• Adcock, S. T., and D. P. Marshall, 2000: Interactions between geostrophic eddies and the mean circulation over large-scale bottom topography. J. Phys. Oceanogr., 30, 32233238, https://doi.org/10.1175/1520-0485(2000)030<3223:IBGEAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bleck, R., 2002: An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Modell., 4, 5588, https://doi.org/10.1016/S1463-5003(01)00012-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bozec, A., 2013: HYCOM for dummies: How to create a double gyre configuration with HYCOM from scratch? Florida State University Center for Ocean-Atmospheric Prediction Studies Rep., 20 pp., http://hycom.org/attachments/349_BB86_for_dummies.pdf.

  • Bretherton, F. P., and D. B. Haidvogel, 1976: Two-dimensional turbulence above topography. J. Fluid Mech., 78, 129154, https://doi.org/10.1017/S002211207600236X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chelton, D. B., M. G. Schlax, and R. M. Samelson, 2011: Global observations of nonlinear mesoscale eddies. Prog. Oceanogr., 91, 167216, https://doi.org/10.1016/j.pocean.2011.01.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dewar, W. K., 1991: Arrested fronts. J. Mar. Res., 49, 2152, https://doi.org/10.1357/002224091784968576.

  • Dewar, W. K., 1992: Spontaneous shocks. J. Phys. Oceanogr., 22, 505522, https://doi.org/10.1175/1520-0485(1992)022<0505:Ss>2.0.Co;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frankignoul, C., N. Sennéchael, Y.-O. Kwon, and M. A. Alexander, 2011: Influence of the meridional shifts of the Kuroshio and the Oyashio Extensions on the atmospheric circulation. J. Climate, 24, 762777, https://doi.org/10.1175/2010JCLI3731.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Furue, R., J. P. McCreary Jr., Z. Yu, and D. Wang, 2007: Dynamics of the southern Tsuchiya jet. J. Phys. Oceanogr., 37, 531553, https://doi.org/10.1175/jpo3024.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Furue, R., J. P. McCreary Jr., and D. Wang, 2009: Dynamics of the northern Tsuchiya jet. J. Phys. Oceanogr., 39, 20242051, https://doi.org/10.1175/2009jpo4065.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Greatbatch, R. J., and G. Li, 2000: Alongslope mean flow and an associated upslope bolus flux of tracer in a parameterization of mesoscale turbulence. Deep-Sea Res. I, 47, 709735, https://doi.org/10.1016/S0967-0637(99)00078-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., J. C. McWilliams, and P. R. Gent, 1992: Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J. Phys. Oceanogr., 22, 882902, https://doi.org/10.1175/1520-0485(1992)022<0882:BCSIAQ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holland, W. R., and P. B. Rhines, 1980: An example of eddy-induced ocean circulation. J. Phys. Oceanogr., 10, 10101031, https://doi.org/10.1175/1520-0485(1980)010<1010:AEOEIO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Holloway, G., 1978: A spectral theory of nonlinear barotropic motion above irregular topography. J. Phys. Oceanogr., 8, 414427, https://doi.org/10.1175/1520-0485(1978)008<0414:ASTONB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hurlburt, H. E., A. J. Wallcraft, W. J. Schmitz, P. J. Hogan, and E. J. Metzger, 1996: Dynamics of the Kuroshio/Oyashio Current System using eddy-resolving models of the North Pacific Ocean. J. Geophys. Res., 101, 941976, https://doi.org/10.1029/95JC01674.

    • Search Google Scholar
    • Export Citation
  • Isoguchi, O., H. Kawamura, and E. Oka, 2006: Quasi-stationary jets transporting surface warm waters across the transition zone between the subtropical and the subarctic gyres in the North Pacific. J. Geophys. Res., 111, C10003, https://doi.org/10.1029/2005JC003402.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Itoh, S., and I. Yasuda, 2010: Characteristics of mesoscale eddies in the Kuroshio–Oyashio Extension region detected from the distribution of the sea surface height anomaly. J. Phys. Oceanogr., 40, 10181034, https://doi.org/10.1175/2009JPO4265.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iwao, T., M. Endoh, N. Shikama, and T. Nakano, 2003: Intermediate circulation in the northwestern North Pacific derived from subsurface floats. J. Oceanogr., 59, 893904, https://doi.org/10.1023/B:JOCE.0000009579.86413.eb.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437471, https://doi.org/10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kida, S., and Coauthors, 2015: Oceanic fronts and jets around Japan: A review. J. Oceanogr., 71, 469497, https://doi.org/10.1007/s10872-015-0283-7.

    • Search Google Scholar
    • Export Citation
  • Kuroda, H., T. Wagawa, Y. Shimizu, S.-I. Ito, S. Kakehi, T. Okunishi, S. Ohno, and A. Kusaka, 2015: Interdecadal decrease of the Oyashio transport on the continental slope off the southeastern coast of Hokkaido, Japan. J. Geophys. Res. Oceans, 120, 25042522, https://doi.org/10.1002/2014JC010402.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, Z., 1997: The influence of stratification on the inertial recirculation. J. Phys. Oceanogr., 27, 926940, https://doi.org/10.1175/1520-0485(1997)027<0926:TIOSOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., M. N. Koshlyakov, Y. A. Ivanov, M. I. Yaremchuk, and G. G. Panteleev, 2001: Hydrophysical experiment “Megapolygon-87” in the northwestern Pacific subarctic frontal zone. J. Geophys. Res., 106, 1414314163, https://doi.org/10.1029/2000JC000436.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McCreary, J. P., Jr., P. Lu, and Z. Yu, 2002: Dynamics of the Pacific Subsurface Countercurrents. J. Phys. Oceanogr., 32, 23792404, https://doi.org/10.1175/1520-0485(2002)032<2379:DOTPSC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Milliff, R. F., J. Morzel, D. B. Chelton, and M. H. Freilich, 2004: Wind stress curl and wind stress divergence biases from rain effects on QSCAT surface wind retrievals. J. Atmos. Oceanic Technol., 21, 12161231, https://doi.org/10.1175/1520-0426(2004)021<1216:WSCAWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mitsudera, H., K. Uchimoto, and T. Nakamura, 2011: Rotating stratified barotropic flow over topography: Mechanisms of the cold belt formation off the Soya Warm Current along the northeastern coast of Hokkaido. J. Phys. Oceanogr., 41, 21202136, https://doi.org/10.1175/2011JPO4598.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mitsudera, H., and Coauthors, 2018: Low ocean-floor rises regulate subpolar sea surface temperature by forming baroclinic jets. Nat. Commun., 9, 1190, https://doi.org/10.1038/s41467-018-03526-z.

    • Crossref
    • Export Citation
  • Miyazawa, Y., and Coauthors, 2009: Water mass variability in the western North Pacific detected in a 15-year eddy resolving ocean reanalysis. J. Oceanogr., 65, 737756, https://doi.org/10.1007/s10872-009-0063-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nakano, H., and H. Hasumi, 2005: A series of zonal jets embedded in the broad zonal flows in the Pacific obtained in eddy-permitting ocean general circulation models. J. Phys. Oceanogr., 35, 474488, https://doi.org/10.1175/JPO2698.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nakano, H., H. Tsujino, and R. Furue, 2008: The Kuroshio Current System as a jet and twin “relative” recirculation gyres embedded in the Sverdrup circulation. Dyn. Atmos. Oceans, 45, 135164, https://doi.org/10.1016/j.dynatmoce.2007.09.002.

    • Search Google Scholar
    • Export Citation
  • Niiler, P. P., N. A. Maximenko, G. G. Panteleev, T. Yamagata, and D. B. Olson, 2003: Near-surface dynamical structure of the Kuroshio Extension. J. Geophys. Res., 108, 3193, https://doi.org/10.1029/2002JC001461.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nishigaki, H., and H. Mitsudera, 2012: Subtropical western boundary currents over slopes detaching from coasts with inshore pool regions: An indication to the Kuroshio nearshore path. J. Phys. Oceanogr., 42, 306320, https://doi.org/10.1175/JPO-D-11-076.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nonaka, M., H. Nakamura , Y. Tanimoto, T. Kagimoto, and H. Sasaki, 2006: Decadal variability in the Kuroshio–Oyashio Extension simulated in an eddy-resolving OGCM. J. Climate, 19, 19701989, https://doi.org/10.1175/JCLI3793.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1996: Ocean Circulation Theory. Springer, 456 pp.

    • Crossref
    • Export Citation
  • Qiu, B., 2002: Large-scale variability in the midlatitude subtropical and subpolar North Pacific Ocean: Observations and causes. J. Phys. Oceanogr., 32, 353375, https://doi.org/10.1175/1520-0485(2002)032<0353:LSVITM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rhines, P., 1970: Edge‐, bottom‐, and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn., 1, 273302, https://doi.org/10.1080/03091927009365776.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rhines, P., 1977: The dynamics of unsteady currents. Marine Modeling, E. D. Goldberg et al., Eds., The Sea—Ideas and Observations on Progress in the Study of the Seas, Vol. 6, John Wiley and Sons, 189–318.

  • Richards, K. J., N. A. Maximenko, F. O. Bryan, and H. Sasaki, 2006: Zonal jets in the Pacific Ocean. Geophys. Res. Lett., 33, L03605, https://doi.org/10.1029/2005GL024645.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneider, N., A. J. Miller, and D. W. Pierce, 2002: Anatomy of North Pacific decadal variability. J. Climate, 15, 586605, https://doi.org/10.1175/1520-0442(2002)015<0586:AONPDV>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smirnov, D., M. Newman, M. A. Alexander, Y.-O. Kwon, and C. Frankignoul, 2015: Investigating the local atmospheric response to a realistic shift in the Oyashio Sea surface temperature front. J. Climate, 28, 11261147, https://doi.org/10.1175/JCLI-D-14-00285.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sue, Y., and A. Kubokawa, 2015: Latitude of eastward jet prematurely separated from the western boundary in a two-layer quasigeostrophic model. J. Phys. Oceanogr., 45, 737754, https://doi.org/10.1175/JPO-D-13-058.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sugimoto, S., N. Kobayashi, and K. Hanawa, 2014: Quasi-decadal variation in intensity of the western part of the winter subarctic SST front in the western North Pacific: The influence of Kuroshio Extension path state. J. Phys. Oceanogr., 44, 27532762, https://doi.org/10.1175/JPO-D-13-0265.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Suginohara, N., 1981: Quasi-geostrophic waves in a stratified ocean with bottom topography. J. Phys. Oceanogr., 11, 107115, https://doi.org/10.1175/1520-0485(1981)011<0107:QGWIAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, S., L. Wu, and B. Qiu, 2013: Response of the inertial recirculation to intensified stratification in a two-layer quasigeostrophic ocean circulation model. J. Phys. Oceanogr., 43, 12541269, https://doi.org/10.1175/JPO-D-12-0111.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Taguchi, B., H. Nakamura, M. Nonaka, N. Komori, A. Kuwano-Yoshida, K. Takaya, and A. Goto, 2012: Seasonal evolutions of atmospheric response to decadal SST anomalies in the North Pacific subarctic frontal zone: Observations and a coupled model simulation. J. Climate, 25, 111139, https://doi.org/10.1175/JCLI-D-11-00046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tailleux, R., and J. C. McWilliams, 2001: The effect of bottom pressure decoupling on the speed of extratropical, baroclinic Rossby waves. J. Phys. Oceanogr., 31, 14611476, https://doi.org/10.1175/1520-0485(2001)031<1461:TEOBPD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Treguier, A. M., 1989: Topographically generated steady currents in barotropic turbulence. Geophys. Astrophys. Fluid Dyn., 47, 4368, https://doi.org/10.1080/03091928908221816.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wagawa, T., S.-I. Ito, Y. Shimizu, S. Kakehi, and D. Ambe, 2014: Currents associated with the quasi-stationary jet separated from the Kuroshio Extension. J. Phys. Oceanogr., 44, 16361653, https://doi.org/10.1175/JPO-D-12-0192.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., M. A. Spall, G. R. Flierl, and P. Malanotte-Rizzoli, 2012: A new mechanism for the generation of quasi-zonal jets in the ocean. Geophys. Res. Lett., 39, L10601, https://doi.org/10.1029/2012GL051861.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waterman, S., and S. R. Jayne, 2011: Eddy-mean flow interactions in the along-stream development of a western boundary current jet: An idealized model study. J. Phys. Oceanogr., 41, 682707, https://doi.org/10.1175/2010JPO4477.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery
    Fig. 1.

