern parts of Bussol Strait, which is capable friction. Term (e) causes a damping of vorticity through of producing bidirectional mean currents as illustrated the horizontal eddy viscosity. in Fig. 12b. Though the vorticity balance is examined during a In previous studies on subinertial tidal currents (e.g., tidal cycle, we show the spatial distributions of each Chapman 1981; Kowalik and Proshutinsky 1995), these term on the rhs of Eq. (9) only when the out¯ow speed vorticity anomalies propagating along isobaths are at- is a maximum in Bussol Strait (Fig. 13). The features tributed to TTWs. In fact, the frequency of these anom- described below are essentially similar for the other tidal alies is estimated as 0.5 ϫ 10Ϫ4 (rad sϪ1), using a linear phases. In general, as in the previous studies, the stretch- dispersion relation of TTW on a constant slope ␣ with ing/squeezing term (a) from the Coriolis effect is most mean depth H, effective in vorticity generation while the other stretch- ing/squeezing term (b) is less so, with the exception that ␣ 1 ␣22f Ϫ1 ␴ ϭϪfkk22ϩ l ϩϩ , (10) term (b) is quite signi®cant in regions of strong relative H 4 HgH2 vorticity such as over the bank to the southeast of Shash- ΂΃ ikotan Island. The vorticity generation due to bottom where ␴ is the frequency, k is the wavenumber in the friction is much smaller than that due to these terms along-isobath direction and l in the across-isobath di- except in spatially small shallow regions (depth less than rection. These values are taken from the ®gure (H ϳ 100 m) such as in the vicinity of Onnekotan Island, 700 m, ␣ ϳ 0.1, 2␲/k ϳ 40 km, 2␲/l ϳ 40 km). The where water exchange between the Okhotsk Sea and the estimated frequency roughly agrees with the K1 fre- North Paci®c is not signi®cant. The damping of vorticity quency (0.7 ϫ 10Ϫ4 rad sϪ1), implying that these anom- is caused primarily by bottom friction, and the effect of alies are TTWs generated by the incoming K1 tidal wave. horizontal eddy viscosity is negligible when compared Although most previous studies on tidal exchange have to that of bottom friction. Thus, the vorticity sources paid little attention to the role played by TTWs, the for generating the bidirectional current structure are above facts strongly suggest that the propagation of vor- JULY 2000 NAKAMURA ET AL. 1635

FIG. 13. The distributions of the generation and damping

terms in the vorticity Eq. (9) for the K1 tide, when the out¯ow speed is maximum around the Bussol Strait: the panels (a)±(e) correspond to the terms (a)±(e) in Eq. (9), respectively. The contour intervals are 1 ϫ 10Ϫ9 sϪ2 for the terms (a)±(d) and 1 ϫ 10Ϫ10 sϪ2 for the term (e). Values in nonshaded areas and the thicker shaded areas are pos- itive and negative, respectively, and the absolute values in the thinner shaded areas are less than one tenth of the minimum contour value.

١H|/H Ͼ ␤/f 0 (e.g., LeBlond and| ticity anomaly as TTWs may be effective in the vorticity dominates ␤ when balance around the Kuril Islands for subinertial tides Mysak 1978), which is roughly estimated as the in- Ϫ7 Ϫ9 such as the K1 tide. Focusing on this point, we inves- equality 10 k 10 . tigate the generation mechanism of mean vorticity in Since the propagation of TTWs such as topographic the Kuril Straits. Rossby waves relates to vorticity change in space and We begin with the following vorticity equation, time, we separate the velocity ®eld according to Holton (1979) as follows. The Helmholtz theorem states that ␻ץ u ϩ damping, (11) any velocity ®eld V can be divided into a nondivergent ´ ١ ١␻ ϭϪf ´ ϩ u t part V␺ plus an irrotational part Virr such thatץ where only the dominant vorticity-generation term (a) V ϭ V␺ ϩ Virr, (12) in Eq. (9) at the Kurils is taken into account for sim- ϫ Virr ϭ 0. If the velocity ١ V␺ ϭ 0 and ´ ١ plicity. Note that, though the ␤ term permits the pres- where ence of barotropic Rossby waves, this term can be ne- ®eld is two dimensional and is denoted by V ϭ (U, V), glected in comparison with topographic variation in the the nondivergent part can be expressed in terms of the Kuril Straits. This is because the topography in¯uence streamfunction ␺ de®ned by 1636 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

