Tidally modified western boundary current drives interbasin exchange between the Sea of Okhotsk and the North Pacific

The interbasin exchange between the Sea of Okhotsk and the North Pacific governs the intermediate water ventilation and fertilization of the nutrient-rich subpolar Pacific, and thus has an enormous influence on the North Pacific. However, the mechanism of this exchange is puzzling; current studies have not explained how the western boundary current (WBC) of the subarctic North Pacific intrudes only partially into the Sea of Okhotsk. High-resolution models often exhibit unrealistically small exchanges, as the WBC overshoots passing by deep straits and does not induce exchange flows. Therefore, partial intrusion cannot be solely explained by large-scale, wind-driven circulation. Here, we demonstrate that tidal forcing is the missing mechanism that drives the exchange by steering the WBC pathway. Upstream of the deep straits, tidally-generated topographically trapped waves over a bank lead to cross-slope upwelling. This upwelling enhances bottom pressure, thereby steering the WBC pathway toward the deep straits. The upwelling is identified as the source of joint-effect-of-baroclinicity-and-relief (JEBAR) in the potential vorticity equation, which is caused by tidal oscillation instead of tidally-enhanced vertical mixing. The WBC then hits the island chain and induces exchange flows. This tidal control of WBC pathways is applicable on subpolar and polar regions globally.


Figure 1. Okhotsk-Pacific Exchange System through different straits. (a) Topographic features of the Kuril
Islands in the COCO model, which is adapted from the Japan Oceanographic Data Center (JODC) and modified by Ono et al. 35 and Matsuda et al. 15 (see the "Methods" section). The shaded areas represent the depth of the ocean and contours denote the iso-depths of 100, 250, 500, 1000, and 1500 m. To illustrate the details of the strait topographic features, the bird's-eye view plot extends only to a depth of 1500 m, whereas the rest of the study area is represented as shades on the floor. The arrows represent the East Kamchatka Current (EKC), the western boundary current, and the major exchange currents through the Kruzensterna and Bussol' Straits. The circled numbers above straits denote the straits from north to south as follows: 1. 1st Kuril Strait, 2. Onekotan Strait, 3. Shiashikotan Strait, 4. Kruzensterna Strait (northern strait), 5. Matua Strait, 6. Rasshua Strait, 7. Ketoy Strait, 8. Simushir Strait,9. Bussol' Strait (southern strait), 10. Urup Strait, 11. Etrof Strait, 12. Kunashiri Strait, 13. Nemuro Strait and 14. Soya Strait. The abbreviation "N. Pacific" stands for North Pacific. All these strait numbers are used in figures throughout this study. (b) Schematic view of the Okhotsk-Pacific exchange system by streamfunction. The black and army green solid line denotes the streamfunction ψ 0 as the offshore boundary of the EKC and the streamfunction ψ 2 as the boundary around the Kamchatka Peninsula, as well as Hokkaido Island, respectively. The red dashed line represents the streamfunction ψ 1 as the core axes of the EKC and the streamfunction around the MIC. The red circle indicates the bifurcation point of the EKC on the MIC. The EKC flows from the North Bank to the MIC by following the streamfunction contour ψ 1 as the main axes with ψ 0 as the offshore boundary of the EKC. When the EKC approaches the MIC, it collides on the streamfunction contour surrounding the MIC and forms the bifurcation point. The transport at the northern and southern straits are thus ψ 2 − ψ 1 and ψ 1 − ψ 2 , respectively. (c) Annual-averaged volume transport through each strait, where the numbers in the horizontal axis correspond to the numbers in (a). Positive values denote a Pacificward flow, whereas negative values are Okhotsk-ward. The tidal case, the non-tidal case, and observation data [6][7][8] are indicated in navy-blue, grey-blue, and dark-orange bars, respectively.