    Long-term (1993–2012) mean velocity at a depth of 10 m from the FRA–JCOPE2 ocean reanalysis (vectors; m s−1) and the bottom depth (color shading; m). Strong velocity vectors exceeding 0.1 m s−1 are shown in red.

  • View in gallery
    Fig. 2.

    Setting of the model. (a) Western region of the model basin. The color shade shows the depth (m). The contours show the theoretical Sverdrup transport (Sv). (b) Wind stress as a function of latitude (N m−2).

  • View in gallery
    Fig. 3.

    The 10-yr mean anomaly of the upper-layer thickness from the initial state (colors; m) and the 10-yr mean current velocity (vectors; m s−1): (a) control run (Expt 1) and (b) flat bottom run (Expt 2). The green box is the area of the seafloor topography, which is shallower than deepest ocean bottom (5500 m). The black dashed line is the boundary between the subarctic and subtropical regions (the latitude of the zero wind stress curl). Strong velocity vectors exceeding 0.2 m s−1 are shown in red.

  • View in gallery
    Fig. 4.

    (a) The 10-yr mean barotropic transport (the total transport of the upper and lower layers; Sv; white contours and color gradients) and barotropic velocity (the weighted average velocity of the upper and lower layers; vectors; m s−1). (b) The 10-yr mean transport of the upper layer (Sv; white contours and color gradients) and the velocity of the upper layer minus the barotropic velocity (vectors; m s−1). (c) As in (b), but for the lower layer. Strong velocity vectors exceeding 0.2 m s−1 are shown in red.

  • View in gallery
    Fig. 5.

    (a) Characteristic curve calculated using Eq. (2) (black contours; the contour interval is 0.1 × 10−5 s−1) and the layer thickness anomaly (colors; m). Open characteristic curves of 0.1 × 10−5 s−1 (yellow) and −0.3 × 10−5 s−1 (blue) are also added. Directions of the phase speeds derived from Qc are schematically added as the black arrows. (b) The layer thickness anomaly (colors; m) integrated along the open characteristic curves of every 0.1 × 10−5 s−1 interval.

  • View in gallery
    Fig. 6.

    Snapshots of the thickness anomalies of the upper layer from days 31 to 135 taken every 13 days in year 32 (m; colors and thin contours). The thick lines indicate characteristic curves. The red (blue) arrows indicate an eddy with thin (thick) layer thickness.

  • View in gallery
    Fig. 7.

    (a) The function of longitude f(λ) in Eq. (3). (b) The theoretical barotropic transport when α = 1. (c) The 10-yr mean barotropic transport in the presence of a seafloor topography when α = 1 (Expt 3a). (d) The 10-yr mean barotropic transport without the seafloor topography when α = 4 (Expt 3b). (e) As in (c), but when α = 4 (Expt 3c). The contour interval in (b) and (c) is 1 Sv. The contour interval in panels (d) and (e) is 4 Sv.

  • View in gallery
    Fig. 8.

    (a) Ambient potential vorticity f/HT (colors; 10−8 s−1) and (b) total potential vorticity (f + ζ)/HT (colors; 10−8 s−1) with the relative vorticity ζ calculated from the 10-yr mean barotropic velocity (vectors; m s−1).

  • View in gallery
    Fig. 9.

    The 10-yr mean anomaly of the upper-layer thickness from the initial state (color shading; m; black contour line at 0) and the 10-yr mean current velocity (vectors; m s−1) of each experiment: (a) Expt 4a, (b) Expt 4b, (c) Expt 5a, and (d) Expt 6. Open characteristic curves of 0.1 × 10−5 s−1 (yellow) and −0.3 × 10−5 s−1 (blue) are also added. Velocity vectors greater than 0.4 m s−1 are colored yellow. Velocity vectors between 0.2 and 0.4 m s−1 are colored red.

  • View in gallery
    Fig. 10.

    The 10-yr mean barotropic transport (Sv; contours and colors) of each experiment: (a) Expt 4a, (b) Expt 4b, (c) Expt 5a, and (d) Expt 6.

  • View in gallery
    Fig. 11.

    The layer thickness anomaly (colors; m) integrated along the open characteristic curves of every 0.1 × 10−5 s−1 interval of each experiment: (a) Expt 4a, (b) Expt 4b, (c) Expt 5a, and (d) Expt 6.

  • View in gallery
    Fig. 12.

    As in Fig. 9c, but for Expt 5b.

  • View in gallery
    Fig. 13.

    (a) Western part of the extended domain for Expt 7. Contours indicate the theoretical Sverdrup transport calculated from the wind stress of Eq. (4). As in Fig. 3a, the 10-yr mean anomaly of the upper-layer thickness from the initial state (color shading; m) and the 10-yr mean current velocity (vectors; m s−1) for the extended domain is shown for (b) Expt 7a and (c) Expt 7b.

  • View in gallery
    Fig. B1.

    The layer thickness anomaly (colors; m) integrated along the open characteristic curves of every 0.1 × 10−5 s−1 interval of the control run (Expt 1). (a) With μ of 2-yr e-folding time scale. (b) With μ of 0.

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Dynamics of a Quasi-Stationary Jet along the Subarctic Front in the North Pacific Ocean (the Western Isoguchi Jet): An Ideal Two-Layer Model

Toru MiyamaApplication Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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Humio MitsuderaInstitute of Low Temperature Science, Hokkaido University, Sapporo, Japan

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Hajime NishigakiFaculty of Science and Technology, Oita University, Oita, Japan

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Ryo FurueApplication Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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ABSTRACT

The dynamics of a quasi-stationary jet along the Subarctic Front in the North Pacific Ocean (the Western Isoguchi Jet) were investigated using an idealized two-layer model. The experiments suggested that a seafloor topography, which is 500 m high, produces a jet along its eastern flank. The formation mechanism of the jet can be explained via baroclinic Rossby wave characteristics. Baroclinic Rossby waves propagate along characteristic curves, which are significantly distorted by anticyclonic barotropic flow on the seafloor topography. A baroclinic surface jet is formed where a characteristic curve originating in the subtropical gyre and one originating in the subpolar gyre meet because the pycnocline depth varies discontinuously at this location. The barotropic flow on the seafloor topography is induced by eddies.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Toru Miyama, tmiyama@jamstec.go.jp

ABSTRACT

The dynamics of a quasi-stationary jet along the Subarctic Front in the North Pacific Ocean (the Western Isoguchi Jet) were investigated using an idealized two-layer model. The experiments suggested that a seafloor topography, which is 500 m high, produces a jet along its eastern flank. The formation mechanism of the jet can be explained via baroclinic Rossby wave characteristics. Baroclinic Rossby waves propagate along characteristic curves, which are significantly distorted by anticyclonic barotropic flow on the seafloor topography. A baroclinic surface jet is formed where a characteristic curve originating in the subtropical gyre and one originating in the subpolar gyre meet because the pycnocline depth varies discontinuously at this location. The barotropic flow on the seafloor topography is induced by eddies.

Denotes content that is immediately available upon publication as open access.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Toru Miyama, tmiyama@jamstec.go.jp

1. Introduction

Recent studies have shown that two quasi-stationary jets exist along the subarctic frontal zone in the western North Pacific Ocean. Using satellite observations and hydrographic data, Isoguchi et al. (2006) identified two warm water tongues driven by these western and eastern quasi-stationary geostrophic jets: J1 and J2 in their paper. In this study, we focus on the western jet (J1), which we call the Western Isoguchi Jet. The existence of the Western Isoguchi Jet was also confirmed by surface drifting buoys (Niiler et al. 2003), subsurface buoys (Iwao et al. 2003), and in situ measurements (Wagawa et al. 2014).

The vectors in Fig. 1 show the surface velocity from the Japanese Fishery Research Agency–Japan Coastal Ocean Predictability Experiment 2 (FRA-JCOPE2) ocean reanalysis with a resolution of 1/12° (Miyazawa et al. 2009). The strong northeastward flow (red vectors) near 40°–45°N, 150°–155°E represents the Western Isoguchi Jet.

Fig. 1.
Fig. 1.

Long-term (1993–2012) mean velocity at a depth of 10 m from the FRA–JCOPE2 ocean reanalysis (vectors; m s−1) and the bottom depth (color shading; m). Strong velocity vectors exceeding 0.1 m s−1 are shown in red.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

There is a link between the Western Isoguchi Jet and Kuroshio Extension. The Western Isoguchi Jet transports warm and saline subtropical water from the Kuroshio Extension, while the water properties of the Western Isoguchi Jet changes as it flows downstream because of mixing with subarctic water (Isoguchi et al. 2006; Wagawa et al. 2014). Because the Western Isoguchi Jet flows the boundary between the subtropical water and subarctic waters, the Western Isoguchi Jet plays an important role in the exchanges between these two water masses.

The Western Isoguchi Jet is accompanied by a strong front in the sea surface temperature (SST). The SST gradient across the Western Isoguchi Jet exceeds 4°–5°C (100 km)−1, which is the strongest within the Subarctic Front and tends to be stronger than that of the Kuroshio Extension (Kida et al. 2015). Since the SST variabilities in the Subarctic Front affect the hemispheric-scale atmospheric circulations (Frankignoul et al. 2011; Smirnov et al. 2015; Taguchi et al. 2012), the behavior of the front could also be important for climate.

