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    Schematic diagram to show the position of the stationary solutions for a single-peaked forcing; the curves represent the E(Φ) = (3/2a)dFN/dΦ of (7), where the solid portions of the curves indicate stable solutions, while the dashed portions indicate unstable solutions. For the single-peaked case, there are two cases according to the sign of the aFN. The dotted–dashed line indicates r. The stationary solutions are achieved where these two lines intersect with each other [i.e., E(Φ) = r] as indicated by the bullets. The phase relationship of the stationary solutions with respect to the forcing is schematically illustrated for both aFN > 0 and aFN < 0 cases.

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    Bottom topography and model grids near the south coast of Japan: contour interval for topography is 1000 m.

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    (a) The LM path obtained in the model. The figure displays the SSH averaging for one year (year 4) in the model. Vectors exhibit velocity field at bottom; contour interval for SSH is 0.1 m and for topography 500 m. (b) The rms of the SSH variance; contour interval is 0.05 m.

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    Sequence of the SSH evolution off the coast of Japan: (a)–(h) Evolution every 15 days starting on model day 1335. Light gray shading denotes SSH higher than 1.4 m, while dark gray denotes SSH lower than 0.5 m; contour interval is 0.1 m.

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    Hovmöller diagram of the SSH in terms of the longitude and the model day. The SSH is averaged over the latitude between the Japanese coast and the line connecting 27°N, 131°E and 32°N, 141°E. Light gray shading denotes SSH higher than 1.1 m, while dark gray denotes SSH lower than 0.8 m; contour interval is 0.1 m. Arrows show that the LM is displaced to the easternmost position in each vacillation event.

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    Sequence of the SSH evolution adjacent to the Izu Ridge: (a)–(f) evolution every 5 days starting on model day 1395.

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    An observed sequence of the Kuroshio path behavior in 1960 (dark solid line → light solid line → dark dashed line → light dashed line; redrawn after Shoji 1972). The Kuroshio rode over the Izu Ridge in early April (dark solid line). In mid-April (light solid line), the Kuroshio axis was located around Hachijo Island. However, it moved northward after that and reached the Japanese coast in three weeks as indicated by a broad arrow. Simultaneously, it was pushed westward away from the ridge, showing the counterclockwise rotation of the axis centering around 32°N, 138°E as indicated by a broad broken arrow.

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    Temperature field at 400-m depth in October 1976 when the Kuroshio displayed the LM path. After Ohtsuka (1978).

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    (a) Bottom pressure torque (color) on model day 1405 superimposed upon the SSH (white contour) and the bottom topography (red contour). Cyclonic torque tendency is produced where the bottom pressure torque is negative; the negative bottom pressure torque that is involved with blocking is indicated by an arrow. (b) Torque balance in (8) along the Kuroshio axis on the same model day: The solid line denotes the bottom pressure torque term, the dashed line the Coriolis term, and dotted line the tendency term (total derivative). The dashed–dotted line denotes the sum of all terms. The shaded area indicates the western slope of the Izu Ridge. The negative peak of the bottom pressure torque around 138.5°E (indicated by an arrow) corresponds to the location where the negative BPT is present in (a).

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    Time series of the torque balance in (8): solid line denotes the bottom pressure torque, dashed line the Coriolis term, and dotted line the tendency term (total derivative). The negative peaks of the bottom pressure torque are indicated by the arrows, corresponding to the times arrowed in Fig. 5, when the LM is displaced to the easternmost position in each vacillation event.

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    Bottom velocity field (vector) over the western slope of the Izu Ridge superimposed upon the SSH (shade) and bottom topography (contour) in the Kuroshio axis: contour interval for SSH is 0.1 m and for topography 500 m. The SSH indicates that the surface current flows northeastward.

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    Evolution of the bottom pressure torque (shade) superimposed upon the streamfunction (contour) and bottom topography (light contour): dark shade indicates negative BPT less than −1 × 10−8 m2 s−2. (a)–(f) The evolution every 5 days starting on model day 1380. Arrows indicate evolution of the negative BPT that interacts with the evolution of the Kuroshio axis; contour interval is 10 × 106 m3 s−1 for the transport function and 500 m for topography.

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    Bottom velocity anomaly (vector) on model day (a) 1385, (b) 1390, (c) 1395, and (d) 1400 superimposed upon the SSH anomaly (shade) and bottom topography (contour): contour interval is 0.1 m for the SSH anomaly and 500 m for topography.

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Blocking of the Kuroshio Large Meander by Baroclinic Interaction with the Izu Ridge

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  • 1 Institute of Low Temperature Science, Hokkaido University, Sapporo, Japan
  • | 2 Department of Meteorology, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii
  • | 3 Department of Environmental and Ocean Engineering, University of Tokyo, Tokyo, Japan
  • | 4 Institute of Observational Research for Global Change, Japan Agency for Marine-Earth Science and Technology, Yokosuka, Japan
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Abstract

This paper discusses the role of the Izu Ridge in blocking the Kuroshio large meander from propagating eastward across the ridge. It is shown that a combination of the sloping bottom with baroclinicity in the Kuroshio flow is important for blocking of the large meander. It produces a cyclonic torque over the western slope of the ridge when the large meander impinges upon it. That is, the cyclonic torque is formed ahead of the large meander, which results in blocking and amplification of the meander upstream of the Izu Ridge. The baroclinicity of the Kuroshio over the ridge is caused by baroclinic topographic Rossby waves generated when the large meander encounters the ridge.

Corresponding author address: Humio Mitsudera, Institute of Low Temperature Science, Hokkaido University, Nishi-8, Kita-19, Sapporo 060-0819, Japan. Email: humiom@lowtem.hokudai.ac.jp

Abstract

This paper discusses the role of the Izu Ridge in blocking the Kuroshio large meander from propagating eastward across the ridge. It is shown that a combination of the sloping bottom with baroclinicity in the Kuroshio flow is important for blocking of the large meander. It produces a cyclonic torque over the western slope of the ridge when the large meander impinges upon it. That is, the cyclonic torque is formed ahead of the large meander, which results in blocking and amplification of the meander upstream of the Izu Ridge. The baroclinicity of the Kuroshio over the ridge is caused by baroclinic topographic Rossby waves generated when the large meander encounters the ridge.