Scientific Reports
| (2021) 11:12037 | https://doi.org/10.1038/s41598-021-91412-y www.nature.com/scientificreports/ circulation theorem (see "Methods" section). However, their configuration is not directly applicable to reality, as the MIC is composed of a chain of islands over a sloping submarine ridge rather than a single island. Further, it is not even evident whether a streamfunction contour can be identified along the EKC that hits the MIC and forms a bifurcation point. For example, a recent simulation of the Ocean General Circulation Model for the Earth Simulator (OFES) with a 1/30° grid resolution 12, 13 demonstrated a reversed + 1.1 Sv Pacific-ward transport through the northern strait, coupled with a − 0.8 Sv Okhotsk-ward current via the southern strait ( Supplementary Fig. S1). By observing the streamfunction, we found that the EKC overshoots bypassing the two deepest straits without forming a bifurcation on the MIC ( Supplementary Fig. S1), resulting in spurious results. This was apparently a hidden problem that was uncovered through the optimized physics of cutting-edge ocean general circulation model (OGCM) approaches, considering that the OFES with a coarser resolution (1/10°) reproduced exchange transport dynamics that were consistent with the observed estimates 7 (Supplementary Fig. S1).
In this study, we demonstrate that tidal forcing is the missing mechanism that drives interbasin exchange caused by the partial intrusion of the EKC. By adopting an ocean model (CCSR Ocean Component model, hereinafter referred to as the COCO 14 ; see "Methods" section and Matsuda et al. 15 ) with a curvilinear coordinate system, a resolution of approximately 5 km (1/20°) around Kuril Islands, and accounting for diurnal tides in the simulation (referred to as the tidal case), the model estimated a throughflow transport of −4.0 Sv through the northern strait and + 8.7 Sv via the southern strait (Fig. 1c), thus realistically reproducing the observed estimates 7 . However, once the tidal forcing was turned off (referred to as the non-tidal case), the throughflow transport almost vanished, as illustrated in Fig. 1c, which represented a spurious result similar to the OFES at a 1/30° resolution mentioned above. This indicates that tidal forcing is an indispensable driver of interbasin exchange. The Kuril Islands region features vigorous tidal oscillations and currents 16 dominated by the diurnal tides 9 , of which the tidal current's amplitude sometimes exceeds 1.5 m s −1 . In a previous study, by implementing a numerical model that only accounted for tides in which the EKC is absent, Nakamura et al. 9 estimated the net exchange transport to be + 0.4 Sv and + 0.9 Sv through the northern and southern straits, respectively, both of which were Pacific-ward. That is, the tide-only model did not accurately represent the proper exchange transport dynamics either. This implies that the interaction between diurnal tides and the EKC is an essential driver of interbasin exchange. Here, we present a new mechanism for tidal control on the EKC's pathway that leads to the partial intrusion to the Sea of Okhotsk from a potential vorticity (PV) dynamics standpoint.

Results
Overview of the tidal and non-tidal flow field. In this section, we analyzed the EKC path difference between the tidal and non-tidal cases and explored the roles of the tides on the exchange processes. The tidal case of the COCO, which was spun up by climatological forcing (see "Methods" section), estimates that the seasonal variation of the throughflow transport ranges from − 5.4 to − 1.9 Sv through the northern strait, and from + 7.6 to + 9.8 Sv via the southern strait (Fig. 2), which is consistent with the observed estimates 7 . Given that the exchange transport difference between the two cases is sufficient in both straits regardless of the season, we will focus on the generality of this difference induced by tides rather than seasonality. The June flow field was used in the following analysis, when the local wind stress curl around the MIC is weak (Supplementary Fig. S2) and the flow pattern is most typical compared to other months, where the EKC's streamfunction contour encompasses most of the MIC, as illustrated in Fig. 1b 6 in the summer and the green lines are the annually-averaged hydrographic transport value of the northern strait (dashed line) and southern strait (solid line) 7 . The abbreviations "N" and "S" correspond to the northern and the southern straits, respectively.  (Fig. 3a). Here, we define [ ] = 1 H η −h dz as a depth-averaged value, where represents arbitrary variables, z denotes the vertical coordinate, and H = η + h represents the local water thickness, which equals the sum of the bottom depth h and the sea surface height η . The EKC deflects westward immediately after it passes the North Bank and approaches the MIC. Figure 3b  where u and v denote the zonal and meridional velocity, and x and y are the zonal and meridional coordinates, respectively. The streamfunction contour ψ = −1.5 × 10 6 m 3 s −1 extends from the North Bank toward the northern strait along with the EKC (red contour in Fig. 3b). At the same time, ψ = −1.5 × 10 6 m 3 s −1 surrounds the MIC. The two contours encounter approximately at 47.8°N, 153.6°E (indicated by a yellow arrow in Fig. 3b), forming a bifurcation point. This indicates that the transport of the EKC represented by −1.5 × 10 6 < ψ 0 www.nature.com/scientificreports/ m 3 s −1 is forced to flow through the northern strait. The geometrical features of the streamfunction in the tidal case agrees with those of Fig. 1b, in which the partial intrusion of the EKC occurs.