It is not yet fully understood why the quasi-stationary jet exists in the open ocean. Past studies (Isoguchi et al. 2006; Niiler et al. 2003) have suggested that a mound (a small hill-like topography) is important for the mechanism of the quasi-steady jet. Figure 1 shows that the Western Isoguchi Jet flows along the eastern flank of the topography. The existence of the seafloor topography in parallel with the jet suggests the involvement of topography in the dynamics of the Western Isoguchi Jet. However, the seafloor topography has an elevation of about 500 m on the Pacific Ocean floor, which has a total depth of over 5500 m. Note that Fig. 1 is colored to highlight the low-rise bottom topography. It is not obvious how such a low-rise bottom topography in appearance could intensify a current such as the Western Isoguchi Jet at the ocean surface.

In this study, we conducted experiments with an idealized isopycnal two-layer model to understand how a low-rise topography could generate an intensified current along the eastern flank of topography. The isopycnal model is an effective tool to understand the essential dynamics because it is easier to treat theoretically than a comprehensive model like the FRA–JCOPE2 reanalysis. We use a theory of propagation of baroclinic Rossby waves whose characteristic curves are deformed by barotropic flows. Mitsudera et al. (2018) applied the same theory to explain the dynamics and variability of the Western Isoguchi Jet in realistic data (the FRA–JCOPE analysis and observations).

This paper is organized as follows: In section 2, we describe the model used in this study. In section 3, we explain how seafloor topography could generate a jet using experiments with and without the seafloor topography. In section 4, we explain the result of section 3 from the viewpoint of baroclinic Rossby wave characteristics. This section shows that the anticyclonic barotropic transport that was generated from the seafloor topography is important. In section 5, we demonstrate that eddies generate anticyclonic barotropic transport. In section 6, we show some additional sensitivity experiments to further understand the dynamics of the jet. In section 7, we summarize and discuss the results of the experiments.

2. Model

Idealized model settings were used to understand the essence of the dynamics. We used the Hybrid Coordinate Ocean Model (HYCOM; Bleck 2002) in its isopycnal two-layer mode (Bozec 2013).

The idealized model basin was rectangular. The basin covered the area 35°–55°N by 141.5°E–158.5°W. The western part of the model basin is shown in Fig. 2a. The zonal grid spacing was 1/12°, and the meridional grid spacing was refined at higher latitudes to keep the grid cells square. The initial upper- and lower-layer thicknesses were 500 and 5000 m, respectively. Because the observation by Wagawa et al. (2014) showed that the Western Isoguchi Jet transported subtropical water to the downstream region in a layer shallower than 400 dbar, the initial upper-layer thickness was set to include the depth. The potential density anomalies σθ of the two layers were 26.7 and 27.65 kg m−3, determined based on the density structure around the Western Isoguchi Jet. The corresponding baroclinic Rossby radius Rd at 45°N is 20.15 × 103 m.

Fig. 2.
Fig. 2.

Setting of the model. (a) Western region of the model basin. The color shade shows the depth (m). The contours show the theoretical Sverdrup transport (Sv). (b) Wind stress as a function of latitude (N m−2).

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

Subgrid-scale turbulence was represented by an eddy viscosity whose coefficient was constant in time and was given by ν = ud Δx with ud = 0.01 m s−1, where Δx is the zonal grid spacing. This gave ν = 65.5 m2 s−1 at 45°N. The thickness diffusion of the model layer thicknesses, the bottom friction, and the friction between the isopycnal layers were set to zero. A no-slip boundary condition is applied to the lateral boundary.

The model was driven by the zonal wind stress τ as a function of latitude, which was specified as follows:
e1
where φ is the latitude, φ0 = 45°, Δφ = 10°, and τ0 = 0.0249 N m−2. The wind stress was a function of only the latitude φ. Figure 2b shows the latitudinal shape of the wind stress.

Given the wind stress, the theoretical linear Sverdrup circulation was a double gyre, as shown in Fig. 2a (contours). The strength of the Sverdrup gyre was approximately 20 Sv (1 Sv = 106 m3 s−1; the maximum and the minimum of the Sverdrup transport function were 19.96 and −19.96 Sv, respectively). The strength of the Sverdrup transport around 35°–55°N was roughly estimated from the climatology of the NCEP–NCAR reanalysis (Kalnay et al. 1996). Because it has been suggested that the latitude of the Subarctic Front is associated with the annual-mean zero wind stress curl line near 45°N (Hurlburt et al. 1996; Milliff et al. 2004), the current setting presented an ideal model of the Subarctic Front as the boundary between the subtropical and subarctic gyres.

An idealized seafloor topography was placed in the interior basin (the color-shaded area in Fig. 2). A shallow constant depth of 5000 m was given over the region of 42°–44°N, 146°–147°E. The depth was linearly increased elsewhere over the region of 38°–48°N, 145°–148°E (the box enclosed by the green lines) to 5500 m. Therefore, the height of the seafloor topography was 500 m. The seafloor topography was located at the boundary between the subtropical and subarctic regions (red dashed line). This configuration corresponds to the relationship between the wind and bottom topography around the Western Isoguchi Jet. Later, in Experiment (Expt) 7b, the northeast–southwest tilted topography, which was an idealized representation of the real topography in Fig. 1, was used.

The experiments were run from a state of rest for 40 years. The averages of the last 10 years in the model runs are shown in this paper unless specified otherwise.

The experiments using this model are summarized in Table 1. In addition to the control run (Expt 1), an experiment with a flat bottom (Expt 2) was conducted to examine the role of the seafloor topography. Experiments 3a–3c investigate the effects of eddies in generating barotropic transport. These experiments are explained in section 5. Experiments 4a–7b are sensitivity experiments to deepen our understanding of the control run. These experiments are explained in section 6.

Table 1.

Conditions of the experiments. In Expts 3a–c, the wind forcing gives no total Sverdrup transport in the western boundary. See the discussion of Eq. (3) for the definition of α.

Table 1.

3. Control run

Figure 3a shows the anomaly of the upper-layer thickness (colors; m) from the initial state (500-m thickness) and the current velocities in the upper layer (vectors; m s−1) in the control run (Expt 1). As expected, a strong current (the jet shown as red vectors), which is our model of the Western Isoguchi Jet, appeared along the eastern flank of the seafloor topography. The maximum absolute velocity along the eastern flank of the topography (41°–45°N, 147°–150°E) was 0.39 m s−1 at 43.57°N, 148.19°E, which was more than 2 times larger than the maximum velocity 0.18 m s−1 in the west (41°–45°N, 143°–147°E). Hereinafter, as the idealized model of the Western Isoguchi Jet, the intensified current along the eastern flank of the topography is referred to as the ICET.

Fig. 3.
Fig. 3.

The 10-yr mean anomaly of the upper-layer thickness from the initial state (colors; m) and the 10-yr mean current velocity (vectors; m s−1): (a) control run (Expt 1) and (b) flat bottom run (Expt 2). The green box is the area of the seafloor topography, which is shallower than deepest ocean bottom (5500 m). The black dashed line is the boundary between the subarctic and subtropical regions (the latitude of the zero wind stress curl). Strong velocity vectors exceeding 0.2 m s−1 are shown in red.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

For comparison, Fig. 3b shows the results of the flat bottom case without seafloor topography (Expt 2). In this case, the ICET did not appear. When the topography was flat, a typical double gyre formed (Haidvogel et al. 1992). While the anomaly of the upper-layer thickness in the subarctic region was negative because of the positive wind curl, the anomaly in the subtropical region was positive because of the negative wind curl. Because of the strong nonlinearity and the no-slip boundary condition at the lateral boundary (Nakano et al. 2008; Sue and Kubokawa 2015), the double gyre did not meet at the latitude of the zero wind stress curl, unlike in the theoretical Sverdrup circulation in Fig. 2a. Therefore, the zonal return flow of the southern (subtropical) gyre formed near 42°N. Likewise, the zonal return flow of the northern (subarctic) gyre formed near 48°N.

With topography (Expt 1; Fig. 3a), the negative thickness anomaly in the northern gyre protruded into the region of the positive thickness anomaly in the southern gyre along the eastern flank of the seafloor topography (the green box). Because of this intrusion, a strong front in the layer thickness formed. Corresponding to this front, the ICET was generated (the red vectors).

Figure 4a shows the barotropic transport (white contours and color gradients; Sv) of the control run. A prominent feature is that anticyclonic circulation forms on the seafloor topography (around A in Fig. 4a). The barotropic transport was approximately 30 Sv. Figure 4a also shows a cyclonic and an anticyclonic barotropic circulation (around B and C) existed west and east of the ICET, respectively.

Fig. 4.
Fig. 4.

(a) The 10-yr mean barotropic transport (the total transport of the upper and lower layers; Sv; white contours and color gradients) and barotropic velocity (the weighted average velocity of the upper and lower layers; vectors; m s−1). (b) The 10-yr mean transport of the upper layer (Sv; white contours and color gradients) and the velocity of the upper layer minus the barotropic velocity (vectors; m s−1). (c) As in (b), but for the lower layer. Strong velocity vectors exceeding 0.2 m s−1 are shown in red.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

Figure 4b shows that the transport of the upper layer (Sv; white contours and color gradients) and the velocity of the upper layer (vectors; m s−1). The strong transport (dense contour) and the strong velocity (large vector) along the eastern flank of the topography indicated the existence of the ICET. The strong velocity even after subtracting the barotropic velocity shows that the ICET has the baroclinic structure: barotropic velocities from the eddies around B and C did not entirely generate the ICET, although they enhanced the ICET.

Figure 4c shows the transport of the lower layer (Sv; white contours and color gradients) and velocity of the lower layer minus the barotropic velocity (vectors; m s−1). Comparison between Figs. 4a and 4c shows that the large part of the closed barotropic circulations around A, B, and C came from the lower layer. Furthermore, the small vectors in Fig. 4c show that most of the velocities in the lower layer were the barotropic velocities.

Although the barotropic velocities in Fig. 4a look relatively small compared with the baroclinic velocity in Fig. 4b, the barotropic velocities are important for the dynamics of the ICET in affecting baroclinic Rossby waves, as shown in section 4. The anticyclonic circulation on the seafloor topography (around A in Fig. 4a) is especially important for generating the southward intrusion of the northern gyre along the eastern flank of the topography. The dynamics of the generation of the anticyclonic barotropic transport over the sea topography is discussed in section 5. The dynamics of the barotropic circulations around B and C are beyond the scope of this study although they are likely to be recirculation gyres generated by the nonlinear nature of the ICET.

4. Characteristics of a baroclinic Rossby wave

This section examines what caused the southward intrusion of the northern gyre along the eastern flank of the topography. We address this question from the viewpoint of baroclinic Rossby wave characteristics (McCreary et al. 2002; Mitsudera et al. 2011, 2018; Nishigaki and Mitsudera 2012; Pedlosky 1996).