Corresponding author address: Humio Mitsudera, Institute of Low Temperature Science, Hokkaido University, Nishi-8, Kita-19, Sapporo 060-0819, Japan. Email: humiom@lowtem.hokudai.ac.jp

1. Introduction

The Izu Ridge is an outstanding topographic feature in the Kuroshio region. Hence the Kuroshio’s paths, which are usually categorized as the large meander (LM), the offshore nonlarge meander, and the nearshore nonlarge meander (Kawabe 1985), should be strongly influenced by the ridge. To model the Kuroshio, therefore, how to deal with the Izu Ridge is an important issue. One widely adopted idea is to view the ridge as an extended “island” with a wall; the gap between the island and the Japanese coast is considered as a gate that channels the Kuroshio over the Izu Ridge (White and McCreary 1976). This simple topography constrains the Kuroshio path where it has to flow. In conjunction with nonlinearity, the Kuroshio’s possible paths are discretized, leading to reproducing its multiple-path characteristics (e.g., Masuda 1982; Chao 1984; Yasuda et al. 1985; Yoon and Yasuda 1987; Akitomo et al. 1991; Masuda and Akitomo 2000; Endoh and Hibiya 2000).

Despite this success, detailed effects of the Izu Ridge on the meander are yet to be investigated. In reality, the Izu Ridge is not an island but a submarine ridge with sloping bottom. The gate models intend to represent the shallow part of the Izu Ridge, and discuss how it forces the surface jet of the Kuroshio to form the various paths. Once the LM path is formed, however, the Kuroshio accompanies a deep cyclonic recirculation so that it is able to interact with the bottom slope of the ridge in the deep ocean. Further, this may in turn feed back to the surface jet and influence the Kuroshio path. We consider that this deep-ocean interaction may be greatly different from the dynamics of the surface jet that impinges upon an island. For example, if a cyclonic circulation propagates downstream and rides over a slope, then the circulation might reduce its strength there rather than causes blocking because the ridge topography would produce anticyclonic vorticity as far as the response is barotropic. Therefore, one may suspect that, rather than maintaining the LM, the Izu Ridge tends to force the LM to decay, leading to the transition from a meandering state to a nonmeandering state.

This question is also motivated by modeling of the LM using a weakly nonlinear theory of resonant flow over topography. This simple model can represent blocking of an incident solitary wave, resembling the behavior of the LM (e.g., Mitsudera and Grimshaw 1994). The blocking occurs if the sign of the forcing and that of incident solitary waves are the same. That is, if an incident wave has cyclonic vorticity, the forcing that produces cyclonic vorticity may amplify and block the incident wave. In case of the Kuroshio, however, vorticity production by a ridge, which is anticyclonic as far as the response is barotropic, has the opposite sign to the vorticity of the LM. Therefore, the weakly nonlinear model suggests that a ridge is not necessarily favorable topography for blocking. We revisit the weakly nonlinear theory in section 2 in order to identify our questions further.

The above considerations raise questions as to how cyclonic vorticity is produced when the LM interacts with the Izu Ridge so that blocking can occur. Since the barotropic response appears to be inappropriate for blocking, we seek to understand baroclinic processes that arise when a cyclonic circulation in a stratified flow impinges upon a ridge. Better understanding to this question becomes increasingly important, not only for understanding the Kuroshio’s path dynamics, but also for conducting better simulation and prediction of the Kuroshio LM’s evolution for its growth, maturity, and decay.

Bearing these considerations in mind, we analyze output of a high-resolution Kuroshio–Oyashio model to understand blocking processes of the LM. The model includes realistic topography, coastline, stratification, and atmospheric forcings. Mitsudera et al. (2001) and Waseda et al. (2002, 2003, 2005) have shown that the model exhibits the typical paths of the Kuroshio in a realistic manner. The model realizes the LM path in terms of the Kawabe (1985) category when the inflow transport is large. These numerical solutions enable us to investigate blocking mechanisms of the Kuroshio in realistic situations. In particular, we will show that baroclinicity in interaction between the ridge and the LM indeed plays an important role in blocking.

This paper is organized as follows. We will briefly discuss the weakly nonlinear thoery in section 2 to identify questions to be resolved. Blocking of the Kuroshio LM revealed in the high-resolution numerical model, as well as comparison with observations, is described in section 3. We then discuss mechanisms of blocking in section 4, focusing our attention on torque balance. These results are summarized in section 5.