␺ from topographic recti®cation of the K1 current over theץ ␺ץ (U␺␺, V ) ϭϪ , . (13) sill. Another conspicuous feature in Fig. 15 is the gen- x eration of signi®cant vorticity anomalies in both positiveץ yץ΂΃ While previous studies focus mainly on the advection and negative senses on the down- and upstream sides of vorticity in the across-isobath direction, TTWs prop- of the sill, respectively. The vorticity anomalies largely agate along the isobaths. Taking this fact into account, propagate along the isobaths [for example, northeast- we take the coordinate x (y) to represent the northeast ward (southwestward) propagation of the positive (neg- (northwest) direction, which is almost along (across) the ative) vorticity anomaly in Figs. 15a,b]. This propa-

sills in the Kuril Island Chain. Accordingly, Hx K Hy gation could be associated with TTWs because the prop- and the component U basically represents the along- agation of TTWs is caused by the difference in the isobath velocity component and V the across-isobath magnitude of vorticity in the along-isobath direction component. The across-isobath velocity V generates a (e.g., Longuet-Higgins 1965) and swifter currents within net across-isobath advection of vorticity through the the strait do, in fact, produce stronger vorticity than in well-known mechanism of tidal recti®cation over var- other regions. In the latter half cycle, almost all of these iable topography, thus producing mean along-isobath features can be seen but their phase is reversed. How- currents (e.g., Robinson 1981). The vorticity can also ever, the propagation of vorticity anomalies is in the be advected in the along-isobath direction by the ve- same direction as in the previous half cycle. locity component U. Considering that an incident K1 wave has very small The stretching/squeezing of water columns by the vorticity in deep regions (one or two orders of magni- motion of the free surface can be neglected when tude less than in the straits; Figs. 14 and 15) and that f 2L 2/gH K 1, where L is the horizontal length scale vorticity change is caused almost solely by the change taken as the lesser of the topographic length scale or of f/H, the component V␺ in a slope region may be

wavelength (e.g., LeBlond and Mysak 1978). In the K1 dominated by the contribution from the vorticity gen- case, L is less than several tens of kilometers, giving a erated by the stretching/squeezing effect. To conve- divergence parameter f 2L 2/gH of the order of 10Ϫ2. niently identify the role of TTWs in the vorticity balance Thus a rigid lid approximation is a reasonable simpli- around the Kuril Islands, we de®ne the velocity com- ␺ ®cation. Hence, the continuity equation (2) yields ponent associated with TTWs (VTTW ) as that represent- ing the propagation of the vorticity anomalies. The rel- u ϭϪ١H ´ u. (14) evance of this will be discussed later. The remainder ´ H١ ␺ Using the notation for V given in Eq. (12), the rhs of (Vrec ) is hereafter called the recti®ed temporal current Eq. (14) is written as in parallel with previous tidal recti®cation studies (e.g., Robinson 1981), although it is in general dif®cult to ␺ Virr). (15) Ϫ١H ´ V ϭϪ١H ´(V ϩ separate the velocity components associated with TTWs Note that under the present approximation, Virr repre- from the recti®ed temporal currents because both are sents the divergent component when neglecting the con- topographically produced. tribution of sea surface elevation to the volume trans- Taking the above facts into account, we therefore sep- port. arate the nondivergent velocity component V␺ as

Substitution of Eqs. (12)±(15) into Eq. (11) yields ␺ ␺␺ V ϭϩVVTTW rec. (17) ␺ These are expressed in terms of the streamfunctions asץ ␺ץ f ץ ␻ ϪϪH ϩ H ١ ´ ϩ V x ΃ץ yץtHxyץ΂΃΂ ␺ץ ␺ץ ␺ TTW TTW f VTTW ϭϪ ,, xץ yץ١H ´ Virr ϩ damping. (16) ΂΃ ϭ H ␺ץ ␺ץ To examine the vorticity balance in the vicinity of the V␺ ϭϪ rec, rec , (18) xץ yץKuril Straits in detail, we look at the temporal changes rec ΂΃ of both velocity and vorticity in the shallow Urup Strait where ␺ and ␺ are the streamfunctions for the during one cycle as an example (Fig. 15). As the north- TTW rec TTWs and the recti®ed current. westward K current ¯owing into the Okhotsk Sea runs 1 We assume that the wave solution for the stream- over the sill, it is clear that a strong northeastward cur- function ␺ associated with TTWs is given as rent appears over the sill after 0.25 cycle (Fig. 15b) due TTW i(kxϩlyϪ␴t) to the occurrence of the along-isobath current arising ␺TTW ϭ ␺Ã TTWe , (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 ϫ 10Ϫ5 sϪ1. Values in non shaded areas and the thicker shaded areas are positive and negative, respectively, and the absolute values in the thinner shaded areas are less than 0.5 ϫ 10Ϫ5 sϪ1. JULY 2000 NAKAMURA ET AL. 1637 1638 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