We consider a quasigeostrophic potential vorticity (PV) equation in a two-layer ocean. The evolution of the baroclinic streamfunction, which is proportional to the interfacial displacement, evolves along an isoline of Qc (a characteristic curve; see appendix A):
e2
where ψT is the barotropic streamfunction, β is the planetary beta, and Rd is the baroclinic deformation radius. The first term of Eq. (2) represents the phase speed of the planetary Rossby wave; the second term represents the barotropic current.

Propagation of the Rossby wave, which carries the layer thickness anomaly produced by wind forcing, is governed by . If the effect of the barotropic transport is not significant, the Rossby wave propagates westward because of the planetary β term [the first term in Eq. (2)]. In this case, the wind effect on the Ekman pumping and suction propagates westward. Therefore, the thick layer thickness is formed with the subtropical gyre south of 45°N, while the thin layer is formed with the subarctic gyre north of 45°N.

Next, the barotropic transport term [the second term in Eq. (2)] is considered. Figure 5a compares the interfacial anomaly (color gradients) with the characteristic curves (contours) based on Eq. (2), including two terms using the barotropic transport in Fig. 4a. Because of the anticyclonic barotropic transport from the seafloor topography, the characteristic curves are significantly distorted. Some of the characteristic curves in the subarctic enter the subtropical gyre along the eastern flank of the seafloor topography (e.g., the yellow curve). The bend of the characteristic curves explains the intrusion of the thin layer of the subarctic gyre into the thick layer of the subtropical gyre well.

Fig. 5.
Fig. 5.

(a) Characteristic curve calculated using Eq. (2) (black contours; the contour interval is 0.1 × 10−5 s−1) and the layer thickness anomaly (colors; m). Open characteristic curves of 0.1 × 10−5 s−1 (yellow) and −0.3 × 10−5 s−1 (blue) are also added. Directions of the phase speeds derived from Qc are schematically added as the black arrows. (b) The layer thickness anomaly (colors; m) integrated along the open characteristic curves of every 0.1 × 10−5 s−1 interval.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

To further demonstrate how the characteristic curve affected layer thickness, the integration along characteristic curves was conducted. The method was described in appendix B. Equation (B3) was integrated along the characteristic curves to estimate the layer thickness anomaly forced by the right-hand side (RHS) of Eq. (B3). The result is shown in Fig. 5b. Although some quantitative differences between Figs. 5a and 5b (colors) exist because of the difficulties discussed in appendix B, Fig. 5b captures overall features of Fig. 5a, especially the strong gradient of the layer thickness along the eastern flank of the topography.

In Fig. 5b, because of the first term on the RHS of Eq. (B3), the layer thickness anomaly (colors) of the characteristic curves that propagated in the subtropical region showed positive values because of the Ekman pumping, while the layer thickness in the subarctic showed negative values because of the Ekman suction. Some of the distorted characteristic curves from the subarctic ocean entered the subtropical ocean. The layer thickness of these characteristic curves continued to be negative despite the Ekman pumping in the subtropics. The contribution of the second term on the RHS in Eq. (B2) was small (about 30 m at most).

The meeting of the characteristic curves from the subtropical gyre (e.g., the blue curve in Fig. 5a) and the subarctic gyre (e.g., the yellow curve in Fig. 5a) formed a discontinuity (front) in the surface layer thickness and hence a baroclinic jet geostrophically corresponding to the strong front in the open ocean. Past studies (Dewar 1991, 1992; Furue et al. 2009, 2007; McCreary et al. 2002) have shown that a narrow jet can form in regions where characteristic curves converge or intersect.

The validity of this distorted characteristic was also observed in the movement of eddies. Although global observations show eddies usually propagate nearly due west at approximately the phase speed of nondispersive baroclinic Rossby waves despite preferences for slight poleward and equatorward deflection of cyclonic and anticyclonic eddies (Chelton et al. 2011), eddies in Expt 1 showed different behaviors. As an example among many similar cases, Fig. 6 shows snapshots of the thickness anomalies of the upper layer from days 31 to 135 taken every 13 days in year 32 (m; colors and thin contours) in Expt 1. While an eddy (thin layer thickness indicated by a red arrow) moved southward along a characteristic curve, another eddy (thick layer thickness indicated by a blue arrow) moved westward along another characteristic curve. Mitsudera et al. (2018) also found that eddy propagations tracked using satellite-derived sea surface height anomalies near the Western Isoguchi Jet are consistent with the characteristic curves deformed by the barotropic flows.

Fig. 6.
Fig. 6.

Snapshots of the thickness anomalies of the upper layer from days 31 to 135 taken every 13 days in year 32 (m; colors and thin contours). The thick lines indicate characteristic curves. The red (blue) arrows indicate an eddy with thin (thick) layer thickness.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

5. Barotropic transport on the seafloor topography

The preceding section showed that barotropic transport on the seafloor topography is essential for the formation of the ICET. This section discusses why the barotropic transport was generated on the topography.

We hypothesize that the barotropic flow is eddy-induced circulation. Past studies using eddy-resolving models have shown that mesoscale eddies cause mean anticyclonic circulation around seafloor topography (Adcock and Marshall 2000; Bretherton and Haidvogel 1976; Holloway 1978; Treguier 1989). As shown in Fig. 6, eddies were active around the seafloor topography in Expt 1. Therefore, it is suggested that these eddies can cause the anticyclonic barotropic transport.

To demonstrate that eddies can cause barotropic transport on the topography, we conducted a series of experiments (Expts 3a–c), where we removed the double gyre around the seafloor topography to show that the anticyclonic circulation was not part of the wind-driven double gyre. We used the wind stress τ′, where the wind stress τ defined by Eq. (1) was multiplied by a constant α, and f(λ) was the function of the longitude λ, as shown in Fig. 7a:
e3
Fig. 7.
Fig. 7.

(a) The function of longitude f(λ) in Eq. (3). (b) The theoretical barotropic transport when α = 1. (c) The 10-yr mean barotropic transport in the presence of a seafloor topography when α = 1 (Expt 3a). (d) The 10-yr mean barotropic transport without the seafloor topography when α = 4 (Expt 3b). (e) As in (c), but when α = 4 (Expt 3c). The contour interval in (b) and (c) is 1 Sv. The contour interval in panels (d) and (e) is 4 Sv.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

Because positive values f(λ) of in the eastern basin were canceled by negative values of f(λ) in the central basin through the westward integration of the wind stress curl, the theoretical Sverdrup gyre was a closed circulation in the interior basin, as shown in Fig. 7b. Therefore, Sverdrup circulation should not exist around the seafloor topography.

When the model was run with α = 1 (Expt 3a; Fig. 7c), the current was weak and nearly linear. Therefore, the vertically integrated transport was close to the theoretical Sverdrup transport. Even though the experiment in Fig. 7c included the seafloor topography, the current over the topography was insignificant.

When α = 4, the strength of the theoretical Sverdrup transport was increased by a factor of 4. In the experiment with α = 4 without the seafloor topography (Expt 3b; Fig. 7d), the resultant temporal-averaged current departed from the theoretical circulation; instead, stripes of zonal currents appeared in the western basin. These zonal currents were generated by eddies, which were generated because the circulation became more nonlinear and unstable in Expt 3b than that in Expt 3a. Past studies showed that eddies cause zonal currents (Nakano and Hasumi 2005; Richards et al. 2006; Wang et al. 2012).

When the seafloor topography was included with α = 4 (Expt 3c; Fig. 7e), an anticyclonic current on the seafloor topography was generated in addition to multiple zonal currents. This experiment supports that the eddies generated anticyclonic barotropic transport in the control run. The velocity over the topography was vertically uniform (not shown).

Topography-following currents induced by eddies can be linked to the mixing of the potential vorticity by eddies (Greatbatch and Li 2000).

Figure 8 compares the ambient potential vorticity f/HT and the total potential vorticity (f+ ζ)/HT with the relative vorticity ζ calculated from the 10-yr mean barotropic velocity of Expt 3c. Figure 8a shows that the topography produced a local maximum in the ambient potential vorticity. Mitsudera et al. (2018) showed that closed contours of f/HT are present west of the Isoguchi jet in the real ocean.

Fig. 8.
Fig. 8.

(a) Ambient potential vorticity f/HT (colors; 10−8 s−1) and (b) total potential vorticity (f + ζ)/HT (colors; 10−8 s−1) with the relative vorticity ζ calculated from the 10-yr mean barotropic velocity (vectors; m s−1).

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

Because the ambient potential vorticity contains the local maximum vorticity on the topography, any inflow into the region has lower potential vorticity. Likewise, any water parcel exiting the region has higher potential vorticity than the surrounding regions. Therefore, water exchange by eddies acts to decrease the total potential vorticity in the region of the maximum ambient potential vorticity. Accordingly, Fig. 8b shows that the total potential vorticity decreased on the topography with respect to Fig. 8a by generating anticyclonic circulation (negative relative potential vorticity; vectors in Fig. 8b). Therefore, the anticyclonic circulation was the result of the mixing of the potential vorticity by the eddies.

6. Sensitivity tests

This section discusses the sensitivity experiments to deepen the understanding of the results from the two-layer model in the previous sections. Sensitivity to viscosity (Expts 4a and 4b), stratification (Expts 5a and 5b), the location of seafloor topography (Expt 6), and latitude of the Kuroshio Extension (Expts 7a and 7b) are discussed in sections 6a, 6b, 6c, and 6d. The purpose of this section is to show how the ICET and the relevant characteristic curves changed in these sensitivity runs rather than completely explain and quantify these runs. The changes in characteristics curves show qualitative shifts in the involvement of the subtropical and subarctic currents.

a. Viscosity

Figure 9a shows the velocity and layer thickness of the upper layer in Expt 4a where the viscosity was increased by a factor of 5 from that used in the control run. Wavy return flows of the southern gyre near 41°–45°N and of the northern gyres near 45°–49°N indicate that the nonlinearity remained even with this larger viscosity. However, the ICET did not occur. The maximum absolute velocity along the eastern flank of the topography (41°–45°N, 147°–150°E) was 0.18 m s−1, which was weaker than 0.21 m s−1 in the west (41°–45°N, 143°–147°E).

Fig. 9.
Fig. 9.

The 10-yr mean anomaly of the upper-layer thickness from the initial state (color shading; m; black contour line at 0) and the 10-yr mean current velocity (vectors; m s−1) of each experiment: (a) Expt 4a, (b) Expt 4b, (c) Expt 5a, and (d) Expt 6. Open characteristic curves of 0.1 × 10−5 s−1 (yellow) and −0.3 × 10−5 s−1 (blue) are also added. Velocity vectors greater than 0.4 m s−1 are colored yellow. Velocity vectors between 0.2 and 0.4 m s−1 are colored red.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

The barotropic transport in Expt 4a (Fig. 10a) shows that the anticyclonic circulation on the seafloor topography was significantly weaker than that in Expt 1 (Fig. 4a). Because the barotropic recirculation of the western boundary current in Expt 4a (Fig. 10a) was as strong as that in Expt 1 (Fig. 4a), simple damping of the barotropic transport by the viscosity does not explain the disappearance of the anticyclonic barotropic transport on the seafloor topography. The disappearance of the barotropic transport occurred because eddies, which induced the anticyclonic circulation on the topography, became weaker in Expt 4a than those in Expt 1 (not shown).