2. Weakly nonlinear stratified flow over a ridge—A revisit

For the first step to understand the blocking processes, we examine a weakly nonlinear problem of a stratified flow over topography from the viewpoint of the Kuroshio LM, as it exhibits blocking solutions that resemble the evolution of the LM (Mitsudera and Grimshaw 1994). We consider a quasigeostrophic model with a channel filled with continuously stratified fluid situated on a β plane. Suppose that a stratified shear flow U = U(y, z) is interacting with a ridge h = h(x, y), where x, y, and z are the along-channel, cross-channel, and vertical coordinates, respectively. In a weakly nonlinear, long-wave limit, the amplitude of the pressure disturbance AN evolves according to a forced evolution equation of the Kortveg–de Vries (KdV) type as follows (see the appendix for derivation; also Warn and Brasnett 1983):
i1520-0485-36-11-2042-e1
where AN(x, t) is the amplitude of a quasigeostrophic pressure disturbance ψ, which has the form ψ = AN(x, t)ϕN(y, z) to the lowest order. Here, ϕN is the associated stationary normal-mode eigenfunction of the linearized quasigeostrophic equation in (A3), whose eigenvalue (i.e., linear phase speed) is zero. This implies that an Nth mode linear long wave is stationary with respect to topography, resulting in resonance. The parameters μ, λ, and r are the nonlinear coefficient, the dispersion coefficient, and frictional coefficient, respectively, whose forms are given in (A4); Δ is the linear phase speed and also represents “detuning” from the exact resonance in that the linear phase speed referring to topography is zero.
In deriving the forcing terms, we assume that the mean current at the bottom, U(y, 0), is the same order as the disturbance, ψ [see (A2)]. Thus we obtain two types of forcing in the right-hand side of (1). The first term, ∂FN/∂x is the forcing due to the background mean current U riding over a ridge: FN is a projection of h(x, y) onto the bottom structure of ϕN such that
i1520-0485-36-11-2042-e2
In more physical terms, F represents vorticity production by vortex stretching/shrinking when the background flow, U, passes over the topographic feature. This type of forcing may be found in previous studies (e.g., Warn and Brasnett 1983).
On the other hand, the second forcing term, G, on the right-hand side of (1) is a novel aspect of this study. This term represents interaction between the topographic feature h and the disturbed flow ψ such that
i1520-0485-36-11-2042-e3
where J is a Jacobian operator. This is obtained by assuming that U(y, 0) is small so that the amplitude of the disturbance is in the same order to the background flow at bottom. Since J(ψ, h) denotes the cross-isobath component of the disturbed flow, GN represents the production of cyclonic vorticity by stretching when the disturbed flow is downslope over topography. We will call G a feedback forcing here.
It is well known that the homogeneous form of (1) has a solitary wave solution of the form
i1520-0485-36-11-2042-e4
where Φ(t) denotes its position. Since the phase speed C is the time derivative of the position, we have
i1520-0485-36-11-2042-e5
We now consider a stationary solution where C = 0. The amplitude is then given by a = −3Δ/μ: With respect to the Kuroshio LM problem, a < 0 is considered as a meandering state because it describes a pressure depression accompanied by a cyclonic circulation. The position of the solitary wave, Φ, may be found from the “energy” equation of (1). That is, multiplying (1) by l sech2l(x − Φ) and integrating with respect to x, we obtain a stationary solution, where Φ is constant, from the following equation:
i1520-0485-36-11-2042-e6
To illustrate this solution, we examine a limit of narrow solitons (i.e., l → ∞) so that l sech2l(x − Φ) approaches to 2δ(x −Φ), where δ(x) is the Dirac’s delta function. Further, we consider only the forcing by the background flow, FN(x), for the illustrative purpose. Then, (6) reduces to
i1520-0485-36-11-2042-e7
The above relationship gives stationary positions Φ in terms of r. We present a solution diagram in Fig. 1 as an example, when FN has a single-peaked localized form. Since the frictional coefficient r is positive, the stationary solutions exist for
i1520-0485-36-11-2042-eq1
That is, the solution exists where adFN/dx is positive. For the single-peaked forcing, therefore, the stationary solutions exist upstream (downstream) of the forcing if aFN > 0 (aFN < 0). Therefore, the relationship between the sign of the solitary wave amplitude and the sign of the forcing is important to determine the position of the stationary disturbance. Note that from (6), characteristics of E as a function of Φ in Fig. 1 qualitatively hold even if solitary waves are broader.
To evaluate the sign of forcing in the case of the Kuroshio, we first consider the lowest barotropic mode disturbance with N = 0, generated by a forcing associated with a background flow:
i1520-0485-36-11-2042-eq2
Since we consider the barotropic mode, ϕ0 is positive for all z. This leads to F0 > 0 for a ridge where h > 0. That is, the upslope flow makes water columns shrink uniformly and produces anticyclonic vorticity (or positive pressure) tendency over the ridge. On the other hand, the amplitude a of the LM should be negative corresponding to depression in the pressure field associated with the cyclonic circulation. Therefore, we obtain aF0/∂x < 0 upstream for the barotropic response. This suggests that a cyclonic solitary disturbance should not be stationary upstream of the ridge according to Fig. 1. We may further say that anticyclonic vorticity is produced over the upstream slope of the ridge, which even damps the incident cyclonic disturbance there.

The above analysis implies that baroclinic processes are likely to be important in blocking of the LM. One case to consider is that the LM is a first-baroclinic-mode long wave with N = 1 in (1). In this case, F1 becomes negative because h > 0 and ϕ1 < 0 for the bottom as in (2), leading to ∂F1/∂x > 0 upstream. This suggests that the upstream blocking could occur if the LM had a first baroclinic mode structure. However, as we will see later in numerical results, the LM has a deep cyclonic circulation, showing the barotropic-mode-like structure. Hence the interaction between the first-baroclinic-mode disturbance and the ridge does not appear to be a plausible mechanism to explain the upstream LM blocking.

A prospective candidate is to have the feedback forcing (3) be negative upstream with respect to the barotropic mode (N = 0), that is, ∂G0/∂x < 0. This suggests aG0/∂x > 0 upstream for a low pressure disturbance, a < 0, so that the condition for the upstream blocking could be satisfied. This occurs when a downslope flow [J(ψ, h) < 0] at the bottom is somehow generated in (3) when the LM interacts with the ridge upstream; the downslope flow causes vortex stretching, generating positive vorticity tendency that is favorable for blocking. Here we would not pursue the theoretical argument further. Rather, we would point out that a realistic numerical model in the following sections exhibits such a downslope flow over the steep western slope when the Kuroshio impinges upon the Izu Ridge. Since the surface Kuroshio flow is upslope, the bottom downslope flow is likely to be produced as a result of a baroclinic response. The downslope flow is a part of topographic Rossby waves generated when the interaction occurs, whose scale is typically the width of the western slope of the Izu Ridge (section 4).

The consideration of the theoretical model suggests the following points to be discussed in the blocking of the LM.

  • Upstream blocking occurs when the conditions aFN/∂x > 0 and/or aG0/∂x > 0 are satisfied upstream of topography. In more physical terms, upstream blocking occurs when the sign of the amplitude of the disturbance and the sign of the vorticity production upstream of topography are the same.
  • The theoretical model suggests that the upstream blocking might not occur by a barotropic response to a ridge. Rather, the barotropic response is likely to damp the cyclonic LM upstream because anticyclonic vorticity is generated there.
  • Baroclinic interaction with the Izu Ridge, which can produce cyclonic vorticity upstream, should be involved in the blocking process. Bottom downslope flow J(ψ, h) < 0 upstream of the ridge, resulting from a baroclinic response, may play an important role in the LM’s blocking through the feedback forcing in (3).