In contrast, the EKC in the non-tidal case bypasses most of the MIC (Fig. 3d,e). As a result, interbasin exchange is almost abolished, with weak Pacific-ward throughflows via both the northern and southern straits (Fig. 3d). The streamfunction depicts a clockwise flow pattern encompassing the MIC that blocks the interbasin exchange, and no bifurcation point forms in this case (Fig. 3e). We observed that the 1/30° resolution OFES (which does not incorporate tidal forcing) also displays a similar clockwise circulation surrounding the MIC, which makes the EKC bypass the deep straits ( Supplementary Fig. S1) in a manner resembling the non-tidal case. These non-tidal results markedly contrast with those of the tidal case, implying that tidal forcing plays an essential role in the partial intrusion of the EKC.
One of the main differences between the tidal and non-tidal cases is the presence of seamount trapped waves in the former that propagate in the clockwise direction around topographic features such as the MIC and the North Bank 9, 17 (see Supplementary Fig. S5 and Supplementary Movie 1). Further, a tidal-period-mean velocity indicates that tidally-rectified, clockwise circulations are generated around the islands and seamounts 9 . The tidally rectified circulation is prominent over the North Bank of the tidal case (compare Fig. 3a, blue arrows point, and Fig. 3d), which has been evidenced in the study site by the trajectories of Argo floats and surface drifters 11 .
To discuss the deflection of the EKC by interaction with these tidal motions, we focused on the bottom velocity around the North Bank. By comparing Fig. 3c,f, we found that the bottom velocity is much stronger in the tidal case, whereas in the non-tidal case, the along-slope bottom velocity is very weak or even reversed downstream of the North Bank ( Fig. 3f; indicated by red arrows). Therefore, the EKC is hardly constrained by the topography in the downstream region in the non-tidal case, and thus the EKC overshoots passing by the deep straits at both ends of the MIC. In other words, bottom steering occurs due to tides, which forces the EKC to bend toward the northern strait after passing the North Bank, leading to the intrusion of the EKC water into the Sea of Okhotsk. The question now is why and how such a bottom steering of the EKC occurs in the tidal case. Is the bottom steering of the EKC a result of the trapped waves and/or the tidally-rectified circulation?
Transition experiment from non-tidal to tidal state. To clarify the mechanisms of tidally-induced interbasin exchange, a transition experiment from the non-tidal state to the tidal state was conducted. Particularly, we focused on the processes that lead to the bottom steering of the EKC around the North Bank. The conditions on the last day of June of the non-tidal case were taken as the initial conditions for the transition experiment. Then, the tidal forcing was activated, and the model was executed for another 65 days (see the "Methods" section). Wind and heat fluxes were kept constant as those of June during the experiment. By doing this, the transition experiment would reveal the mechanisms by which tidal forcing produces the EKC's bottom steering and shifts its pathway.
Transport through the two straits is both Pacific-ward initially with approximately + 3 Sv according to the June state of the non-tidal case. After accounting for tidal forcing on Day 0, the transport through the northern and southern straits varied until Day 30 and reached an almost steady state thereafter (Fig. 4a). We may divide the period of the transition into two stages on Day 14. The period between Day 0 and Day 14 represents an initial impact by imposing the tidal forcing. In the northern strait, the Okhotsk-ward inflow (with a negative sign) increases up to Day 8 but decreases afterward until Day 14, when the transport via the northern strait exhibits 0 Sv. From Day 14 to Day 26, transport through the northern strait increases again and finally achieves a steadystate with − 2.8 Sv. The transport through the southern strait behaves similarly, displaying a two-stage development. These periods will hereinafter be referred to as "transition stage 1" and "transition stage 2", respectively.
