Editorial Type:
Article
Article Type:
Research Article

Hysteresis of a Western Boundary Current Leaping across a Gap

Vitalii A. Sheremet Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Print Publication:
01 May 2001
DOI:
https://doi.org/10.1175/1520-0485(2001)031<1247:HOAWBC>2.0.CO;2
Page(s):
1247–1259
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Abstract

An idealized problem of a western boundary current of Munk thickness LM flowing across a gap in a ridge is considered using a single-layer depth-averaged approach. When the gap (of width 2a) is narrow, a ⩽ 3.12LM, viscous forces alone restrict penetration of the current through the gap. However, the gap is “leaky” in the linear case and some very weak flow still passes through. For larger gap width, the boundary current may leap across the gap due to inertia, characterized by the Reynolds number, completely choking off water exchange between the two basins. For a ≥ 4.55LM the flow may be in one of two regimes (penetrating or leaping) for the same parameters, depending on previous evolution. The penetrating branch solutions become unsteady with eddies forming west of the gap between the two counterflowing zonal jets. As the boundary current slowly accelerates, transition from the penetrating to leaping regime happens when the width of a zonal jet near the gap becomes comparable with a, implying the Reynolds number ReP ≅ (a/LM)3. On the other hand, as the boundary current slowly decelerates, the leaping regime persists while the meridional advection dominates the β effect in a wiggle of the current core within the gap, implying that the leaping regime breaks at ReL ≅ a/LM. Thus hysteresis occurs over the range of Reynolds numbers ReL < Re < ReP. This behavior is analogous to the well-known teapot effect.

Corresponding author address: Vitalii A. Sheremet, MS #21, Woods Hole Oceanographic Institution, Woods Hole, MA 02543.

Email: vsheremet@whoi.edu

Abstract

An idealized problem of a western boundary current of Munk thickness LM flowing across a gap in a ridge is considered using a single-layer depth-averaged approach. When the gap (of width 2a) is narrow, a ⩽ 3.12LM, viscous forces alone restrict penetration of the current through the gap. However, the gap is “leaky” in the linear case and some very weak flow still passes through. For larger gap width, the boundary current may leap across the gap due to inertia, characterized by the Reynolds number, completely choking off water exchange between the two basins. For a ≥ 4.55LM the flow may be in one of two regimes (penetrating or leaping) for the same parameters, depending on previous evolution. The penetrating branch solutions become unsteady with eddies forming west of the gap between the two counterflowing zonal jets. As the boundary current slowly accelerates, transition from the penetrating to leaping regime happens when the width of a zonal jet near the gap becomes comparable with a, implying the Reynolds number ReP ≅ (a/LM)3. On the other hand, as the boundary current slowly decelerates, the leaping regime persists while the meridional advection dominates the β effect in a wiggle of the current core within the gap, implying that the leaping regime breaks at ReL ≅ a/LM. Thus hysteresis occurs over the range of Reynolds numbers ReL < Re < ReP. This behavior is analogous to the well-known teapot effect.

Corresponding author address: Vitalii A. Sheremet, MS #21, Woods Hole Oceanographic Institution, Woods Hole, MA 02543.

Email: vsheremet@whoi.edu

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Journal of Physical Oceanography

  • Charney, J. G., 1955: The Gulf Stream as an inertial boundary layer. Proc. Natl. Acad. Sci.,41, 731–740.

  • Cleary, S. P., 1987: A generalized heat equation. M.S. thesis, Dept. of Mathematics, Michigan Technological University, Library Call Number LD3300.R1987 C623, 33 pp.

  • Farris, A., and M. Wimbush, 1996: Wind-induced Kuroshio intrusion into the South China Sea. J. Oceanogr.,52, 771–784.

  • Gill, A. E., and R. K. Smith, 1970: On similarity solutions of the differential equation ψzzzz + ψx = 0. Proc. Cambridge Philos. Soc.,67, 163–171.

  • Gilmore, R., 1981: Catastrophe Theory for Scientists and Engineers. J. Wiley, 666 pp.

  • Ierley, G. R., and W. R. Young, 1991: Viscous instabilities in the western boundary layer. J. Phys. Oceanogr.,21, 1323–1332.

  • ——, and V. A. Sheremet, 1995: Multiple solutions and advection-dominated flows in the wind-driven circulation. Part I: Slip. J. Mar. Res.,53, 703–737.

  • Kistler, S. F., and L. E. Scriven, 1994: The teapot effect: Sheet-forming flows with deflection, wetting and hysteresis. J. Fluid Mech.,263, 19–62.

  • Munk, W. H., 1950: On the wind-driven ocean circulation. J. Meteor.,7, 79–93.

  • Nitani, H., 1972: Beginning of the Kuroshio. Kuroshio: Its Physical Aspects, H. Stommel and K. Yoshida, Eds., University of Tokyo Press, 129–163.

  • Pedlosky, J., 1994: Ridges and recirculations: Gaps and jets. J. Phys. Oceanogr.,24, 2703–2707.

  • ——, and M. Spall, 1999: Rossby normal modes in basins with barriers. J. Phys. Oceanogr.,29, 2332–2349.

  • Qiu, B., D. A. Koh, C. Lumpkin, and P. Flament, 1997: Existence and formation mechanism of the North Hawaiian Ridge Current. J. Phys. Oceanogr.,27, 431–444.

  • Sheremet, V. A., G. R. Ierley, and V. M. Kamenkovich, 1997: Eigenanalysis of the two-dimensional wind-driven ocean circulation problem. J. Mar. Res.,55, 57–92.

  • Stommel, H., 1982: Is the South Pacific Helium-3 plume dynamically active? Earth Planet. Sci. Lett.,61, 63–67.

  • ——, and A. B. Arons, 1960: On the abyssal circulation of the World Ocean—I. Stationary planetary flow patterns on a sphere. Deep-Sea Res.,6, 140–154.

  • Vanden-Broeck, J.-M., and J. B. Keller, 1986: Pouring flows. Phys. Fluids,29, 3958–3962.

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