3. Numerical results of large meander

a. Model configuration

The numerical model is based on a sigma-coordinate, primitive equation ocean model described by Blumberg and Mellor (1987). A curvilinear coordinate grid is used, with the resolution sometimes as high as 1/12° near the Japanese coast. Bottom topography is smoothed so that spurious flow due to pressure error by the sigma coordinate should not occur. The model topography and grids near the Japanese coast are displayed in Fig. 2. The surface boundary conditions include the wind stress of Hellerman and Rosenstein (1983), surface heat flux derived from the Comprehensive Ocean–Atmosphere Data Set (COADS) with weak relaxation to the climatological SST of Levitus (1982), and the climatological sea surface salinity. Further, temperature and salinity are relaxed to the climatology on the lateral boundaries. The Kuroshio and Oyashio are forced from the lateral boundaries by specifying their transport, which is estimated from a global high-resolution ocean model (Ishida et al. 1998). The Kuroshio–Oyashio model has been used extensively to study the Kuroshio path dynamics in Mitsudera et al. (2001) and Waseda et al. (2002, 2003, 2005), which successfully represents the short-term meander by eddy–Kuroshio interaction.

b. Large meander in the model

This numerical model is capable of reproducing the various Kuroshio pathways. For example, Fig. 3a displays a 1-yr average of the sea surface height (SSH) that exhibits the LM path, where the inflow at the western boundary is set to be 45 Sv (Sv ≡ 106 m3 s−1). The Kuroshio flows along Kyushu, separates from the coast off Shikoku and shows its southernmost position off the Kii Peninsula. Then the Kuroshio returns back to the coast upstream of the Izu Ridge, passes the northern flank of Hachijo Island, and finally outflows to the Kuroshio Extension region. According to Kawabe’s (1985) classification, this is the typical LM path, although the inflow transport (45 Sv) is probably greater than reality. Inshore of the LM exists a cyclonic recirculation at the surface as well as at the bottom. Further, there is an anticyclonic recirculation off Shikoku south of the Kuroshio, which will be referred to as the “Shikoku Recirculation Gyre” (SRG) here. These are also typical features of the LM. Note that, with a smaller inflow transport, the nonlarge meander paths were realized (Waseda et al. 2002, 2003, 2005).

Figure 3b shows the root-mean-square of SSH variations. The rms is large along the mean axis of the Kuroshio. It is particularly large around the southern tip of the meander, indicating that the amplitude of the LM varies greatly upstream of the Izu Ridge. Indeed, cyclonic eddies are often pinched off from the meander. There is also a relatively high rms in the SRG along 28°N. This is associated with propagation of eddies in the SRG, which interacts with the Kuroshio axis and causes strong variability in the Kuroshio’s path (see, e.g., Waseda et al. 2002, 2003).

c. East–west vacillation of the LM

Figure 4 displays SSHs every 15 days for the last 100 days of the year-4 run to show an example of the LM fluctuations. In Fig. 4a, the center of the LM is located at about 137°E. In Figs. 4b–d, the center of the LM moves upstream, while reducing its amplitude. Then, it reverses direction and starts moving eastward when a strong anticyclonic eddy in the SRG pushes the LM eastward (Figs. 4e–g). This eddy–Kuroshio interaction is similar to those discussed in Waseda et al. (2003). As the meander approaches the Izu Ridge, the high SSH is also extended eastward from the SRG. Because of this high SSH, the LM bends toward the Izu Ridge and hence the southern part of the LM encounters the ridge first. After this encounter, the LM’s eastward propagation is blocked; the LM is stretched in the onshore–offshore direction upstream of the ridge (Fig. 4h). More detailed description of this blocking process will be given in section 4.

Figure 5 shows a Hovmöller diagram of the SSH along the Japanese coast for the year-4 run of the 45-Sv case. The low SSH wobbling about 137°E represents vacillation of the center of the LM, whereas the high SSH about 134°E is associated with variations of the SRG. Several east–west vacillation events can be seen in the diagram; the LM moves to the easternmost location around 1150, 1200, 1290, and 1400 model days (indicated by arrows). Therefore, vacillations have a time scale from about 50 to 100 days in the model. The arrow at 1200 days is given based on the eastward movement of the contours larger than 0.7 m that indicate the Kuroshio’s axis (see Fig. 4a), although the core of the LM does not move greatly at that time. Clearly, fluctuations of the LM and the SRG are coupled. That is, the LM tends to move eastward when the SRG is strong. This LM eastward movement is blocked when it encounters the Izu Ridge as discussed above.

The vacillation of the large meander is a well-known observed feature. For example, Sekine et al. (1985) reported periodic thermocline depth variations at the center of the LM. The LM is strengthened when the thermocline becomes shallow. They argued that the periodical shoaling of the thermocline should be important to maintain the LM. Consistent with Sekine et al. (1985), the present model (Fig. 5) also exhibits periodical deepening of SSH (corresponding to the periodical shoaling of the thermocline) when the LM is located eastward.

d. Sequence of blocking

Here we discuss the blocking processes in more detail. Initially, the LM moves eastward before the blocking shown in Figs. 4 and 5. This eastward propagation is likely to be induced by the high SSH southward extending from the SRG (Figs. 4c–e). That is, a cyclonic circulation by the LM to the north and an anticyclonic circulation by the high SSH to the south form a vortex-pair structure, supporting the eastward propagation of each other by mutual advection. Therefore, the tip of the meander bends toward the east so that the Kuroshio path on the eastern side of the meander exhibits the “S” shape over the ridge. Furthermore, the SRG is elongated farther eastward.

Figure 6 displays a detailed sequence of the blocking event in the SSH field every 5 days. Figure 6a (corresponding to Fig. 4e) shows that the LM moves eastward and is about to ride over the Izu Ridge. The Kuroshio path encounters the ridge at around 31.5°N, 138.5°E where the Kuroshio path is broadened. Then, as in Figs. 6b and 6c, a high SSH packet is separated from the SRG, and starts moving northward along the western slope of the ridge. Associated with this, the Kuroshio path on the eastern side of the meander (i.e., the segment spanning 136°–139°E) rotates in a counterclockwise direction over the western slope and is finally pushed away from the Izu Ridge (Fig. 6d). As a result, eastward propagation of the LM is blocked. Further, the Kuroshio meander is amplified and stretched in the north–south direction. The time scale of this process is about 30 days in this simulation.