Transition stage 1 is characterized by the generation of seamount trapped waves (Supplementary Movie 1) and tidally rectified circulation around islands and seamounts ( Fig. 4b-e and Supplementary Movie 2). For example, a bi-directional flow occurs in both the northern and southern straits (Fig. 4b). However, ψ displays a large positive value encompassing the MIC which still forces the EKC to bypass these straits. This suggests that during stage 1, the tidal rectification due to seamount trapped waves is the main factor that drives the development of transport through straits, as discussed in Nakamura et al. 9 (see Supplementary Movie 2). In the upstream surrounding the North Bank, an anticyclonic circulation due to tidal rectification forms on Day 4. However, it does not yet alter the EKC path.
During transition stage 2, the EKC starts bending on Day 14 immediately downstream of the North Bank ( Fig. 4c and Supplementary Movie 2). As the EKC bends and collides with the northern part of the MIC, the Okhotsk-ward throughflow becomes predominant in the northern strait. By Day 26, the EKC approaches the MIC steered by relatively shallow bathymetric contours (Fig. 4d). The EKC then bifurcates (indicated by the red dots in Fig. 4d-e) when it encounters approximately the 1500 m isobath surrounding the MIC, where the value of ψ decreases significantly compared with the initial value. Because of the formation of the bifurcation point, the Okhotsk-ward throughflow occurs via the northern strait similarly to that illustrated in Fig. 1b. Interbasin transport tends to become steady after Day 26. The flow pattern of the Okhotsk-Pacific exchange on Day 65 is almost the same as that of the tidal case. This experiment demonstrates that the interaction between tidallyinduced circulation and the EKC over the North Bank drives the interbasin exchange in the tidal case.
Tidal-period-mean PV budget of the EKC over the North Bank. To investigate the dynamic effects of tides on the EKC pathway, we diagnosed the EKC via the barotropic PV:   where τ is wind stress, ρ 0 is the referential density, C d is the bottom drag coefficient, and χ is defined by: where ρ is density and g is gravity acceleration. and t represent the mean and tidal component as a function of the diurnal tide period, and J denotes the Jacobian of a given variable. The first term on the right-hand-side of Eq. (3) is the joint-effect-of-baroclinicity-and-relief (JEBAR). This represents the effects of baroclinicity on bottom pressure across the topography, which causes torque on the water column 18,19 . Further, in Eq. (3), the original PV advection term [u] · ∇q is decomposed as follows: where −[u] t · ∇q t on the right-hand-side of Eq. (3) represents PV production due to tidal rectification. Given that the wind stress in the transition experiment is constant as a function of time, the tidal effects on the EKC's PV budget can be evaluated by the three other terms in the right-hand-side of Eq. (3).
The tidal-period-mean PV advection [u] · ∇q (hereinafter referred to as 'mean PV advection') balances well with the sum of the PV production terms (Fig. 5a) along Section A to the south of the North Bank, where the EKC starts deflecting westward. The mean PV advection [u] · ∇q exhibits almost a constant value ≈−4.2 m×10 −13 m −1 s −2 during transition stage 1, except for a negative peak between Day 2 and Day 6, when the difference with the sum of the PV production terms reaches a maximum. The difference corresponds to the local vorticity production ∂q/∂t , which represents the generation of clockwise, tidally-rectified circulation around the North Bank by −[u] t · ∇q t and exhibits a conspicuous peak during the same period.
In transition stage 2, the mean PV advection increases from − 4.2×10 −13 m −1 s −2 to − 2.6×10 −13 m −1 s −2 when the EKC shifts. The tidal rectification and bottom friction terms remain almost constant in the PV budget during transition stage 2. The wind stress term is constant throughout the experiment despite having a high value (2.5×10 −12 m −1 s −2 ). Therefore, the only term that changes with time is the JEBAR, which can balance with changes in mean PV advection.
