Article Type:
Research Article

Stability of a Two-Layer Quasigeostrophic Vortex over Axisymmetric Localized Topography

E. S. Benilov Department of Mathematics, University of Limerick, Limerick, Ireland

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Print Publication:
01 Jan 2005
DOI:
https://doi.org/10.1175/JPO-2660.1
Page(s):
123–130
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Abstract

The stability of a quasigeostrophic vortex over a radially symmetric topographic feature (elevation or depression) in a two-layer ocean on the f plane is examined. This article’s concern is with compensated vortices, that is, those in which the lower layer is at rest (the disturbances, however, are present in both layers). Through numerical solution of the linear normal-mode problem, it is demonstrated that a bottom elevation is a stabilizing influence for a cyclone and a destabilizing influence for an anticyclone, whereas a bottom depression acts in the opposite way. These conclusions are interpreted using an asymptotic theory developed for the case of a thin upper layer. It is demonstrated that an elevation moves the critical level of an unstable mode toward the periphery of the cyclone, which leads to its stabilization. Estimates based on realistic oceanic parameters show that stabilization occurs for relatively small topography (5%–15% of the lower layer’s depth).

Corresponding author address: Eugene Benilov, Department of Mathematics, University of Limerick, Limerick, Ireland. Email: eugene.benilov@ul.le

Abstract

The stability of a quasigeostrophic vortex over a radially symmetric topographic feature (elevation or depression) in a two-layer ocean on the f plane is examined. This article’s concern is with compensated vortices, that is, those in which the lower layer is at rest (the disturbances, however, are present in both layers). Through numerical solution of the linear normal-mode problem, it is demonstrated that a bottom elevation is a stabilizing influence for a cyclone and a destabilizing influence for an anticyclone, whereas a bottom depression acts in the opposite way. These conclusions are interpreted using an asymptotic theory developed for the case of a thin upper layer. It is demonstrated that an elevation moves the critical level of an unstable mode toward the periphery of the cyclone, which leads to its stabilization. Estimates based on realistic oceanic parameters show that stabilization occurs for relatively small topography (5%–15% of the lower layer’s depth).

Corresponding author address: Eugene Benilov, Department of Mathematics, University of Limerick, Limerick, Ireland. Email: eugene.benilov@ul.le

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  • Baey, J. M., and X. Carton, 2002: Vortex multipoles in two-layer rotating shallow-water flows. J. Fluid Mech., 460 , 151–175.

  • Benilov, E. S., 2003: Instability of quasigeostrophic vortices in a two-layer ocean with thin upper layer. J. Fluid Mech., 475 , 303–331.

    • Search Google Scholar
    • Export Citation

  • Benilov, E. S., 2004: Stability of vortices in a two-layer ocean with uniform potential vorticity in the lower layer. J. Fluid Mech., 502 , 207–232.

    • Search Google Scholar
    • Export Citation

  • Benilov, E. S., D. Broutman, and E. P. Kuznetsova, 1998: On the stability of large-amplitude vortices in a continuously stratified fluid on the f-plane. J. Fluid Mech., 355 , 139–162.

    • Search Google Scholar
    • Export Citation

  • Carton, X. J., and J. C. McWilliams, 1989: Barotropic and baroclinic instabilities of axisymmetric vortices in a quasigeostrophic model. Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier Oceanography Series, Vol. 50, Elsevier, 225–244.

    • Search Google Scholar
    • Export Citation

  • Carton, X. J., and B. Legras, 1994: The life-cycle of the barotropic tripolar vortex. J. Fluid Mech., 267 , 53–82.

  • Dewar, W. K., and P. D. Killworth, 1995: On the stability of oceanic rings. J. Phys. Oceanogr., 25 , 1467–1487.

  • Flierl, G. R., 1988: On the instability of geostrophic vortices. J. Fluid Mech., 197 , 349–388.

  • Helfrich, K. R., and U. Send, 1988: Finite-amplitude evolution of two-layer geostrophic vortices. J. Fluid Mech., 197 , 331–348.

  • Ikeda, M., 1981: Instability and splitting of mesoscale rings using a two-layer quasi-geostrophic model on an f-plane. J. Phys. Oceanogr., 11 , 987–998.

    • Search Google Scholar
    • Export Citation

  • Katsman, C. A., P. C. F. Van der Vaart, H. A. Dijkstra, and W. P. M. de Ruijter, 2003: On the stability of multi-layer ocean vortices: A parameter study including realistic Gulf Stream and Agulhas rings. J. Phys. Oceanogr., 33 , 1197–1218.

    • Search Google Scholar
    • Export Citation

  • Killworth, P. D., J. R. Blundell, and W. K. Dewar, 1997: Primitive equation instability of wide oceanic rings. Part I: Linear theory. J. Phys. Oceanogr., 27 , 941–962.

    • Search Google Scholar
    • Export Citation

  • Lai, D. Y., and P. L. Richardson, 1977: Distribution and movement of Gulf Stream rings. J. Phys. Oceanogr., 7 , 670–683.

  • Mariotti, A., B. Legras, and D. G. Dritschel, 1994: Vortex stripping and the erosion of coherent structures in two-dimensional flows. Phys. Fluids, 6 , 3954–3962.

    • Search Google Scholar
    • Export Citation

  • McKiver, W. J., and D. G. Dritschel, 2003: The motion of a fluid ellipsoid in a general linear background flow. J. Fluid Mech., 474 , 147–173.

    • Search Google Scholar
    • Export Citation

  • Meacham, S. P., K. K. Pankratov, A. F. Shchepetkin, and V. V. Zhmur, 1994: The interaction of ellipsoidal vortices with background shear flows in a stratified fluid. Dyn. Atmos. Oceans, 21 , 167–212.

    • Search Google Scholar
    • Export Citation

  • Mied, R. P., A. D. Kirwan Jr., and G. J. Lindemann, 1992: Rotating modons over isolated topographic features. J. Phys. Oceanogr., 22 , 1569–1582.

    • Search Google Scholar
    • Export Citation

  • Nycander, J., and J. H. Lacasce, 2004: Stable and unstable vortices attached to seamounts. J. Fluid Mech., 507 , 71–94.

  • Olson, D. B., 1991: Rings in the ocean. Annu. Rev. Earth Planet. Sci., 19 , 283–311.

  • Reznik, G. M., 1999: On generation of sub-surface motions in stratified ocean over sloping bottom. Okeanologiya, 39 , 325–327.

  • Ripa, P., 1992: Instability of a solid-body rotating vortex in a two-layer model. J. Fluid Mech., 242 , 395–417.

  • Schecter, D. A., and M. T. Montgomery, 2003: On the symmetrization rate of an intense geophysical vortex. Dyn. Atmos. Oceans, 37 , 55–88.

    • Search Google Scholar
    • Export Citation

  • Schecter, D. A., M. T. Montgomery, and P. D. Reasor, 2001: A theory for the vertical alignment of a quasigeostrophic vortex. J. Atmos. Sci., 59 , 150–168.

    • Search Google Scholar
    • Export Citation

  • Sutyrin, G., 2001: Effects of topography on the beta-drift of a baroclinic vortex. J. Mar. Res., 59 , 977–989.

  • Swaters, G. E., 1998: Dynamics of radiating cold domes on a sloping bottom. J. Fluid Mech., 364 , 221–251.

  • Velasco Fuentes, O. U., and G. J. F. van Heijst, 1994: Experimental study of dipolar vortices on a topographic beta-plane. J. Fluid Mech., 259 , 79–106.

    • Search Google Scholar
    • Export Citation
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