The high SSH packet has a scale representing the width of the slope of the Izu Ridge. The high SSH is separated from the eastern head of the SRG and turns to the north when it impinges upon the ridge. Apparently, the transient behavior of the Kuroshio path in the model is linked to the northward propagation of the high SSH packet along the slope.

e. Observations

The evolution of the Kuroshio path, which resembles the numerical results, has been observed in reality. In Fig. 7, we display an example of the evolution of the Kuroshio axis during a LM period (redrawn from Shoji 1972). In early April 1960 the Kuroshio axis rode over the Izu Ridge at about 139°E, showing the S-shaped structure on the eastern side of the meander. From 18 to 24 April the current axis is located around Hachijo Island, over the ridge away from the Japanese coast. Then, the axis started moving northward and finally reached the Japanese coast within three weeks. At the same time, the current axis on the western slope of the ridge between 137° and 139°E rotated counterclockwise. Consequently, the LM was pushed westward, and its eastward propagation was blocked. The time scale of this process is about one month.

Comparing Figs. 6 and 7, we found that the evolution of the Kuroshio path in the model corresponds well with the observed transient behavior of the Kuroshio over the Izu Ridge. In particular, the northward movement of the axis along the western slope of the ridge, as well as its simultaneous counterclockwise rotation centering around 32°N, 138°E, are common in both the observation and the simulation. Further, the time scale of this process is about one month in both model and observation, also in good agreement with each other.

Another interesting feature observed in the numerical results is the high SSH packet separating from the SRG. This process appears also to be involved in blocking in reality. For example, Fig. 8 displays a horizontal distribution of temperature at 400-m depth measured by XBTs (see, e.g., Ohtsuka 1978). The measurement was conducted in 1976, about one year after formation of the LM. In this observation, the LM exhibited a typical feature, with its eastern part riding over the ridge. Further, the 15° isotherm in Fig. 8 is likely to extend eastward from the SRG to the Izu Ridge, showing an elongated structure. This elongated SRG is similar to the SSH structure shown in the numerical results (e.g., Fig. 4e). Subsequently, the Kuroshio axis was pushed westward in a similar manner to that in Fig. 7.

These observations suggest that the model captures characteristics of the LM’s behavior associated with blocking in a realistic manner. This motivates us to analyze the numerical model results further to identify blocking mechanisms.

4. Discussion

a. Torque balance

In this section, we will discuss the effects of baroclinicity in light of torque balance. The torque equation that governs evolution of the depth-integrated transport function, Ψ, may be written as follows (e.g., Ezer and Mellor 1994; Kagimoto and Yamagata 1997):
i1520-0485-36-11-2042-e8
where pb denotes pressure at the bottom, Γxy) denotes the x (y) component of advection and diffusion terms, and ρ0 denotes a typical density; H is the depth of the ocean. Note that the sign of −∇H is the same as the sign of ∇h of the weakly nonlinear model. The first term on the left-hand side represents local torque tendency, and the second term is advection and diffusion of depth-integrated relative vorticity. The third term is the advection of planetary vorticity, and the fourth term is bottom pressure torque (BPT).
We focus our attention on the effects of the BPT term, J(pb, −H)/ρ0, in (8) as it involves the production of barotropic torque due to interaction between baroclinic disturbances and a sloping bottom. To see this explicitly, we may decompose the BPT term in (8) into two parts as follows (see Mertz and Wright 1992):
i1520-0485-36-11-2042-e9
where p is the depth-averaged pressure, while
i1520-0485-36-11-2042-eq3
represents the bottom pressure due to baroclinic flow structure, ρ0χ = H(ppb). Therefore, the first term on the rhs of (9) is the torque production due to the depth-averaged pressure associated with “barotropic” flow, while the second term is the one with the baroclinic flow. The latter is often called the joint effect of baroclinicity and relief (JEBAR; see, e.g., Mertz and Wright 1992).

The barotropic term J(p, − H)/ρ0 is positive when a depth-averaged geostrophic flow is upslope. The term produces anticyclonic torque tendency; that is, − J(p, −H)/ρ0 < 0, representing that the water column shrinks uniformly over there. In order for the BPT term to be negative, therefore, the JEBAR term −HJ(χ, H−1) should be negative and overcome the barotropic term.

Figure 9a shows the BPT of the 1410 days in the simulation superimposed upon the SSH (white contours) and topography (red contour lines). The SSH corresponds to that in Fig. 6c, when the Kuroshio path is pushed westward away from the ridge, with rotating counterclockwise centering at about 32°N, 138°E over the western slope. As expected, Fig. 9a shows a negative BPT below the Kuroshio path (arrowed in Fig. 9a), which produces cyclonic torque tendency there. This further indicates that the baroclinic term, or the JEBAR, should be important in the BPT term during the blocking process of the Kuroshio large meander.

Figure 9b is a torque balance along the axis of the Kuroshio at the same time as in Fig. 9a. The Shikoku Basin (see the label in Fig. 9) is flat in this model so that the balance there is achieved between the torque tendency term and the Coriolis term. Here, the tendency term combines the local tendency and the advection terms, so it is considered as the total derivative of the torque evolution. Once the Kuroshio rides over the ridge, however, the BPT term becomes an important term. The magnitude of the BPT term is equivalent to those of other terms. Furthermore, the tendency term is inversely correlated with the BPT term, indicating that BPT is a dominant mechanism in changing the torque over the ridge. A strong negative BPT is found around 138.5°E, corresponding to the location arrow in Fig. 9a. The torque tendency is positive there, implying that the evolution of the Kuroshio path over the Izu Ridge, including its counterclockwise rotation, is caused by the negative BPT associated with the large JEBAR term.

Figure 10 displays a time series of the terms in the depth-integrated torque, Eq. (8), at the location centering at 32°N, 138.5°E over the western flank of the Izu Ridge. This figure also exhibits the negative correlation between the tendency term and the BPT term. The time scale of the torque changes is about 10–100 days. On the other hand, the Coriolis term is always positive because the Kuroshio always flows northward at this location, whose variations are not necessarily well correlated with the other two terms. Therefore, the cyclonic torque tendency is commonly generated when the BPT becomes negative over the western slope of the Izu Ridge.