Maps of the PV budget difference between Day 30 and Day 1, defined by (PV ) Day30 − (PV ) Day1 , are illustrated in Fig. 5b-e. Since q ≈ f 0 /H , where f 0 is the Coriolis parameter around the North Bank, the difference of the mean PV advection in terms of time is approximated as follows: where T is an operator representing the difference between Day 30 and Day 1. According to Eq. (5), the difference in the mean PV advection corresponds to the velocity difference between Day 30 and Day 1, T [u] , across PV (or bathymetric) contours. Since � T [u] · ∇q > 0 in Section A, T [u] takes place in the upslope direction ( ∇ f 0 H > 0) , as seen in the vectors in Fig. 5b. That is, the positive difference in the mean PV advection around Section A corresponds to an upslope transition of the EKC pathway.
The difference of the mean PV advection around the North Bank balances well with the sum of the change of the tidal rectification and JEBAR terms in the right-hand-side of Eq. (3) (Fig. 5b,c). Particularly, the JEBAR's contribution (Fig. 5e) is dominant around Section A, which can be expressed as follows: where the subscript A denotes the region around Section A, and This result indicates that the JEBAR change due to � T χ , associated with the density change, � T ρ , in a given water column drives the EKC's upslope transition over the North Bank across PV contours. However, the source of the JEBAR change remained to be determined.

Source of JEBAR change for the EKC's path shift.
The JEBAR term is incorporated into PV Eq. (3) as a wind stress curl that generates flows across PV contours once a density field is specified 18 . In the tidal case, JEBAR forces the EKC upslope to relocate and bend it toward the MIC, resulting in interbasin exchange. Here, we identified the impact of tidal forcing that alters the density field, leading to JEBAR changes over the North Bank.   To examine the mechanism of JEBAR increase, we inspected the density structure in Section A1 (Fig. 6, right panels), which is 15 km upstream of Section A, and identified an overturning cell on the slope depicted by the vertical velocity. The formation of the overturning cell associated with the tidally-rectified circulation has been widely discussed in previous studies [20][21][22] . The overturning cell in Fig. 6 is composed of a downwelling on the slope of a seamount and upwelling around the outer rim of the tidally-rectified circulation. Since the overturning redistributes the density field vertically and horizontally, the JEBAR change due to � T χ should occur through the density change � T ρ according to Eq. (7).
Further, we introduced the bottom pressure torque J(p b /ρ 0 , H) to explore the effect of bottom steering on the EKC (Fig. 6, left panels), where p b denotes bottom pressure. p b is related to χ through p b = [p] − ρ 0 χ H , where [p] represents depth-averaged pressure 18,19 . The relationship between the bottom pressure torque and the overturning cell is illustrated in Fig. 6. The overturning cell is generated on the slope along Section A1 as soon as the tidally-rectified circulation forms by Day 4 (Fig. 6a,b). The bottom pressure torque exhibits a supply of negative vorticity at 1000-2000 m depths around A1, which likely turns the bottom velocity clockwise. This strongly indicates the cross-slope upwelling reinforces the bottom pressure torque by shoaling isopycnals up to ~ 700 m (Fig. 6c,d). Concurrently, an along-isobath bottom flow occurs downstream of Section A1 around the North Bank at depths of 1000-1500 m, where the positive bottom pressure torque (on Day 0) is canceled by the negative torque supply until the end of transition stage 2. The bottom steering drives the EKC in an upslope direction and reaches a similar state to that of the tidal case (Fig. 3a). Since the density change associated with the overturning cell, which is generated by the tidal rectification, produces the JEBAR's change for the transition of the EKC, we refer to this process as a "tidally driven JEBAR mechanism. " Tidally-modified EKC drives the interbasin exchange. Finally, Fig. 7 summarizes our overarching findings. In the absence of tidal forcing, the EKC tends to bypass the deep straits and does not induce interbasin exchange. Once the tidal forcing is incorporated, however, the EKC is forced to bend westward after passing the North Bank, and approaches the MIC along with the streamfunction contour ψ 1 as depicted in Fig. 7a. Afterward, the bifurcation point on ψ 1 occurs around the MIC and the EKC branches northward and southward (Fig. 7a). The northern branch of the EKC passes through the northern strait Okhotsk-ward and drives the interbasin transport. Upstream of the MIC, the westward deflection of the EKC occurs as a result of steering by the topography of the North Bank when the tidal forcing is imposed (Fig. 7b). The cross-slope overturning cell in response to the tidally-rectified circulation raises the bottom pressure torque via shoaling of the isopycnals at depth. Increases in the bottom pressure intensified the bottom velocity along isobaths and relocated the EKC pathway across the PV contours by the JEBAR term.