Fig. 10.
Fig. 10.

The 10-yr mean barotropic transport (Sv; contours and colors) of each experiment: (a) Expt 4a, (b) Expt 4b, (c) Expt 5a, and (d) Expt 6.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

The lack of the anticyclonic barotropic transport significantly changed the characteristic curves; the conversion of the characteristic curve that made the ICET in the control run (the yellow and blue curves in Fig. 5a) did not occur in Expt 4a (the yellow and blue curves in Fig. 9a).

Figure 11a shows the layer thickness anomaly obtained using the integration along the characteristic curves. With the weak barotropic transport, the intrusion of negative layer thickness over the topography from the subarctic to the subtropical region along the characteristic curves, which existed in Expt 1 (Fig. 5b), disappeared in Expt 4a (Fig. 11a). Therefore, the mechanism that made the ICET in the control run disappeared in Expt 4a.

Fig. 11.
Fig. 11.

The layer thickness anomaly (colors; m) integrated along the open characteristic curves of every 0.1 × 10−5 s−1 interval of each experiment: (a) Expt 4a, (b) Expt 4b, (c) Expt 5a, and (d) Expt 6.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

Discussion using the integration along the characteristic curves has some limitations. The method in appendix B cannot quantify the positive layer thickness anomaly over the topography north of 42°N because the open characteristic curves did not exist there. Unrealistic negative values on a characteristic curve within 40°–45°N, 141°–145°E is likely because the dissipation in the western boundary region where the characteristic curve went through was too weak in the method described in appendix B. Despite these limitations, the characteristic curve helps to visualize the difference between Expts 1 and 4a.

When the viscosity was increased by a factor of 50 from that in the control run, the circulation became nearly linear, as one would expect from the Sverdrup theory in Fig. 2a. Figures 9b and 10b show the circulation of the upper layer and barotropic transport, respectively, of Expt 4b. Note that, despite the strong viscosity, the anomalies of the layer thickness and the velocities along the western boundary (Fig. 9b) were larger than those in Expt 1 (Fig. 3a). The strong response to the wind forcing occurred in Expt 4b because the wind-forced circulation was trapped in the upper layer without barotropization by eddies (Holland and Rhines 1980; Rhines 1977).

b. Stratification

To show the sensitivity to stratification, the density difference between the two layers in Expt 5a was increased by a factor of 2 from that in the control run (Expt 1). For a comparison, the same case as Expt 5a without the seafloor topography (Expt 5b) was also conducted. The strong zonal return flows from the western boundary currents existed both in the northern and southern gyres in Expt 5b (Fig. 12). The zonal return flows were stronger in Expt 5b (Fig. 12) than those in Expt 2 (Fig. 3b). The stronger the circulation with stronger stratifications has also been discussed by Liu (1997) and Sun et al. (2013).

Fig. 12.
Fig. 12.

As in Fig. 9c, but for Expt 5b.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

When the seafloor topography was included (Expt 5a in Fig. 9c), the current along a zonally wide range of the zonal return flow of the southern gyre was enhanced compared with Fig. 12. On the other hand, the zonal return flow in the northern gyre was weakened. Figure 9c shows east–west asymmetry of the jet strength across the topography does not occur in Expt 5a. The maximum absolute velocity along the eastern flank of the topography (41°–45°N, 147°–150°E) was 0.44 m s−1, which was weaker than 0.48 m s−1 in the west (41°–45°N, 143°–147°E).

The barotropic transport on the topography was not greatly affected by the stratification (Fig. 10c) because the eddies were still active. The characteristic curves from the northern gyre were, therefore, still distorted over the topography (Fig. 9c and Fig. 11c). However, protrusion of the characteristic curves from the northern gyre into the southern gyre was weaker in Expt 5a than that in the control run because the strong stratification (twice larger than that of the control run) made the barotropic transport term (the second term) in Eq. (2) relatively small. Because of the relatively stronger planetary β effect, the current was zonally more uniform in Expt 5a (Fig. 9c) than in Expt 1 (Fig. 3a). As a consequence, the zonal return flow of the subtropical gyre over a wide zonal range of the topography was enhanced in Expt 5a (Fig. 9c).

There are other interesting questions in the results of Expt 5a, for example, why the zonal return in the subarctic gyre in Fig. 9c became weaker than that in Fig. 12. Because the purpose of this study is about the ICET, we do not further analyze Expt 5a. The purpose of Expt 5a is to demonstrate how the stratification changes the existence of the ICET drastically.

c. Location of the seafloor topography

Expt 6 modeled the case where the seafloor topography was located in the subtropical gyre (the green box in Fig. 9d is the area of the seafloor topography). The ICET occurred: the maximum absolute velocity along the eastern flank of the topography (41°–45°N, 147°–150°E) was 0.25 m s−1 at 43.14°N, 148.78°E; while the maximum velocity was 0.16 m s−1 in the west (41°–45°N, 143°–147°E). However, the velocity (0.25 m s−1) in Expt 6 was weaker than the velocity (0.39 m s−1) in the control run. The weaker velocity corresponded to the higher-layer thickness over the topography north of 41°N in Expt 6 than those in the control run.

While the barotropic transport on the seafloor topography was strong (Fig. 10d), the location of the anticyclonic barotropic transport in Expt 6 moved more southward with topography than that in the control run. The different location of the anticyclonic transport significantly changed the characteristic curves. While the characteristic curve of 0.1 × 10−5 s−1 was bent from the subarctic region to the subtropical region in the control run (yellow line in Fig. 5a), such a bend did not occur in Expt 6 (yellow line in Fig. 9d). Instead, the characteristic curve that went through the western boundary region in the subarctic region entered over the topography north of 41°N (Fig. 11d). The values of the layer thickness estimated along these characteristic curves (Fig. 11d) underestimated the layer thickness of the model (Fig. 9d) over the topography possibly caused by too weak dissipation in the western boundary current region during the integration along the characteristic curves as suggested in section 6a. Although the quantification using the characteristic curve was not possible, Expt 6 shows that the location of the anticyclonic transport drastically changes the characteristic curves that affect the layer thickness.

d. Latitude of the Kuroshio Extension

In the idealized control run, only a part of the subtropical region was included in the model domain. Therefore, the center of the subtropical circulation and the separation from the western boundary current of the subtropical gyre was farther north than in reality. The separation of the subtropical gyre from the western boundary in reality occurs in the form of the Kuroshio Extension, which is located farther south of the Subarctic Front and the seafloor topography that generates the Western Isoguchi Jet.

In Expt 7a, the southern boundary of the model domain was extended to 15°N. The location of the seafloor topography was the same as in Expt 1. The wind stress was given by
e4
where φ1 = 15°, φ2 = 45°, φ3 = 55°, τ1 = 0.0748 N m−2, and τ2 = 0.0249 N m−2.

The theoretical Sverdrup transport calculated from the wind stress given by Eq. (4) is shown in Fig. 13a. The Sverdrup circulations for Figs. 13a and 2a were the same in that of the double gyres, approximately 20 Sv. The latitude of the boundary of the subtropical and subarctic gyres (the latitude of the wind stress curl zero) was also the same for Figs. 13a and 2a.

Fig. 13.
Fig. 13.

(a) Western part of the extended domain for Expt 7. Contours indicate the theoretical Sverdrup transport calculated from the wind stress of Eq. (4). As in Fig. 3a, the 10-yr mean anomaly of the upper-layer thickness from the initial state (color shading; m) and the 10-yr mean current velocity (vectors; m s−1) for the extended domain is shown for (b) Expt 7a and (c) Expt 7b.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

Figure 13b shows the result of Expt 7a. The separation of the subtropical circulation from the western boundary appeared at approximately 35°N, similar to the latitude of the real Kuroshio Extension. According to the theory of Nakano et al. (2008), the zonal jet corresponding to the Kuroshio Extension should be located north of the southern relative recirculation gyre (RRG). The southern RRG should be located, because of its stability, just north of the center of the Sverdrup subtropical gyre, which is defined as the latitude of the Sverdrup streamfunction maximum. In Expt 7a, the center of the Sverdrup subtropical gyre is 30°N. Therefore, the theory of Nakano et al. (2008) explains the latitude of the Kuroshio Extension near 35°N in Expt 7a.

Regardless of the model domain and the realistic latitude of the Kuroshio Extension, the intensification of the current along the eastern flank of the topography still existed because of the southward intrusion of the subarctic gyre (A in Fig. 7a). The maximum absolute velocity along the eastern flank of the topography (41°–45°N, 147°–150°E) was 0.18 m s−1 at 43.57°N, 147.94°E, which was larger than 0.07 m s−1 in the west (41°–45°N, 143°–147°E). The southward intrusion of the subarctic gyre occurred because the anticyclonic barotropic transport still existed over the seafloor topography (not shown). Expt 8a indicates that the ICET exists as long as the topography is located across the Subarctic Front (near the latitude of the zero wind stress curl) and the anticyclonic barotropic transport is generated because of the eddy activity.

In Expt 7a, the ICET (0.18 m s−1) was weaker than it was in Expt 1 (0.39 m s−1). One reason for this weakness is that the distance between the subtropical gyre (the thick layer thickness; B in Fig. 8a) and the subarctic gyre (the thin layer thickness; A in Fig. 8a) was large despite the southward intrusion of the subarctic gyre along the eastern flank of the seafloor topography. In Expt 7b, the northeast–southwest-tilted topography, which was an idealized representation of the real topography in Fig. 1, was used. In this case, the ICET was enhanced (red vectors in Fig. 13c) because the distance became short between the thick layer from the subtropical gyre (C in Fig. 8b) and the thin layer from the subarctic gyre (A in Fig. 7b) along the eastern flank of the topography. The maximum absolute velocity was 0.32 m s−1 at 42.47°N, 153.86°E.

The purpose of this study is to understand the basic dynamics of the Western Isoguchi Jet using an idealized model; therefore, an investigation of the factors deciding the strength of the Western Isoguchi Jet in more realistic situations is left to studies using more comprehensive models.

7. Summary and discussion

To understand the dynamics of the Western Isoguchi Jet, we conducted experiments with an idealized isopycnal two-layer model. A low-rise bottom topography across the boundary between the subtropical and subarctic gyres generated a jet, which is our model of the Western Isoguchi Jet along the eastern flank of the topography. The jet can be explained via baroclinic Rossby wave characteristics. The characteristic curves, along which the baroclinic Rossby waves propagate, were bent by an anticyclonic barotropic flow on the seafloor topography. The jet was formed where a strong pycnocline front formed because of the convergence of a characteristic curve originating in the subtropical gyre and one originating in the subpolar gyre.