Comparing Fig. 10 with Fig. 5, we further see that the negative peaks of the BPT at about 1150, 1200, 1290, and 1400 days are associated with the eastward movement and strengthening of the LM. This indicates that the negative BPT, produced when the LM encounters the ridge, is also a common feature in this model.

b. Interaction between baroclinic current structure and bottom topography

To see the effects of baroclinicity on the negative BPT, we may write a vorticity equation in terms of the depth-averaged relative vorticity (Mertz and Wright 1992). Taking vorticity of the momentum equations to eliminate pressure terms and then averaging it vertically, we obtain
i1520-0485-36-11-2042-e10
where the overbar denotes the depth average. Furthermore, v is the current vector, vb is the current at bottom, and ζ is the relative vorticity.
Equation (10) indicates that the depth-averaged relative vorticity is generated as a result of the bottom current across bathymetric contours; the cyclonic relative vorticity is produced by a downslope flow on the western side of the ridge, that is,
i1520-0485-36-11-2042-eq4
in (10). Figure 11 displays the bottom current field on the western slope superimposed upon the SSH and the bottom topography. As expected, there is a downslope flow toward the southwest at the bottom centering at 32°N, 138.5°E, where the cyclonic torque production is strongest. This bottom flow is in the opposite direction to the surface flow that is upslope. That is, baroclinicity is dominant in the flow structure where the negative BPT forms.

Now we discuss the correspondence between the simple weakly nonlinear model (1) and the torque balance in the numerical results. From the depth-integrated torque equation in (8), we may consider that JEBAR is a forcing term acting as a feedback from the baroclinic flow to the barotropic streamfunction, Ψ. If JEBAR in BPT (9) is dominant or BPT is negative, the cyclonic vorticity tends to be generated over the western slope owing to the downslope flow vb < 0 generated there. On the other hand, as we discussed in section 2, the feedback forcing (3) in the theoretical model yields ∂G0/∂x < 0 upstream of the forcing if a downslope flow J(ψ, h) < 0 is present. Therefore, the negative BPT in the numerical model corresponds to ∂G0/∂x < 0 in the theoretical model. This further implies that the negative BPT, acting on a negative pressure disturbance like the LM, corresponds to the positive feedback forcing aG0/∂x < 0 upstream of the ridge. This is consistent with the blocking condition in the weakly nonlinear theory of (1) according to Fig. 1. Of course, we are aware that the area of negative BPT in the model is rather localized, so the simple theory is not applicable directly. Nevertheless, the downslope flow under the current axis due to baroclinicity is likely a common condition for blocking to occur in both the theoretical model and the realistic numerical model. Therefore, we think that the theoretical consideration made here is useful to understand the LM dynamics.

c. Origin of baroclinic disturbances

How does this slope-scale baroclinic disturbance appear? Figure 12 displays an example of the evolution of the BPT every five days after the southern part of the LM encounters the ridge, where Fig. 12f corresponds to Fig. 9a in terms of the model day. In Fig. 12a, when the LM rides over the Izu Ridge, a negative BPT (indicated by an arrow) appears over the slope. The negative BPT is located around 30.5°N initially. It then starts propagating northward with the speed of about 10 cm s−1. Associated with this propagation, the Kuroshio axis rotates in the counterclockwise direction. Note that the negative BPT propagates where the ocean is deeper than 1500 m. Therefore, the interaction occurs between the deep current and the deep western slope rather than between the surface jet and a vertical wall.

To further understand mechanisms of generating the negative BPT, we display the anomaly of the SSH and that of the bottom current in Figs. 13a–d, taken at the same time as in Figs. 12b–e, respectively. In Fig. 13a, there is a positive SSH anomaly (SSHA) around 30.0°N, 138.5°E, which is typically scaled with the width of the slope. This positive SSHA corresponds to the eastward extension of the SRG.

Initially, the SSHA accompanies an anticyclonic current anomaly at the bottom. With a closer look, however, there is a downslope flow generated at the eastern side of the SSHA around 30.0°N, 139.0°E (Fig. 13a). This downslope flow coincides with the negative BPT indicated by the arrow in Fig. 12b.

We can also see clear correspondence between the negative BPT (Figs. 12c–e) and the downslope flow (Figs. 13b–d) thereafter, consistent with the discussion in the previous section. A cyclonic bottom circulation (or shear) therefore develops over the western slope owing to the negative BPT. At the same time, the positive SSHA moves onto the slope. Consequently, in Figs. 13c and 13d, the cyclonic bottom circulation almost coincides with the location of the SSHA maximum. Since the positive SSHA causes anticyclonic circulation at the surface while the bottom circulation is cyclonic, the velocity field exhibits a baroclinic structure. The SSHA moves northward, indicative of a baroclinic topographic Rossby wave. In other words, the SSHA is a surface expression of the topographic Rossby wave whose scale is typically the width of the slope of the ridge.

Last, the bottom downslope flow is seen to occur at the northern part of the SSHA where the Kuroshio axis is located (e.g., Fig. 13d). Therefore, we can conclude that the negative BPT is produced under the Kuroshio by the downslope flow that is a part of the baroclinic topographic wave.

In summary, the present model results show that the northward propagation of the baroclinic topographic Rossby wave forces the Kuroshio axis to move northward over the Izu Ridge. Furthermore, the bottom downslope flow associated with this topographic wave produces the cyclonic BPT over the western slope. These result in blocking of the LM, or prevent the LM from propagation farther eastward across the ridge. Since the observed Kuroshio behavior (Fig. 7) and the model Kuroshio behavior (Fig. 6) closely resemble each other, we conclude that the baroclinic interaction between the LM and the Izu Ridge, discussed here, is probably an important process in reality.

5. Summary and conclusions

Many modeling studies of the Kuroshio meander so far have assumed the Izu Ridge to be an island with a wall. In those studies, the strait between the island and the Japanese coast is considered as a gate that the Kuroshio has to flow through. There has been progress in understanding of the Kuroshio dynamics, such as its multiple paths, by utilizing this simple model configuration. Nevertheless, detailed effects of the Izu Ridge on the Kuroshio dynamics are yet to be investigated. In reality, the Izu Ridge is a submarine ridge with sloping bathymetry rather than a vertical wall. For the first step to understand interaction of the Kuroshio with the ridge, we have investigated blocking of the eastward propagation of the large meander. We are particularly interested in the interaction between the deep cyclonic circulation associated with the LM and the bottom slope of the ridge.