High-resolution simulations typically improve the representation of the flow through straits of WBCs, as described by Metzger and Hurlburt 23 . Concretely, the authors found that the existence of an underwater bank in the Luzon Strait blocks the intrusion of the Kuroshio as the model resolution increased, which is consistent with the observations. This phenomenon was defined as the "blocking effect" 23 and resembles our non-tidal case. However, as discussed in this study, improving the model resolution does not necessarily reproduce the interbasin exchange accurately as shown in the non-tidal case because of the non-linearity. Sheremet 24 evaluated whether a WBC leaps across a strait caused by the current's inertia, overcoming the westward bending due to planetary Rossby waves. In linear models, planetary Rossby waves enforce the EKC deflecting to the MIC and drive the interbasin exchange 10 . In high-resolution models, however, inertia of WBCs tends to dominate over the Rossby wave dynamics and thus the interbasin exchange is blocked as shown in the non-tidal case. Clearly, a better understanding of the physical processes that drive the WBCs is necessary as the model resolution increases.
Our study proposes a novel mechanism for the interaction between tidally-rectified circulation and the boundary current through JEBAR. We also demonstrated that the interaction between boundary currents and tides, which is usually lacking in modeling studies, is key to improve high-resolution OGCM performance.

Discussion
Our study elucidated the impact of tidal forcing on the relocation of the EKC pathway due to the changes in JEBAR, which consequently leads to the partial intrusion of the EKC into the Sea of Okhotsk. However, the diurnal tides not only generate rectified circulation but also cause strong vertical mixing along the Kuril Islands by breaking of internal tides 9,17 . Although the impact of tidally-induced vertical mixing along the Kuril Islands on the North Pacific's thermohaline circulation was suggested 25,26 , its influence on the Okhotsk-Pacific exchange system was seldom mentioned.  www.nature.com/scientificreports/ Vertical mixing observed along the Kuril Islands is as high as 25 cm 2 s −1 27 , which is two orders of magnitude stronger than that in the ocean int erior 27 . In the COCO, vertical mixing was parameterized as the vertical diffusivity coefficients evaluated by the turbulent closure scheme 28 . The vertical diffusivity coefficients around the islands were approximately 23.9 cm 2 s −1 and 13.6 cm 2 s −1 in the tidal and non-tidal cases, respectively (see Supplementary Fig. S6). To evaluate the impacts of vertical mixing with no tidal oscillations on the Okhotsk-Pacific exchange system, we conducted an experiment in which the vertical diffusivity coefficients extracted from the tidal case were substituted with those of the non-tidal case (Supplementary Fig. S6; see the "Methods" section). This case is henceforth referred to as the "non-tidal-TM case, " where TM denotes Tidal Mixing.
We found that the interbasin exchange in the non-tidal-TM case exhibited the most unrealistic throughflow transport estimates of + 0.9 Sv and + 0.8 Sv at the northern and southern straits, respectively (Fig. 8a,b). This scenario exhibited an intense clockwise circulation surrounding the MIC (Supplementary Fig. S7), which was similar to the results of the non-tidal case (Fig. 3e). Therefore, enhanced vertical mixing does not drive the intrusion of the EKC into the Sea of Okhotsk. That is, vertical mixing is not a factor that causes interbasin exchange in the tidal case.
For further sensitivity testing, an experiment in which the vertical diffusivity coefficient was set to zero was conducted with the tidal-case configuration (henceforth referred to as the "tidal-NoM" case, where "NoM" means no-mixing; see the "Methods" section). The interbasin exchange in the tidal-NoM case was the largest among all cases (Fig. 8a,b). The EKC exhibits a sharp deflection around the North Bank and bifurcates at the MIC's northern corner by following the streamfunction contour ψ = −5.81 × 10 6 m 3 s −1 , resulting in a strong Okhotsk-ward throughflow transport (Fig. 8c).