Our results show that the bottom topography is important to generate the Western Isoguchi Jet even though the topography is about 500 m. Isoguchi et al. (2006) showed that the eastern Isoguchi jet (J2 in their paper) also flows along the eastern flank of a low-rise seafloor topography. The mechanism discussed in this paper may be applicable to the eastern Isoguchi jet. While Wagawa et al. (2014) found from their observations that the Western Isoguchi Jet was not collocated with the topographic slope, this does not mean that the topography is not important. The strong current in Fig. 3a is located next to the seafloor topography, not over the slope of the topography.

Eddies induce anticyclonic barotropic circulation on the seafloor topography. Even a small change in depth can produce a closed contour of the ambient potential vorticity in high latitudes compared to low latitudes because of the large Coriolis parameter and small planetary beta. Expt 3c (Fig. 8) demonstrated that an anticyclonic barotropic circulation occurs in such a place. Because observations show that eddies are active around the Western Isoguchi Jet (Itoh and Yasuda 2010; Maximenko et al. 2001; Wagawa et al. 2014), eddy-induced barotropic flow is likely to occur. In fact, the FRA–JCOPE2 reanalysis also shows anticyclonic barotropic transport of approximately 30 Sv on the seafloor topography (Mitsudera et al. 2018). As pointed out by Wagawa et al. (2014), the northeastward Western Isoguchi Jet is opposite a southwestward flow expected as an eddy-driven flow (shallower region on its right). Our result shows that the eddy-driven barotropic flow indirectly causes the Western Isoguchi Jet by bending characteristic curves.

As shown in section 6, the generation of the anticyclonic barotropic transport on the seafloor topography, and therefore the Western Isoguchi Jet, is sensitive to physical parameters. This sensitivity might explain why the Western Isoguchi Jet has not appeared in some models [e.g., Fig. 7 of Nonaka et al. (2006) using the Ocean General Circulation Model for the Earth Simulator]. However, it is beyond the current study to determine which parameters decide realistic conditions in more comprehensive models.

Our study showed that the low-rise seafloor topography enhances close contact between the subtropical and subarctic oceans. Using a high-resolution numerical model, Hurlburt et al. (1996) reproduced a realistic distance between the Subarctic Front and the Kuroshio Extension. They showed that the Subarctic Front dipped farther south and that the Kuroshio Extension extended farther north in simulations with realistic topography than that in simulations with a flat bottom. Our results explain the dynamics of the southward dip of the Subarctic Front. As a result of the close contact at the Western Isoguchi Jet, water exchange between the subtropical and subarctic ocean occurs easily. In fact, from observations, Isoguchi et al. (2006) and Wagawa et al. (2014) showed that mixing between waters from the subtropical and subarctic oceans occurs as water flows through the Western Isoguchi Jet.

An understanding of the dynamics of the Western Isoguchi Jet could also be important for air–sea interactions through the SST front. It is known that part of the Subarctic Front is quasi-stationary (Sugimoto et al. 2014) while the movement of the Subarctic Front induces anomalous atmospheric circulations in the Northern Hemisphere spanning from the western Pacific to North America and even to western Europe (Frankignoul et al. 2011). The dynamics proposed in this study explain the reason for this quasi-stationary behavior. Therefore, this study suggests the importance of the low-rise bottom topography in controlling the SST front. While the location is quasi-stationary, the strength of the Western Isoguchi Jet and the associated SST front varies interannually (Isoguchi et al. 2006; Sugimoto et al. 2014; Wagawa et al. 2014). Mitsudera et al. (2018) showed that frontal-scale SST variations in the western subarctic Pacific depend significantly on the strength of the warm quasi-stationary jet. The dynamics of the Western Isoguchi Jet variability is a topic of our ongoing studies.

Acknowledgments

This work is a part of the Japan Coastal Ocean Predictability Experiment (JCOPE) promoted by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC). This study is financially supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan, Grants-in-Aid for Scientific Research (A) 26247076. This study was also partly supported by the Grant for Joint Research Program of the Institute of Low Temperature Science, Hokkaido University, 16-39. The authors thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

APPENDIX A

Baroclinic Rossby Wave Characteristics in the Presence of Bottom Topography

The aim of appendix A is to derive characteristic curves [Eq. (2)] from a two-layer quasigeostrophic equation. Governing equations for the baroclinic and barotropic streamfunctions are derived in appendix A, section a. Appendix A, section b, yields an approximate formula using a scaling that represents long baroclinic Rossby waves. In appendix A, section c, the free propagation of baroclinic Rossby waves in the presence of topography is discussed from the point of view of characteristics. The role of recirculation on the characteristic curves is also discussed briefly. Appendix A, section d, presents forced baroclinic Rossby waves and associated characteristic curves in the presence of topography. Appendix A, section e, gives a summary.

a. Governing equations for baroclinic and barotropic streamfunctions

We start with a dimensional, two-layer quasigeostrophic equation on a β plane [e.g., (3.3.1) and (3.3.2) of Pedlosky 1996]:
eaa1a
eab1b
where ψ1 and ψ2 are streamfunctions of the upper and the lower layers, respectively; γ is the reduced gravity; wE denotes the Ekman pumping; Zb denotes bottom topography; and f0 is the Coriolis parameter. The terms H1 and H2 denote upper- and lower-layer thicknesses, respectively. Define
eq1
where HT = H1 + H2 and hence
eq2
Substituting these ψ1 and ψ2 into (A1a) and (A1b), we finally obtain, for the evolution of ψc:
eaa2a
where
eab2b
and
ea3
For the evolution of ψT, we obtain
eaa4a
where
eab4b

b. Scaling with respect to long baroclinic Rossby waves

We pay attention to the evolution of long baroclinic Rossby waves over bottom topography. The variables are decomposed as
eq3
where an overbar denotes a long-term mean, and a prime denotes deviations. Although we will discuss a long-term mean field associated with characteristic curves, the time derivative is retained in the following formulations for the sake of physical interpretation from the point of view of baroclinic Rossby waves.
Taking account of the propagation of long baroclinic Rossby waves whose phase speed is , variables are then nondimensionalized as follows:
eq4
eq5
eq6
where the asterisk denotes nondimensional variables. Here, L is a typical length of topography, U is a typical barotropic current speed, W is a typical Ekman pumping velocity, and δ is a typical ratio between the topographic height and the total depth of the ocean. As for eddies, a typical length may be represented by Rd if eddies are produced by baroclinic instability, so that
eq7
where κ represents the intensity of eddies. Then the nondimensional equations for may be written as
eq8
where
eq9
eq10
eq11
and the parameters are defined by
eq12
Here, we consider a barotropic flow U whose speed is similar to the phase speed of long baroclinic Rossby waves. Numerical results in appendix A, sections c and d, in this paper indicate that this velocity scaling is appropriate. Hence, we put , which yields
eq13
Now, these parameters are evaluated with respect to the model configuration in appendix A, section b, where we take L = 200 km and the height of topography ||Zb|| = 500 m so that topographic slope is properly scaled. Since the dimensional internal Rossby deformation radius Rd is about 20 km in the present configuration, we obtain
eq14
The above scaling argument implies that the terms with and are negligible since their magnitude is O(10−2). Therefore, we obtain
ea5
where
ea7
for the evolution of long baroclinic Rossby waves. Note that the elliptic terms are dropped because of this scaling.
Similarly, with the time scale of the baroclinic Rossby waves , develops according to
eq15
where
eq16
eq17
Neglecting the terms with respect to and , we finally obtain
ea8
where
ea9
ea10
In Eq. (A9), the barotropic relative vorticity term in the potential vorticity is negligible because of small .

A set of Eqs. (A5)(A10) represents long baroclinic Rossby waves in the presence of topography. In the following sections, these equations are further reduced considering the effects of topography.

c. Characteristics for free baroclinic Rossby waves over topography without external forcing

1) Free baroclinic Rossby waves over topography
In this section, we show that Eqs. (A5)(A10) represent baroclinic Rossby waves in which the vertical structure is modified by the effect of topography . Since the free waves are considered here, the forcing terms , , and are removed from Eqs. (A5) to (A10). This also implies that there are no steady barotropic flows driven by and . The coupled evolution equation for the free baroclinic Rossby waves over topography becomes
eaa11a
eab11b
from Eqs. (A5) and (A8) with , , and . The terms on the RHS of Eqs. (A11a) and (A11b) represent coupling between and through topography.

Here, we consider modification of free baroclinic Rossby waves by the effects of topography. Suppose a baroclinic wave whose basic structure is represented by . Then, a barotropic correction is generated responding to through the term on the RHS of Eq. (A11b); this term is called the joint effect of baroclinicity and bottom relief (JEBAR).

Suppose an arbitrary that satisfies at the boundary of the domain. Integrating Eq. (A11b) along an isoline of from the boundary, we obtain a JEBAR correction such that
ea12
where is the coordinate parallel (perpendicular) to the contour; corresponds to over a flat bottom.
To understand the effects of bottom topography, we first consider a plane wave over a constant slope ( are constants) so that = is constant, where is a wavenumber vector, is a frequency, and is the position vector or . Then, Eq. (A12) yields
ea13
where is the component of the wavenumber vector. For a flat bottom, because corresponds to and , indicating that the JEBAR correction does not occur as expected. The JEBAR correction increases as the slope increases because the absolute value of the second term on the RHS of Eq. (A13) decreases. If the slope becomes sufficiently steep where , then , and therefore,
eq18
irrespective of the value of ϵ. The lower-layer motion decreases to 0 in this case because
eq19
while the motion is concentrated on the upper layer, that is, . Thus, the JEBAR tends to cause the decoupling between the upper- and the lower-layer motions in the presence of steep topography for any ϵ, which is consistent with previous studies (e.g., Rhines 1970; Suginohara 1981; Tailleux and McWilliams 2001). As a result, scales with ϵ from Eq. (A13) irrespective of the steepness of the slope. This implies that the lower-layer motion is always small as long as ϵ ≪ 1.
With the above considerations, we assume ϵ ≪ 1 so that of Eq. (A12), that is, the JEBAR correction, is evaluated to be O(ϵ) ≪ 1 for any . We may thus take = O(1) with ϵ ≪ 1. In the present model setting, since H1 = 500 m, ||Zb|| = 500 m, HT = 5000 m, and , we obtain
eq20
which is relevant to the scaling of the ICET in the subarctic North Pacific Ocean.
Consequently, we obtain the evolution equation for the free baroclinic Rossby waves by substituting Eq. (A12) into Eq. (A11a) such that
ea14
to the lowest order in terms of ϵ, where
eq21
and
ea15
The term in Eq. (A15) represents characteristic curves for the free baroclinic Rossby waves in the presence of bottom topography. This indicates that the waves propagate zonally, having little influence from a rise even if its slope is steep .
2) Recirculation caused by closed contours and its influence on characteristic curves
If contours are closed, another free solution occurs from the barotropic vorticity equation (A11b):
eq22
where denotes a barotropic streamfunction on a closed contour, and the subscript “recirc” denotes the recirculation. This yields a recirculation solution where contours are parallel to closed contours, that is,
eq23
It is well known that barotropic PV inside the recirculation tends to be diffused and homogenized (e.g., Bretherton and Haidvogel 1976; Waterman and Jayne 2011). In this case, the barotropic relative vorticity term should be retained in , so that
eq24
Since the relative vorticity term is O(1) in the recirculation, scales with unity, and hence, the dimensional barotropic flow speed Urecirc scales with βL2. Note that Urecirc is much larger than . That is, the barotropic speed inside the closed contours tends to be much greater than that outside.
In conjunction with , inside the recirculation (denoted as ) that includes relative vorticity terms yields
eq25
where the O(ϵ) terms are dropped. The third term on the RHS of is as large as , corresponding to the large barotropic speed scaling with Urecirc.