We first revisited a weakly nonlinear problem of a stratified flow over topography to illustrate issues to be resolved. This analysis suggested that blocking of the LM should involve some baroclinic processes during interaction between the ridge and the LM. Otherwise, the cyclonic circulation associated with the LM should be damped over the western side of the ridge.

A major concern of this paper is to identify baroclinic processes that are responsible for blocking. For this purpose, we analyzed a high-resolution model output that represents the Kuroshio path in a realistic manner. The LM in terms of Kawabe’s (1985) category is realized in this model in which the entire meander exists upstream of the Izu Ridge. Further, it has been found that the model successfully reproduces detailed Kuroshio path evolution over the Izu Ridge associated with the blocking of the LM (e.g., compare numerical results, Fig. 6, with an observation, Fig. 7).

This realistic simulation motivates us to analyze the model output in more detail. We examined the torque balance and found that negative bottom pressure torque associated with baroclinic flow over the submarine ridge (or JEBAR) is important for blocking. When the LM propagates eastward and impinges upon the Izu Ridge, the bottom pressure torque becomes negative under the Kuroshio axis and causes cyclonic torque tendency there. Corresponding to the simple weakly nonlinear model, JEBAR tends to act like a feedback forcing in (1) with aG0/∂x < 0 upstream, consistent with the upstream blocking of a solitary wave (see Fig. 1).

The negative bottom pressure torque is produced essentially by the downslope flow near the bottom under the Kuroshio axis. Since the Kuroshio is upslope there, the flow near the bottom is opposed to the surface flow. This structure is associated with a baroclinic topographic Rossby wave generated when the large meander impinges upon the Izu Ridge. Correspondingly, the portion of the negative bottom pressure torque propagates northward as topographic Rossby waves, preventing the LM from propagating farther eastward.

Occasional intensification of the LM has been observed in reality, as well as in the model. Sekine et al. (1985) showed that the cold water mass inside the LM is spinning up and down periodically when a LM is maintained for a long time. They argued that such an intensification process is necessary for a long-lived LM to survive from damping due to bottom friction. This study has shown that the cyclonic torque generation upon the LM’s encounter with the Izu Ridge is one of the mechanisms for such intensification. Another mechanism of the LM intensification is the interaction with anticyclonic eddies in the Shikoku Recirculation Gyre. This mechanism is discussed in detail in Waseda et al. (2003). Apparently, these two mechanisms are related to each other as seen in Figs. 4 and 5; the LM moves eastward and is blocked by the ridge when the eddies in the SRG becomes strong.

Clearly, more work is needed to understand the role of Izu Ridge in the Kuroshio path dynamics. One of outstanding questions is the transition process from the LM to the nonlarge meander, in which the Izu Ridge should play a major role (see, e.g., the argument of Masuda and Akitomo 2000). The present study shed lights on the importance of baroclinic topographic Rossby waves along the Izu Ridge during the interaction between the large meander and the ridge, particularly for blocking. It is not yet clear, however, in what condition the eastward propagation of the meander is prohibited, or if it is allowed to overcome the ridge. This awaits further study.

Acknowledgments

We thank Dr. Akio Ishida of JAMSTEC for discussions that initiated this study, and Ms. Di Henderson for editorial review. Author HM was supported by FRSGC when he was affiliated with IPRC, and completed this work after moving to the ILTS of the Hokkaido University. Author TW was also supported by the FRSGC program, through its sponsorship of the IPRC, before moving to the University of Tokyo. We deeply appreciate stimulative discussions with our IPRC colleagues.

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APPENDIX

Derivation of the Evolution Equation of the KdV Type

We consider a channel model of width L and depth H with a rigid lid, which is filled with continuously stratified fluid, situated in a β plane. A ridge, whose shape is defined as h = h(x, y), exists around x = 0, where x and y denote alongshore and offshore directions, respectively: U = U(y, z) is supposed to be a basic current, where z denotes the vertical coordinate.

Here a long wave is to be examined, where its alongshore scale is ϵ−1L. We also assume that the amplitude of the disturbance is scaled with α ≪ 1 relative to the background flow, so the total streamfunction ψ̃ may be written as
i1520-0485-36-11-2042-eqa1
where ψ is a streamfunction associated with the disturbance. After scaling variables, the quasigeostrophic equation for the interior flow may be written in the following nondimensional form:
i1520-0485-36-11-2042-eqa2
and
i1520-0485-36-11-2042-ea1
where S is the stratification parameter of the form S1/2 = NH/fL, with the Coriolis parameter f and Brunt–Väisälä frequency N.
For boundary conditions we assume that the topographic feature scales with α. We also suppose that the basic flow near the bottom is small [i.e., U(y, 0) → O(α)]. We will see that with this scaling the feedback forcing term and the topographic forcing term are of the same order. The boundary conditions therefore become
i1520-0485-36-11-2042-ea2
The first term on the rhs of the boundary condition (A2) represents forcing by the background flow over topography, while the second term on the rhs is the feedback forcing term representing vorticity production by the disturbance interacting with the topography.

The third term denotes bottom friction associated with Ekman pumping, which acts to dissipate disturbances.