where k and l are the wavenumbers in the x and y di- and the variation in the along-isobath direction are con- rections, respectively. Using Eqs. (17)±(19), the second sidered. term on the lhs of Eq. (16) becomes To easily assess whether or not the treatment of TTWs in this study [Eqs. (17)±(19)] is reasonable, we make a ff ␺␺ -١H ´(V Ϫ V TTW) comparison between the intrinsic phase speed cx esti Ϫ (ϪHilxyϩ Hik)␺TTWϪ HH mated from Eq. (22) and that appearing in the model f results, for example, around Urup Strait as shown in ١H ´ V␺ Fig. 15. Equation (22) for the intrinsic phase speed c ϭ (cikϩ cil)(Ϫk22Ϫ l )␺ Ϫ xy TTWH rec x of ␻wave in the along-isobath direction yields approxi- f mately Ϯ0.3 m sϪ1 on the northern (southern) side of (١H ´ V␺ . (20 ١␻ Ϫ ´ ϭ c waveH rec the sill using the values estimated earlier. On the other hand, in Figs. 15a,b, the apparent speed of the positive Here, ␻wave is the vorticity component associated with (negative) vorticity anomaly corresponding to A (B)in ␺TTW such that the along-sill direction is estimated to be about ϩ1.0 m Ϫ1 Ϫ1 ␺ 2 s (Ϫ0.1 m s ). According to Eq. (23), the intrinsic (ϫϭٌVTTW ␺TTW ϭ ␻wave. (21 ١ phase speed cx of these anomalies is given by subtracting The quantity c ϭ (cx, cy) in Eq. (20) represents the phase the along-isobath current speed U from the apparent speed of the vorticity anomalies and is given by speeds of the vorticity anomalies. Since the correspond- ing speed U calculated in the model is about 0.6 m H fHf ϩ c ϭ y , c ϭϪ x . (22) sϪ1 (ϩ0.2 m sϪ1) for the positive (negative) anomaly, xyk22ϩ lH k 22ϩ lH so the intrinsic phase speed cx of the modeled positive Interestingly, this is the same form as the phase velocity (negative) anomaly seen in Fig. 15 is estimated ap- of a nondivergent linear topographic Rossby wave (e.g., proximately as ϩ0.4 m sϪ1 (Ϫ0.3msϪ1), in good agree- ment (approximately 80%) with the value of cx of the Cushman-Roisin 1994). Since Hx K Hy, the propagation vorticity anomaly corresponding to ␻wave from Eq. (22). of the vorticity ␻wave is dominated by the component cx. Substitution of Eq. (20) into Eq. (16) yields Note that both anomalies move with the shallower side on the right in a similar sense to TTWs. This provides .some support for the treatment of TTWs in this studyץץ ( ␻ Ϫ ␻) ١ ´ ␻ ϩϩV ١´(ϩ (V ϩ c t wave Based on the above consideration, the formation ofץt waveץ ΂΃΂΃the bidirectional mean current in deep straits such as f Bussol Strait can be interpreted as follows. In the North- (١H ´(Virr ϩ V␺ ) ϩ damping. (23 ϭ H rec ern Hemisphere, the intrinsic phase velocity c of TTWs is in the along-isobath direction with shallower regions Equation (23) shows that the interaction between the on the right. When the K1 tidal current moving toward net across-sill (across-isobath) current and the topog- the Okhotsk Sea ¯ows over a sill such as that in the raphy shallow Urup Strait adjacent to the deep Bussol Strait, f the along-sill (along-isobath) current U is generated on irr ␺ ١H ´(V ϩ Vrec) the sill slope and ¯ows like a recti®ed temporal current H with a positive (negative) value of topographically gen- generates two vorticity components that are governed erated vorticity to the north (south), as seen in Fig. 15b. by different dynamics. Note that as in previous studies, At this moment, on the positive vorticity side to the ␺ Vrec is dominated by the along-isobath component and, north of the sill top, the along-sill current (U) is in the hence, the effect of the current associated with the K1 same direction as the intrinsic phase velocity (cx) of the tidal waves (ϳVirr) coming from the North Paci®c dom- TTWs with positive vorticity anomaly, as is shown sche- inates the vorticity generation in the Kuril Straits. The matically in Fig. 16b. In contrast, on the negative vor-