According to the tidally driven JEBAR mechanism, the northward relocation of the EKC toward the MIC is expressed by the PV supply via JEBAR on the North Bank's eastern slope. The tidal-NoM case shows a larger JEBAR value around Section A than that of the tidal case (Fig. 8d). The vertical profiles of density and along-slope velocity on Section A indicate that the EKC in the tidal-NoM case locates further upslope compared with that of the tidal case ( Supplementary Fig. S6). The effects of the tidally-rectified circulation on the EKC are enhanced in the tidal-NoM case compared with the tidal case by strengthening the tidally driven JEBAR mechanism. Considering the results of the sensitivity experiments, we concluded that tidally-induced vertical mixing tends to reduce the interbasin transport between the Sea of Okhotsk and the North Pacific.
Vertical mixing is often incorporated in OGCMs through parameterizations over rough topography to estimate the global distribution of tidal energy available for turbulent mixing 29,30 . In contrast, the dynamic effects of tides such as the interaction between western boundary currents and tidal motions are often overlooked in basin-wide or global-scale modeling. However, as discussed in the introduction, high-resolution OGCMs are uncovering inconspicuous problems inherent to relatively low-resolution models due to improvements in physics modeling.
Our results suggest that the tidal forcing and the resulting tidally driven JEBAR mechanism are a missing piece for high-resolution OGCMs in which strong boundary currents and topographic features are accurately characterized in high-latitude areas. The tidally driven JEBAR mechanism may also apply to various regions where both boundary currents and intensive diurnal tides coexist. For example, the Aleutian Arc and the Antarctic continental shelves are candidates; in the former, the Alaskan Stream controls the interbasin exchange between the Bering Sea and the North Pacific 31, 32 , whereas in the latter case, the Antarctic Slope Current regulates the heat transport to the ice shelf 33,34 . where u denotes a horizontal velocity vector, ∇ is the horizontal gradient operator, f andζ denote the planetary and relative vorticity, respectively, ρ 0 is a typical density, and p represents pressure. τ s and τ b denote wind stress and bottom stress, respectively, and F denotes horizontal viscosity. Afterward, taking a circulation integral along a closed constant-depth contour H = H 0 , circulation can be expressed as follows:  where l is an along-isobath coordinate, and t and n denote unit vectors along-and cross-isobath coordinates, respectively. Kida and Qiu 10 derived a streamfunction value on the wall of a single island over a flat bottom by evaluating assuming a steady-state with spatially constant wind stress τ s in a deep ocean where bottom stress τ b is negligible. Note that the vorticity flux term (i.e., the second term in the left-hand-side) is identically zero along the island wall in their simple model. In reality, the vorticity flux term across isobaths (e.g., 1500 m) is not zero, as the MIC is not a single island on a flat bottom but a chain of islands over a submarine ridge. Vorticity flux convergence may therefore occur and drive an anti-cyclonic circulation encompassing the MIC that blocks the interbasin exchange. This may potentially explain the spurious results of the recent high-resolution GCMs.  15 , which covers the Pacific Ocean from 10°S to 67°N meridionally and 100°E to 90°W zonally. This includes all important marginal seas of the North Pacific, including the Sea of Okhotsk, the Bering Sea, the South China Sea, the Japan Sea, and the Indonesian Straits. The Sea of Okhotsk is configured to be high resolution (finer than 3 km in the northern shelf region and 5 km around the Kuril Islands that divide the Sea of Okhotsk from the North Pacific) by using a curvilinear coordinate grid. Vertical grids are totally 84 layers composed of 7 sigma coordinate layers shallower than 35 m, followed by 36 z-coordinates layers with 10 m thickness intervals, and 41 z-coordinate layers by thickness interval exponentially increases from 12 to 600 m. The model's bottom topography is adapted from the Japan Oceanographic Data Center (JODC) and modified by Ono et al. 35 and Matsuda et al. 15 However, we eliminated the extra vertical diffusivity around the Kuril Islands added by Matsuda et al. 15 .   15 for further details of the model configuration.