To lowest order, (A1) gives a linear eigenvalue problem. The streamfunction may be separated such that
i1520-0485-36-11-2042-eqa3
where ϕn(y, z) is an eigenfunction satisfying
i1520-0485-36-11-2042-ea3
where cn is the corresponding eigenvalue. In a physical term cn represents the phase speed of the nth mode Rossby wave relative to topography.
We consider a case in which the phase speed of the Nth mode wave relative to topography is close to zero, that is, cN = αΔ, where Δ may be thought as detuning from the exact resonance. In this case, resonance occurs as a result of topographic forcing and the amplitude of the stationary disturbances grows with time. As the disturbances grow, nonlinearity comes into balance. Hence, t may be rescaled to represent the nonlinear evolution such that
i1520-0485-36-11-2042-eqa4
Further, we adopt the following scalings to derive an evolution equation of the KdV type:
i1520-0485-36-11-2042-eqa5
The former represents a balance between the nonlinear and dispersion terms, while the latter assumes a weak frictional term that is in the same order to the other terms. Note that the forcing terms are of the same order to these terms as we can see from (A2). Since the Nth mode wave is in resonance, its amplitude becomes much larger than the other wave modes. Therefore, ψ may be expanded as
i1520-0485-36-11-2042-eqa6
where ϕN(y, z) denotes the eigenfunction with cN = 0 in (A3). With these scalings, the time derivative term, the nonlinear term, dispersive term the topographic forcing terms, and the dissipative term are in the same order. Multiplying ψn by (A3) and ϕn by (A1), then subtracting and integrating in y and z, we obtain a solvability condition, which yields an evolution equation of the KdV type [equivalent to (1)]:
i1520-0485-36-11-2042-eqa7
Here
i1520-0485-36-11-2042-ea4
where Πy is given as
i1520-0485-36-11-2042-eqa8
and δ(z) is the Dirac delta. Here, note that ϕN is normalized as
i1520-0485-36-11-2042-eqa9
For the problem to be posed, we assume that U and Πy in I are the single-signed functions in the whole domain. This assumption is equivalent to the fact that the linear wave is stable. Under this condition, we may assume Πy > 0 without any restriction. Note that the forcing terms FN and GN are given as (2) and (3) in the text.

Fig. 1.
Fig. 1.

Schematic diagram to show the position of the stationary solutions for a single-peaked forcing; the curves represent the E(Φ) = (3/2a)dFN/dΦ of (7), where the solid portions of the curves indicate stable solutions, while the dashed portions indicate unstable solutions. For the single-peaked case, there are two cases according to the sign of the aFN. The dotted–dashed line indicates r. The stationary solutions are achieved where these two lines intersect with each other [i.e., E(Φ) = r] as indicated by the bullets. The phase relationship of the stationary solutions with respect to the forcing is schematically illustrated for both aFN > 0 and aFN < 0 cases.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 2.
Fig. 2.

Bottom topography and model grids near the south coast of Japan: contour interval for topography is 1000 m.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 3.
Fig. 3.

(a) The LM path obtained in the model. The figure displays the SSH averaging for one year (year 4) in the model. Vectors exhibit velocity field at bottom; contour interval for SSH is 0.1 m and for topography 500 m. (b) The rms of the SSH variance; contour interval is 0.05 m.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 4.
Fig. 4.

Sequence of the SSH evolution off the coast of Japan: (a)–(h) Evolution every 15 days starting on model day 1335. Light gray shading denotes SSH higher than 1.4 m, while dark gray denotes SSH lower than 0.5 m; contour interval is 0.1 m.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 5.
Fig. 5.

Hovmöller diagram of the SSH in terms of the longitude and the model day. The SSH is averaged over the latitude between the Japanese coast and the line connecting 27°N, 131°E and 32°N, 141°E. Light gray shading denotes SSH higher than 1.1 m, while dark gray denotes SSH lower than 0.8 m; contour interval is 0.1 m. Arrows show that the LM is displaced to the easternmost position in each vacillation event.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 6.
Fig. 6.

Sequence of the SSH evolution adjacent to the Izu Ridge: (a)–(f) evolution every 5 days starting on model day 1395.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 7.
Fig. 7.

An observed sequence of the Kuroshio path behavior in 1960 (dark solid line → light solid line → dark dashed line → light dashed line; redrawn after Shoji 1972). The Kuroshio rode over the Izu Ridge in early April (dark solid line). In mid-April (light solid line), the Kuroshio axis was located around Hachijo Island. However, it moved northward after that and reached the Japanese coast in three weeks as indicated by a broad arrow. Simultaneously, it was pushed westward away from the ridge, showing the counterclockwise rotation of the axis centering around 32°N, 138°E as indicated by a broad broken arrow.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 8.
Fig. 8.

Temperature field at 400-m depth in October 1976 when the Kuroshio displayed the LM path. After Ohtsuka (1978).

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 9.
Fig. 9.

(a) Bottom pressure torque (color) on model day 1405 superimposed upon the SSH (white contour) and the bottom topography (red contour). Cyclonic torque tendency is produced where the bottom pressure torque is negative; the negative bottom pressure torque that is involved with blocking is indicated by an arrow. (b) Torque balance in (8) along the Kuroshio axis on the same model day: The solid line denotes the bottom pressure torque term, the dashed line the Coriolis term, and dotted line the tendency term (total derivative). The dashed–dotted line denotes the sum of all terms. The shaded area indicates the western slope of the Izu Ridge. The negative peak of the bottom pressure torque around 138.5°E (indicated by an arrow) corresponds to the location where the negative BPT is present in (a).

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 10.
Fig. 10.

Time series of the torque balance in (8): solid line denotes the bottom pressure torque, dashed line the Coriolis term, and dotted line the tendency term (total derivative). The negative peaks of the bottom pressure torque are indicated by the arrows, corresponding to the times arrowed in Fig. 5, when the LM is displaced to the easternmost position in each vacillation event.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 11.
Fig. 11.

Bottom velocity field (vector) over the western slope of the Izu Ridge superimposed upon the SSH (shade) and bottom topography (contour) in the Kuroshio axis: contour interval for SSH is 0.1 m and for topography 500 m. The SSH indicates that the surface current flows northeastward.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 12.
Fig. 12.

Evolution of the bottom pressure torque (shade) superimposed upon the streamfunction (contour) and bottom topography (light contour): dark shade indicates negative BPT less than −1 × 10−8 m2 s−2. (a)–(f) The evolution every 5 days starting on model day 1380. Arrows indicate evolution of the negative BPT that interacts with the evolution of the Kuroshio axis; contour interval is 10 × 106 m3 s−1 for the transport function and 500 m for topography.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

Fig. 13.
Fig. 13.

Bottom velocity anomaly (vector) on model day (a) 1385, (b) 1390, (c) 1395, and (d) 1400 superimposed upon the SSH anomaly (shade) and bottom topography (contour): contour interval is 0.1 m for the SSH anomaly and 500 m for topography.

Citation: Journal of Physical Oceanography 36, 11; 10.1175/JPO2945.1

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