vorticity component (␻ Ϫ ␻wave) is transported only by ticity side to the south of the sill top, the along-sill advection and causes the well-known process of tidal current (U) is in the opposite direction to the propa- recti®cation (e.g., Chen and Beardsley 1995). In con- gation of TTWs of negative vorticity anomaly. When

trast, the transport of the vorticity anomaly ␻wave is driv- the K1 tidal current reverses, a similar situation occurs en not only through advection by the currents (U, V) but the positive (negative) vorticity side is to the south but also by the propagation of TTWs with phase speed (north) of the sill. Consequently, the TTWs with positive c. This means that there are additional vorticity changes vorticity anomaly appearing on the downstream side of caused by the propagation of TTWs at all locations the sill move faster than those with negative vorticity along the wave paths. Accordingly, TTWs are able to on the upstream side of the sill due to the difference in

affect the mean vorticity ®eld at locations (e.g., the deep the direction between the phase velocity (cx) and the Bussol Strait) well away from the generation region along-sill current (U) during the ebb and ¯ood tides as (e.g., the shallow Urup Strait). This effect has important seen in Fig. 15. This means, in a sense, that the mag- implications but is absent unless both subinertial tides nitude of the positive vorticity ¯ux created by TTWs in JULY 2000 NAKAMURA ET AL. 1639 the along-isobath direction is larger than that of the are qualitatively the same. However, when undertaking negative vorticity ¯ux over a tidal cycle, and eventually the modeling problem in shallow embayments in coastal leads to the presence of a net ¯ux of positive vorticity region, some improvements to this model will be nec- in a clockwise sense around the islands as schematically essary. illustrated in Fig. 16c. We performed another experiment for the K1 tide in In shallow straits, since TTWs hardly cross the shal- which grid sizes were reduced to 2.5 km ϫ 2.5 km since low sills, the above process has little effect on the for- the resolution of topographically trapped waves (a mation of mean vorticity. In contrast, in deep and wide wavelength or about 40 km) is not suf®cient. The result straits such as the Bussol and Kruzenshterna Straits, shows better agreement with observations of elevation mean vorticity generation through the classical tidal rec- and the rms error reduces by 1 cm. The qualitative fea- ti®cation process is small but the TTWs coming from tures of the calculated mean current ®eld is common in the adjacent shallow straits such as Urup Strait can cross both cases although the amount of water exchange the deep sills, thus producing positive mean vorticity. through the straits becomes 9.5 Sv (Fig. 17). Despite This leads to the formation of a bidirectional mean cur- the substantial increase in mean transport, the increase rent structure around both ends of the deep sills. In of maximum current and mean current speeds in the addition, weak negative mean vorticity generated by Kuril Straits are about 20% (1.6 to 1.9 m sϪ1) and 30% large-scale tidal currents in the central part of the straits (0.7 to 0.9 m sϪ1), respectively. The current structure remains unaffected by TTWs. These processes may pro- of a topographically trapped wave (e.g., in Urup Strait) duce the mean vorticity distribution illustrated in Fig. is reproduced more clearly (not shown). These are prob- 12b. ably due to the better resolution of current structure, Rough estimates of the transport associated with the vorticity generation in a slope region and thus topo-