Methods
The tidal forcing of the K1 constituent is given by the tidal potential ξ in the barotropic momentum equations such that where u T is the barotropic velocity and A H is the horizontal eddy diffusivity. The tidal potential is written as ξ = Ksin2φcos(σ t + ) for the diurnal tide, where φ and are the latitude and longitude, respectively, with the amplitude K = 0.14 m, frequency σ = 0.72921 × 10 −4 s −1 , and (α 0 , β 0 ) = (0.90, 0.69) 39 . The model configuration for the non-tidal cases does not consider ξ in the barotropic momentum equation. Please see Matsuda et al. 15 for more details on the validation of simulated tidal currents.   15 . We then span it up for 60 years by the climatology OMIP dataset same as Matsuda et al. 15 but without tidal forcing. We used the model's final outputs as our initial conditions. We next span it up for 45 years by the same climatology OMIP forcing with the tidal and non-tidal configurations according to Matsuda et al. 15 as the tidal and non-tidal cases, respectively. The last year's model output was used for analysis. Ocean general circulation model for the earth simulator (OFES). The ocean model output from the Ocean General Circulation Model for the Earth Simulator (OFES) 1/30°1 2, 13 was also used for this study. The model domain ranges from 100°E to 70°W and from 20°S to 68°N with 100 vertical levels, encompassing the marginal seas in the North Pacific. The bathymetry data was obtained by merging the General bathymetric Chart of the Oceans (GEBCO) (1 min) 40 and JTOPO30 41 . Vertical mixing in the mixed layer was parameterized as the vertical diffusivity coefficients by Noh and Kim 28 . First, we conducted the climatological integration of the OFES 1/10° simulation for 15 years, which was 30 years spun up by the temperature and salinity data of WOA13 as the initial state 12 . Afterward, a hindcast OFES 1/10° simulation was conducted from 1979 until 2000. Ultimately, the OFES 1/30° simulation spanned from January 1, 2000, to December 31, 2003, which was forced by the historical atmospheric reanalysis data of the JRA-25 42 . Data corresponding to the year 2003 was used in this study.
Transition experiment. The transition experiment was conducted by activating tidal forcing ( ξ ) in the momentum Eq. (8) for 65 days of simulation. The initial state of the experiment is the final day of June of the non-tidal case, and the rest of the forcing parameters, including heat flux, wind stress, and freshwater flux, remained the same as those in June. The impacts of tidal forcing with no influence from other forcing parameters were modeled by maintaining wind and heat forcing constant for 65 days from the end of June. The analyses were conducted using the model output recorded every 1.1975  Vertical mixing experiments. The vertical mixing in the COCO model is modeled by a turbulent closure scheme by Noh and Kim 28 such that where A v is the vertical viscosity, and K v is the vertical diffusivity. l and q are turbulence length scale and rootmean-square velocity of turbulence, respectively. S is a coefficient parameterized as S = S 0 / √ 1 + αR it , where S 0 is given as 0.39, α = 3 is a constant for proportionality, and R it is the turbulent Richardson number, R it = Nl/q 2 , where N 2 is the buoyancy frequency, −gρ 0 −1 ∂ρ/∂z . P r is the Prandtl number, where P r = P r0 + βR i , P r0 and β are constants equal to 0.8 and 7, respectively, and R i is the Richardson Number, R i = N 2 / (∂u/∂z) 2 + (∂v/∂z) 2 .
Here we designed two different types of model experiments, testing the vertical diffusivity function in water exchange transport. The first experiment was the non-tidal-TM case, which was executed by substituting the tidal case's vertical diffusivity value into the non-tidal case monthly for 5 years to detect the influences of tidal mixing without residual tidal currents. Second, we conducted sensitivity tests enforcing the vertical diffusivity value to be zero in the tidal model configuration, which we referred to as the tidal-NoM case. The models were spun up for 5 years under climatological forcing. The model outputs of the last year were used for analysis in both settings. Figures 1a, 3, 4b-e, 5b-e, 6, 7, and 8c-d were produced using Matlab (Matlab R2019b, https:// www. mathw orks. com/ produ cts/ new_ produ cts/ relea se201 9b. html). The topography data is obtained from the COCO model (see the "Methods" section). Figure 1b is illustrated by PowerPoint (PowerPoint 2016, https:// www. micro soft. com/ ja-jp/ downl oad/ detai ls. aspx? id= 53373). All data are available from the authors on reasonable request.