Comparing inside the recirculation with [Eq. (A15)] outside, there is a large jump of the order of between the two. Because of this large jump, the westward propagation of baroclinic Rossby waves is blocked by the recirculation; the incident waves then propagate along the periphery of the recirculation where the large jump occurs. Therefore, the characteristic curves cannot enter the recirculation gyre but avoid it. The same discussion is applicable to recirculation gyres over a flat bottom, although the length scale may be smaller than the topographic scale L. To sum up, we pay attention to characteristic curves in the area outside closed contours, where the barotropic flow speed scales with .

d. Baroclinic Rossby wave characteristics over topography with external forcing

As discussed in the previous section, a strong barotropic recirculation may be generated inside closed contours, while the barotropic flow scaling with is expected on open contours surrounding the recirculation. Specific solutions should be discussed with respect to the forcing terms , , and included in Eqs. (A5)(A10). As for the present numerical solutions, an anticyclonic circulation is driven by eddies over the seafloor elevation (Fig. 8), whose barotropic speed Urecirc is ~0.1 m s−1 inside the closed contours of (dimensional) ; Urecirc is much larger than ~0.01 m s−1. Therefore, baroclinic Rossby waves cannot enter the recirculation over topography but propagate outside the recirculation where the barotropic speed scales with [or in the nondimensional form]. Consequently, it is the barotropic flow on open contours that deforms the characteristic curves of baroclinic Rossby waves over topography. Strong barotropic flows are also seen in recirculation gyres on the flat bottom area (Fig. 4a), which deform the characteristic curves around the gyres. Besides, barotropic flows are generated by winds according to Eq. (A8), which yields the Sverdrup balance for the flat bottom. The wind-driven barotropic flow deforms the characteristic curves as well (e.g., Pedlosky 1996).

In this study, we consider that the barotropic flow caused by eddies and wind is an ambient parameter with respect to the propagation of long baroclinic Rossby waves. In this respect, the characteristic curves, shown later in Eq. (A20), are regarded as a diagnostic tool to examine the propagation of long baroclinic Rossby waves for a given ambient barotropic flow of the order of unity.

Consequently, in conjunction with the JEBAR term (A12), we obtain the barotropic streamfunction
ea16
Substituting Eq. (A16) into Eqs. (A5) and (A6), we obtain
ea17
to the lowest order of ε, where characteristic curves for baroclinic Rossby waves are represented by
ea18
and we recall

The RHS of Eq. (A17) represents the forcing terms. The first term denotes the Ekman pumping. The second term represents the eddy forcing given by Eq. (A7), in which corresponds to the divergence of eddy thickness flux, and other terms represent the divergence of eddy vorticity flux. The third term represents the influence of the barotropic flow over topography. This term causes elevation of the density interface when the ambient barotropic flow rides over the bottom elevation .

e. Summary

Equations (A17) and (A18) represent the propagation of long baroclinic Rossby waves in the presence of barotropic flow and topography in a nondimensional form. Here, we present a dimensional form as a summary. Considering the scaling given in appendix A, section b, the dimensional form of Eqs. (A17) and (A18) yields
ea19
where with
ea20
and denotes a dimensional, ambient barotropic streamfunction, rewritten from ; is defined by , where is the depth-averaged ambient velocity. Here, of Eq. (A20) corresponds to Qc of Eq. (2) in the text. Isolines of represent dimensional characteristic curves, where the first term on the RHS denotes westward propagation of baroclinic Rossby waves, and the second term represents advection by the ambient barotropic flow. In the present study, we take as a given parameter and consider that a set of Eqs. (A19) and (A20) is a diagnostic tool to examine the propagation of long baroclinic Rossby waves for a known ambient barotropic flow.

APPENDIX B

Integration along Characteristic Curves

To demonstrate how characteristic curves affect layer thickness, integration along characteristic curves was conducted.

The layer-1 thickness h and the baroclinic streamfunction ψc has the relation [Eq. (3.2.15) of Pedlosky 1996]
eb1
Therefore, Eq. (A19) can be converted to the equation for h:
eb2
The third term on the RHS is the effect of eddies. Because this term is a difficult term to quantify, we simplified it to a Newtonian dissipation term, −μh. Integration along the Rossby wave characteristics with a Newtonian dissipation term has been widely used to understand wind-driven circulations (e.g., Qiu 2002; Schneider et al. 2002). Thus, Eq. (B2) becomes
eb3

Equation (B3) was integrated along characteristic curves from the eastern model boundary. The 6-yr e-folding time scale [the value used in Qiu (2002) and Kuroda et al. (2015) for the western Pacific Subarctic Gyre] was used for μ. The initial value for h at the eastern boundary was taken from h in the numerical model. The integration was conducted only along open characteristic curves. The quantification on the closed curves needs further theoretical developments and is beyond the scope of this study. The result of the integration in the control run on every 0.1 × 10−5 s−1 interval of the characteristic curves is shown in Fig. 5b.

The parameterization using the Newtonian dissipation is a rough parameterization of the eddy effect. Also, the assumption of the constant value for μ, which should vary in space, is likely to be too simple. In fact, the value obtained by the integration (colors in Fig. 5b) did not exactly match with the value in the model (colors in Fig. 5a). Despite these difficulties of the quantification, the purpose of Fig. 5b is to show how the distorted characteristic curve produced the strong gradient of the layer thickness along the eastern flank of the bottom topography. To show the robustness of the existence of the layer thickness gradient, Figs. B1a and B1b show the results of the integration using μ of 2-yr e-folding time scale (strong dissipation) and 0 (no dissipation), respectively. In either case, the gradient of the layer thickness along the eastern flank of the bottom topography existed although the quantitative strength of the gradient varied. Understanding and quantification of the role of eddies is a subject of future studies.

Fig. B1.
Fig. B1.

The layer thickness anomaly (colors; m) integrated along the open characteristic curves of every 0.1 × 10−5 s−1 interval of the control run (Expt 1). (a) With μ of 2-yr e-folding time scale. (b) With μ of 0.

Citation: Journal of Physical Oceanography 48, 4; 10.1175/JPO-D-17-0086.1

In Fig. 11, the results of the integrations for the sensitivity experiments are shown. For Expts 4a (Fig. 11a) and 4b (Fig. 11b), μ was decreased by factors of 5 and 50, respectively, corresponding to the decreases of eddies caused by the increase of the viscosities. Although there is not a solid quantitative base for these decreases of μ, the reduced μ values were qualitatively used to show the effects of the reduced eddies in Figs. 11a and 11b.

There are some more limitations of the characteristic curves. First, the integration can be conducted only along open characteristic curves. As shown in the discussion of the barotropic recirculation in appendix A, section c, the dynamics of the closed contours (e.g., around C in Fig. 4; around A in Fig. B1), where the barotropic relative vorticity term should be retained, is different from that assumed for the Eq. (B3). Because we are interested in how the wind-forced Rossby wave propagates along the open characteristic curve, we focus on the open characteristic curves.

Second, the quantification along the characteristic curve past the western boundary (e.g., around B in Fig. B1) is likely to be unrealistic because the role of eddies in the western boundary current cannot be simply expressed by −μh in the same way as the interior ocean. The long-wave approximation that used to derive Eq. (B3) also fails in the western boundary current.

Third, in the same manner as the western boundary, quantification on the characteristic curves past the ICET (at C in Fig. B1) is likely to be unrealistic because nonlinearity becomes importance once the jet is generated. While past studies (Dewar 1991, 1992; Furue et al. 2009, 2007; McCreary et al. 2002) showed that convergence or intersection of characteristic curves can generate a jet in the interior ocean, they also showed that characteristic curves break down at the jet. This limitation, as well as the limitation caused by the western boundary, is likely to be the cause of the overestimation of the gradient of the layer thickness in Fig. 5b compared with Fig. 5a along the western flank of the seafloor topography (around D in Fig. B1). The generation mechanism of the jet using the characteristic curves is only applicable when the strong convergence of the characteristic curves first occurs (at C in Fig. B1).

REFERENCES

  • Adcock, S. T., and D. P. Marshall, 2000: Interactions between geostrophic eddies and the mean circulation over large-scale bottom topography. J. Phys. Oceanogr., 30, 32233238, https://doi.org/10.1175/1520-0485(2000)030<3223:IBGEAT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bleck, R., 2002: An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates. Ocean Modell., 4, 5588, https://doi.org/10.1016/S1463-5003(01)00012-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bozec, A., 2013: HYCOM for dummies: How to create a double gyre configuration with HYCOM from scratch? Florida State University Center for Ocean-Atmospheric Prediction Studies Rep., 20 pp., http://hycom.org/attachments/349_BB86_for_dummies.pdf.

  • Bretherton, F. P., and D. B. Haidvogel, 1976: Two-dimensional turbulence above topography. J. Fluid Mech., 78, 129154, https://doi.org/10.1017/S002211207600236X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chelton, D. B., M. G. Schlax, and R. M. Samelson, 2011: Global observations of nonlinear mesoscale eddies. Prog. Oceanogr., 91, 167216, https://doi.org/10.1016/j.pocean.2011.01.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dewar, W. K., 1991: Arrested fronts. J. Mar. Res., 49, 2152, https://doi.org/10.1357/002224091784968576.