TTWs for the K1 tide is about 50% of the total transport, graphically trapped waves. The better resolution may assuming that the transport by the bidirectional currents result in greater water exchange. in the Bussol (the out¯ow from the central part is ex- In section 5b, we neglected the ␻ term (b) (i.e., -u) in the formulation of the generation of bidi ´ cluded) and Kruzenshterna Straits are due to TTWs. Ϫ␻١ Thus, TTWs play an important role in producing effec- rectional mean currents in deep straits. Here, we brie¯y tive water exchange through the Kuril Straits in the discuss the effect of this on the generation of bidirec- model, by generating strong bidirectional mean currents tional mean currents in deep straits based on Eq. (23), in deep and wide straits. However, this mechanism has which is the ®nal formula for the analysis. When term little effect on tidal exchange for the case of superinertial (b) is taken into consideration, the intrinsic phase ve- tides (e.g., the M 2 tide) because they are inef®cient gen- locity c and the forcing term on the rhs of Eq. (23) are erators of TTWs as seen in section 3. This is a possible altered through the change of f to f ϩ ␻. As for the explanation for the fact that subinertial diurnal tides phase velocity, Eq. (22) implies that the along-isobath cause more ef®cient water exchange through the Kuril phase speed (cx) of TTWs on the positive (negative) Straits than superinertial semidiurnal tides, as estimated vorticity side increases (decreases) in the northern hemi- in section 4. sphere. For example, when the magnitude of ␻ is as- sumed to be 0.2 ϫ 10Ϫ4 (a typical value in the present shallow straits), the speed increases (decreases) by about 6. Discussion 20% on the positive (negative) vorticity side. This acts Although we used a quadratic friction form in this to enhance the net positive vorticity ¯ux from shallow study, a different scheme for bottom friction may lead straits to deep straits, which is described in section 5b. to different results in coastal embayments (shallower Similarly, the change in the forcing term strengthens than some tens of meters) according to past studies. (weakens) the generation of positive (negative) vortic- However, bottom friction is not strong enough to change ity. Thus, the net effect becomes signi®cant as relative the calculated current ®eld in the Kuril Straits qualita- vorticity ␻ increases, modifying the net positive vor- tively because most straits are deeper than several hun- ticity ¯ux to deep straits from that expected from Eq. dred meters. In fact, the term balance of the vorticity (23). However, once relative vorticity is transported equation (Fig. 13) shows that the bottom friction terms away from shallow straits into deeper regions by TTWs, are more than one order of magnitude less than the the subsequent transport and the resulting mean vorticity dominant stretching/squeezing terms in the Kuril Straits, formation could be qualitatively similar to that ex- except in very shallow and narrow regions (some tens plained in section 5b because relative vorticity in the of meters deep). Thus, the essential results obtained here deep regions is expected to be very small. are largely valid, with the proviso that the strength of We investigated the basic features and the generation mean currents is somewhat changeable for the choice mechanism of mean transport for each component. of the friction law. For example, Huthnance (1981) in- However, it is desirable to run the model with several dicated by analytical study that the magnitude of a mean tidal components simultaneously in order to make an current produced by the quadratic friction form is 2/3 actual quantitative estimate of tidal exchange. Accord- times that by linear friction and the current structures ing to Kowalik and Polyakov (1998), the K1 and O1 1640 JOURNAL OF PHYSICAL OCEANOGRAPHY 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 ϫ 10Ϫ5 sϪ1 and the dashed lines denote negative values of vorticity. The arrow A: positive vorticity; the arrow B: negative vorticity. Shaded area is shallower than 1200 m. tides are the major constituents around the Kuril Islands, ture current measurements for comparison and improve- which interact nonlinearly, producing mainly a fort- ment of our estimates of tidal exchange. Nevertheless, nightly tide (the linear fortnightly modulation is en- bidirectional mean currents in the Straits, through which hanced) and an M 2 tide although the dominant com- these tidal exchanges are effectively produced, are con- ponent remains the K1 tidal current. Such nonlinear in- sistent with the current structure observed in infrared teractions between the components might cause differ- images taken by NOAA-12 and mentioned in the earlier ence in calculated transport. It remains a subject for work by Moroshkin (1966) and Leonov (1960). To em- future investigation. phasize this point, we have tracked numerous labeled Owing to the lack of current measurements, the re- particles in the calculated velocity ®eld following earlier liability of the calculated current ®eld is dif®cult to as- works (e.g., Miyama et al. 1995). Focusing on Bussol sess. We compare the model results with observation Strait, where most of the discharge is considered to only in elevation data. Accordingly, although the results occur, we performed 10 cycles of tracking from the ebb suggest that tidal exchange is a possible mechanism of tide (Fig. 18). The calculated ¯ow pattern of the Okhotsk water exchange through the Kuril Straits, we await fu- 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 ϫ 2.5 km grid sizes case and the contour unit of 0.8 Sv.

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 Paci®c and is located north of the critical latitude for diurnal tides. This indicates the im- FIG. 16. Schematic illustration of the formation mechanism of mean portance of direct current measurements for the esti- vorticity by topographically trapped waves. (a) Vorticity generation by the stretching/squeezing effect. (b) Generation of a net ¯ux of mation of water exchange between the two basins so positive vorticity due to the combined effect of advection by the that barotropic mean ¯ow induced by subinertial tides along-isobath current and the propagation of topographically trapped can be precisely taken into account. waves. (c) Net positive vorticity ¯ux is conveyed by topographically trapped waves from a shallow strait to a deep strait where the waves can cross the sill, producing the mean bidirectional current structure. 7. Summary Our regional model has successfully reproduced the

observed barotropic K1 tidal ®eld in the Okhotsk Sea, a qualitatively similar appearance to that of the infrared although the reliability of the calculated current ®eld is image. The simulation data in Fig. 18 exhibit such fea- dif®cult to assess owing to the lack of current mea- tures as bidirectional and along-sill mean currents. Dis- surements. Using the calculated tidal currents, the Eu- charge from the middle of Bussol Strait is also visible, lerian mean out¯ow from the Okhotsk Sea is estimated part of which joins the coastal side of the Oyashio cur- to reach the signi®cant value of 5.0 Sv for the K1 tide, rent ¯owing offshore. the main part of which is conducted through the Bussol, On the other hand, from geostrophic calculations Kruzenshterna, and Chetverty Straits. In addition to the based on CTD data, Kawasaki and Kono (1994) indi- K1 tide, the O1, P1, M 2, and S 2 tides induce Eulerian cated that 1) out¯ows take place from Matsuwa Island mean exchanges estimated at 3.5, 1.0, 0.3, and 0.1 Sv, to Kruzenshterna Strait and north of Simusir Island to respectively. These tidal exchanges are produced by bi- Bussol Strait, 2) in¯ows take place from Nadezhdy directional mean currents in the straits, consistent with Strait to Ketoy Island, and 3) strong vertical and hori- the current structure observed in infrared images taken zontal mixing is caused at the northern straits and Bussol by NOAA-12 and mentioned in the earlier work by Mo- Strait by tidal currents, providing 2.9 Sv of Okhotsk roshkin (1966) and Leonov (1960). Therefore, it is sug- Sea water and 2.5 Sv of mixed water, both of which gested that tidal currents play an important role in water join the Oyashio (12.8 Sv). Their results are different exchange between the Okhotsk Sea and the North Pa- from our results in quantity, but the similarity in ex- ci®c, although con®rmation of this prediction and im- change and mixing locations with these observations provements in accuracy await future observations. suggests that their geostrophic calculation contains part We have shown that the mean currents are produced of the tide-induced mean currents, which are in geo- through the effects of topographically trapped waves as 1642 JOURNAL OF PHYSICAL OCEANOGRAPHY 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 recti®cation. In shal- the effect of topographically trapped waves. Last the low straits (depth 200ϳ600 m), tidal recti®cation mainly mean exchanges induced by subinertial tides are much due to advection, vorticity generation by the stretching/ greater than those expected from the previous theories squeezing effect, and damping by bottom friction pro- for tidal recti®cation which consider only the case of duces the strong along-sill and weak bidirectional mean superinertial tides because superinertial tides are inef- currents. On the other hand, in deep straits, such as ®cient at generating topographically trapped waves. Bussol strait, a net ¯ux of positive vorticity from the Thus, it is suggested that the energy of subinertial tides adjacent shallow straits to the deep strait is caused by is effectively cascaded upscale to produce bidirectional topographically trapped waves and produces strong bi- mean exchange currents in geostrophic balance, causing directional mean currents there. This net ¯ux is caused signi®cant water exchange between two