  • Dewar, W. K., 1992: Spontaneous shocks. J. Phys. Oceanogr., 22, 505522, https://doi.org/10.1175/1520-0485(1992)022<0505:Ss>2.0.Co;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frankignoul, C., N. Sennéchael, Y.-O. Kwon, and M. A. Alexander, 2011: Influence of the meridional shifts of the Kuroshio and the Oyashio Extensions on the atmospheric circulation. J. Climate, 24, 762777, https://doi.org/10.1175/2010JCLI3731.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Furue, R., J. P. McCreary Jr., Z. Yu, and D. Wang, 2007: Dynamics of the southern Tsuchiya jet. J. Phys. Oceanogr., 37, 531553, https://doi.org/10.1175/jpo3024.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Furue, R., J. P. McCreary Jr., and D. Wang, 2009: Dynamics of the northern Tsuchiya jet. J. Phys. Oceanogr., 39, 20242051, https://doi.org/10.1175/2009jpo4065.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Greatbatch, R. J., and G. Li, 2000: Alongslope mean flow and an associated upslope bolus flux of tracer in a parameterization of mesoscale turbulence. Deep-Sea Res. I, 47, 709735, https://doi.org/10.1016/S0967-0637(99)00078-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haidvogel, D. B., J. C. McWilliams, and P. R. Gent, 1992: Boundary current separation in a quasigeostrophic, eddy-resolving ocean circulation model. J. Phys. Oceanogr., 22, 882902, https://doi.org/10.1175/1520-0485(1992)022<0882:BCSIAQ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holland, W. R., and P. B. Rhines, 1980: An example of eddy-induced ocean circulation. J. Phys. Oceanogr., 10, 10101031, https://doi.org/10.1175/1520-0485(1980)010<1010:AEOEIO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holloway, G., 1978: A spectral theory of nonlinear barotropic motion above irregular topography. J. Phys. Oceanogr., 8, 414427, https://doi.org/10.1175/1520-0485(1978)008<0414:ASTONB>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hurlburt, H. E., A. J. Wallcraft, W. J. Schmitz, P. J. Hogan, and E. J. Metzger, 1996: Dynamics of the Kuroshio/Oyashio Current System using eddy-resolving models of the North Pacific Ocean. J. Geophys. Res., 101, 941976, https://doi.org/10.1029/95JC01674.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Isoguchi, O., H. Kawamura, and E. Oka, 2006: Quasi-stationary jets transporting surface warm waters across the transition zone between the subtropical and the subarctic gyres in the North Pacific. J. Geophys. Res., 111, C10003, https://doi.org/10.1029/2005JC003402.

    • Search Google Scholar
    • Export Citation
  • Itoh, S., and I. Yasuda, 2010: Characteristics of mesoscale eddies in the Kuroshio–Oyashio Extension region detected from the distribution of the sea surface height anomaly. J. Phys. Oceanogr., 40, 10181034, https://doi.org/10.1175/2009JPO4265.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Iwao, T., M. Endoh, N. Shikama, and T. Nakano, 2003: Intermediate circulation in the northwestern North Pacific derived from subsurface floats. J. Oceanogr., 59, 893904, https://doi.org/10.1023/B:JOCE.0000009579.86413.eb.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437471, https://doi.org/10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kida, S., and Coauthors, 2015: Oceanic fronts and jets around Japan: A review. J. Oceanogr., 71, 469497, https://doi.org/10.1007/s10872-015-0283-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuroda, H., T. Wagawa, Y. Shimizu, S.-I. Ito, S. Kakehi, T. Okunishi, S. Ohno, and A. Kusaka, 2015: Interdecadal decrease of the Oyashio transport on the continental slope off the southeastern coast of Hokkaido, Japan. J. Geophys. Res. Oceans, 120, 25042522, https://doi.org/10.1002/2014JC010402.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, Z., 1997: The influence of stratification on the inertial recirculation. J. Phys. Oceanogr., 27, 926940, https://doi.org/10.1175/1520-0485(1997)027<0926:TIOSOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., M. N. Koshlyakov, Y. A. Ivanov, M. I. Yaremchuk, and G. G. Panteleev, 2001: Hydrophysical experiment “Megapolygon-87” in the northwestern Pacific subarctic frontal zone. J. Geophys. Res., 106, 1414314163, https://doi.org/10.1029/2000JC000436.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McCreary, J. P., Jr., P. Lu, and Z. Yu, 2002: Dynamics of the Pacific Subsurface Countercurrents. J. Phys. Oceanogr., 32, 23792404, https://doi.org/10.1175/1520-0485(2002)032<2379:DOTPSC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Milliff, R. F., J. Morzel, D. B. Chelton, and M. H. Freilich, 2004: Wind stress curl and wind stress divergence biases from rain effects on QSCAT surface wind retrievals. J. Atmos. Oceanic Technol., 21, 12161231, https://doi.org/10.1175/1520-0426(2004)021<1216:WSCAWS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mitsudera, H., K. Uchimoto, and T. Nakamura, 2011: Rotating stratified barotropic flow over topography: Mechanisms of the cold belt formation off the Soya Warm Current along the northeastern coast of Hokkaido. J. Phys. Oceanogr., 41, 21202136, https://doi.org/10.1175/2011JPO4598.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mitsudera, H., and Coauthors, 2018: Low ocean-floor rises regulate subpolar sea surface temperature by forming baroclinic jets. Nat. Commun., 9, 1190, https://doi.org/10.1038/s41467-018-03526-z.

    • Crossref
    • Export Citation
  • Miyazawa, Y., and Coauthors, 2009: Water mass variability in the western North Pacific detected in a 15-year eddy resolving ocean reanalysis. J. Oceanogr., 65, 737756, https://doi.org/10.1007/s10872-009-0063-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nakano, H., and H. Hasumi, 2005: A series of zonal jets embedded in the broad zonal flows in the Pacific obtained in eddy-permitting ocean general circulation models. J. Phys. Oceanogr., 35, 474488, https://doi.org/10.1175/JPO2698.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nakano, H., H. Tsujino, and R. Furue, 2008: The Kuroshio Current System as a jet and twin “relative” recirculation gyres embedded in the Sverdrup circulation. Dyn. Atmos. Oceans, 45, 135164, https://doi.org/10.1016/j.dynatmoce.2007.09.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Niiler, P. P., N. A. Maximenko, G. G. Panteleev, T. Yamagata, and D. B. Olson, 2003: Near-surface dynamical structure of the Kuroshio Extension. J. Geophys. Res., 108, 3193, https://doi.org/10.1029/2002JC001461.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nishigaki, H., and H. Mitsudera, 2012: Subtropical western boundary currents over slopes detaching from coasts with inshore pool regions: An indication to the Kuroshio nearshore path. J. Phys. Oceanogr., 42, 306320, https://doi.org/10.1175/JPO-D-11-076.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nonaka, M., H. Nakamura , Y. Tanimoto, T. Kagimoto, and H. Sasaki, 2006: Decadal variability in the Kuroshio–Oyashio Extension simulated in an eddy-resolving OGCM. J. Climate, 19, 19701989, https://doi.org/10.1175/JCLI3793.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1996: Ocean Circulation Theory. Springer, 456 pp.

    • Crossref
    • Export Citation
  • Qiu, B., 2002: Large-scale variability in the midlatitude subtropical and subpolar North Pacific Ocean: Observations and causes. J. Phys. Oceanogr., 32, 353375, https://doi.org/10.1175/1520-0485(2002)032<0353:LSVITM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rhines, P., 1970: Edge‐, bottom‐, and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn., 1, 273302, https://doi.org/10.1080/03091927009365776.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rhines, P., 1977: The dynamics of unsteady currents. Marine Modeling, E. D. Goldberg et al., Eds., The Sea—Ideas and Observations on Progress in the Study of the Seas, Vol. 6, John Wiley and Sons, 189–318.

  • Richards, K. J., N. A. Maximenko, F. O. Bryan, and H. Sasaki, 2006: Zonal jets in the Pacific Ocean. Geophys. Res. Lett., 33, L03605, https://doi.org/10.1029/2005GL024645.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schneider, N., A. J. Miller, and D. W. Pierce, 2002: Anatomy of North Pacific decadal variability. J. Climate, 15, 586605, https://doi.org/10.1175/1520-0442(2002)015<0586:AONPDV>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smirnov, D., M. Newman, M. A. Alexander, Y.-O. Kwon, and C. Frankignoul, 2015: Investigating the local atmospheric response to a realistic shift in the Oyashio Sea surface temperature front. J. Climate, 28, 11261147, https://doi.org/10.1175/JCLI-D-14-00285.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sue, Y., and A. Kubokawa, 2015: Latitude of eastward jet prematurely separated from the western boundary in a two-layer quasigeostrophic model. J. Phys. Oceanogr., 45, 737754, https://doi.org/10.1175/JPO-D-13-058.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sugimoto, S., N. Kobayashi, and K. Hanawa, 2014: Quasi-decadal variation in intensity of the western part of the winter subarctic SST front in the western North Pacific: The influence of Kuroshio Extension path state. J. Phys. Oceanogr., 44, 27532762, https://doi.org/10.1175/JPO-D-13-0265.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Suginohara, N., 1981: Quasi-geostrophic waves in a stratified ocean with bottom topography. J. Phys. Oceanogr., 11, 107115, https://doi.org/10.1175/1520-0485(1981)011<0107:QGWIAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, S., L. Wu, and B. Qiu, 2013: Response of the inertial recirculation to intensified stratification in a two-layer quasigeostrophic ocean circulation model. J. Phys. Oceanogr., 43, 12541269, https://doi.org/10.1175/JPO-D-12-0111.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Taguchi, B., H. Nakamura, M. Nonaka, N. Komori, A. Kuwano-Yoshida, K. Takaya, and A. Goto, 2012: Seasonal evolutions of atmospheric response to decadal SST anomalies in the North Pacific subarctic frontal zone: Observations and a coupled model simulation. J. Climate, 25, 111139, https://doi.org/10.1175/JCLI-D-11-00046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tailleux, R., and J. C. McWilliams, 2001: The effect of bottom pressure decoupling on the speed of extratropical, baroclinic Rossby waves. J. Phys. Oceanogr., 31, 14611476, https://doi.org/10.1175/1520-0485(2001)031<1461:TEOBPD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Treguier, A. M., 1989: Topographically generated steady currents in barotropic turbulence. Geophys. Astrophys. Fluid Dyn., 47, 4368, https://doi.org/10.1080/03091928908221816.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wagawa, T., S.-I. Ito, Y. Shimizu, S. Kakehi, and D. Ambe, 2014: Currents associated with the quasi-stationary jet separated from the Kuroshio Extension. J. Phys. Oceanogr., 44, 16361653, https://doi.org/10.1175/JPO-D-12-0192.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, J., M. A. Spall, G. R. Flierl, and P. Malanotte-Rizzoli, 2012: A new mechanism for the generation of quasi-zonal jets in the ocean. Geophys. Res. Lett., 39, L10601, https://doi.org/10.1029/2012GL051861.

    • Search Google Scholar
    • Export Citation
  • Waterman, S., and S. R. Jayne, 2011: Eddy-mean flow interactions in the along-stream development of a western boundary current jet: An idealized model study. J. Phys. Oceanogr., 41, 682707, https://doi.org/10.1175/2010JPO4477.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
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