basins even if by the fact that the along-isobath currents are in the they are separated by sills. same direction as the phase velocity of the topograph- We have clari®ed the mechanisms of the horizontal ically trapped waves with positive vorticity and are in exchange induced by the tidal currents which dominate the opposite direction to that with negative vorticity. the Kuril Straits region. However, since we use a depth- The mean currents produced by topographically averaged model, the vertical structure is still unclear. trapped waves have three important properties: First, Many observations indicate strong vertical mixing at the mean currents induced by these waves are in near- the straits. Based on the vertical distributions of oxygen geostrophic balance, since these waves are characterized and density across Bussol Strait, Yasuoka (1967) sug- as a rotational wave. Second, because this mechanism gested a surface layer in¯ow, a sinking out¯ow in the is responsible for the water exchange through deep intermediate layer, and strong in¯ow over the sill. Tidal straits, its depth makes the amount of the mean transport currents may also contribute signi®cantly to vertical signi®cant. In fact, roughly half of the total exchange mixing and formation of the vertical circulation through induced by the K1 tide is considered to be caused by the generation of internal waves, which are thought to JULY 2000 NAKAMURA ET AL. 1643 have a major in¯uence on water modi®cation, as dis- ticularly in regard to cold waters. Bull. Far Seas Fish. Res. Lab., cussed in the accompanying paper (Nakamura et al. 9, 45±77. Kowalik, Z., and A. Yu. Proshutinsky, 1995: Topographic enhance- 2000). Therefore, an investigation of the vertical struc- ment of tidal motion in the western Barents Sea. J. Geophys. ture of tidal currents around the straits, which includes Res., 100, 2613±2637. the baroclinic effect, may be important for our under- , and I. Polyakov, 1998: Tides in the Sea of Okhotsk. J. Phys. standing of the detailed transport processes and water Oceanogr., 28, 1389±1409. mass transformation. LeBlond, P. H., and L. A. Mysak, 1978: Waves in the Ocean. Elsevier Scienti®c, 602 pp. Besides tidal currents, water exchange and mixing can Leonov, A. K., 1960: The Sea of Okhotsk. National Technical In- be caused by eddies (which often appear along the is- formation Service, Spring®eld, VA. lands), ¯ow driven by local winds, and advection and Longuet-Higgins, M. S., 1965: Some dynamical aspects of ocean diffusion due to the difference in strati®cation between currents. Quart. J. Roy. Meteor. Soc., 91, 425±457. Mazzega, P., and M. BergeÂ, 1994: Ocean tides in the Asian semien- the Okhotsk Sea and the North Paci®c. In particular, closed seas from TOPEX/POSEIDON. J. Geophys. Res., 99, although exchange by the western boundary current of 24 867±24 881. the subarctic gyre itself is of secondary importance as Miyama, T., T. Awaji, K. Akitomo, and N. Imasato, 1995: Study of it ¯ows along the Kuril Island Chain, this current can seasonal transport variations in the Indonesian Seas. J. Geophys. have a signi®cant effect when it interacts with oscillat- Res., 100, 20 517±20 541. Moroshkin, K. V., 1966: Water masses of the Sea of Okhotsk. U.S. ing tidal currents. We should combine knowledge of the Dept. of Commerce Joint Publication Research Service 43, 942, tidal currents with these effects in the future in order 98 pp. to identify and quantify the impact of the Okhotsk Sea Nakamura, T., T. Awaji, T. Hatayama, K. Akitomo, T. Takizawa, T. upon the North Paci®c. Kono, Y. Kawasaki, and M. Fukazawa, 2000: The generation of large-amplitude unsteady lee waves by subinertial K1 tidal ¯ow: A possible vertical mixing mechanism in the Kuril Straits. J. Acknowledgments. We wish to acknowledge Prof. S. Phys. Oceanogr., 30, 1601±1621. Saitoh (Hokkaido University, Japan) for the kind offer Odamaki, M., 1994: Tides and tidal currents along the Okhotsk coast of NOAA-12 AVHRR imagery. We also thank Dr. J. P. of Hokkaido. J. Oceanogr., 55, 265±279. Matthews and anonymous reviewers for their critical Ogura, S., 1923: Tides in the Sea of Okhotsk (in Japanese). Suiro reading and useful comments. Numerical Calculations Zasso, 10 (274), 71±88. Orlanski, I., 1976: A simple boundary condition for unbounded hy- were done on the FACOM M1800 and VP2600 at the perbolic ¯ows. J. Comput. Phys., 21, 251±269. Data Processing Center of Kyoto University. Reed, R. K., 1990: A year-long observation of water exchange be- tween the North Paci®c and the Bering Sea. Limnol. Oceanogr., 35 (7), 1604±1609. REFERENCES Reid, J. L., 1965: Intermediate Waters of the Paci®c Ocean. Johns Hopkins Press, 85 pp. Awaji, T., N. Imasato, and K. Kunishi, 1980: Tidal exchange through Ridderinkhof, H., 1989: Tidal and residual ¯ows in the Western Dutch a strait: A numerical experiment using a simple model basin. J. Wadden Sea: Vorticity balances. Neth. J. Sea Res., 24, 9±16. Phys. Oceanogr., 10, 1499±1508. Robinson, I. S., 1981: Tidal vorticity and residual circulation. Deep- Chapman, D. C., 1989: Enhanced subinertial diurnal tides over iso- lated topographic features. Deep-Sea Res., 36, 815±824. Sea Res., 28A, 195±212. Chen, C., and R. C. Beardsley, 1995: A numerical study of strati®ed Schwiderski, E. W., 1979: Global Ocean Tides, II: The semidiurnal principal lunar tide (M ). Atlas of Tidal Charts and Maps, Naval tidal recti®cation over ®nite-amplitude banks. Part I: Symmetric 2 banks. J. Phys. Oceanogr., 25, 2090±2110. Surface Weapons Center. Cushman-Roisin, B., 1994: Introduction to Geophysical Fluid Dy- , 1980: On charting global ocean tides. Rev. Geophys., 18, 243± namics. Prentice-Hall, 320 pp. 268. Favorite, F., A. J. Dodimead, and K. Nasu, 1976: Oceanography of , 1981: Global Ocean Tides, IV: The diurnal luni-solar decli- the Subarctic Paci®c region: 1960±1971. Int. North Paci®c Fish- nation tide (K1). Atlas of Tidal Charts and Maps, Naval Surface eries Commission, 33, 1±187. Weapons Center. Haidvogel, D. B., A. Beckmann, D. C. Chapman, and R. Q. Lin, Stabeno, P. J., R. K. Reed, and J. E. Overland, 1994: Lagrangian 1993: Numerical simulation of ¯ow around a tall isolated sea- measurements in the Kamchatka Current and Oyashio. J. Ocean- mount. Part II: Resonant generation of trapped waves. J. Phys. ogr., 50, 653±662. Oceanogr., 23, 2373±2391. Suzuki, K., and S. Kanari, 1986: Tides in the Sea of Okhotsk (in Hatayama, T., T. Awaji, and K. Akitomo, 1996: Tidal currents in the Japanese). Oceanogr. Mag., 18, 455±463. Indonesian Seas and their effect on transport and mixing. J. Talley, L. D., 1991: An Okhotsk Sea water anomaly: Implications for Geophys. Res., 101, 12 353±12 373. ventilation in the North Paci®c. Deep-Sea Res., 38, 171±190. Holton, J. R., 1979: An Introduction to Dynamic Meteorology. 2d ed. , 1993: Distribution and formation of North Paci®c Intermediate Academic Press, 391 pp. Water. J. Phys. Oceanogr., 23, 517±537. Huthnance, J. M., 1973: Tidal current asymmetries over the Norfolk Thomson, R. E., P. H. LeBlond, and A. B. Rabinovich, 1997: Oceanic Sandbank. Estuar. Coastal Mar. Sci., 1, 89±99. odyssey of a satellite-tracked drifter: North Paci®c variability , 1981: On mass transports generated by tides and long waves. delineated by a single drifter trajectory. J. Oceanogr., 53, 81± J. Fluid Mech., 102, 367±387. 87. Kawasaki, Y., and T. Kono, 1992: Baroclinic water exchange in the Warner, M. J., J. L. Bullister, D. P. Wisegraver, R. H. Gammon, and Kuril Basin and the northwestern Paci®c in summer (in Japa- R. F. Weiss, 1996: Basin-wide distributions of chloro¯uorocar- nese). Sea and Sky, 68, 41±54. bons CFC-11 and CFC-12 in the North Paci®c. J. Geophys. Res., , and , 1994: Distribution and transport of Subarctic Waters 101, 20 525±20 542. around the middle of Kuril Islands (in Japanese). Sea and Sky, WuÈst, G., 1930: Meridionale Schichtung und Tiefenzirkulation in der 70, 71±84. Westhalften der drei Ozeane. J Cons. Int. l'Explor. Mer, 5, 21 Kitani, K., 1973: An oceanographic study of the Okhotsk SeaÐPar- pp. 1644 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30

Yasuda, I., 1997: The origin of the North Paci®c intermediate water. Yasuoka, T., 1967: Hydrography in the Okhotsk SeaÐ(1). Oceanogr. J. Geophys. Res., 102, 893±910. Mag., 19, 61±72. , K. Okuda, and Y. Shimizu, 1996: Distribution and formation Zimmerman, J. T. F., 1978: Topographic generation of residual cir- of North Paci®c Intermediate Water in the Kuroshio±Oyashio culation by oscillatory (tidal) currents. Geophys. Astrophys. Flu- interfrontal zone. J. Phys. Oceanogr., 26, 448±465. id Dyn., 11, 35±47.