Editorial Type:
Article
Article Type:
Research Article

Stability of Baroclinic Vortices on the β Plane and Implications for Transport

M. V. Rudko Department of Ocean Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

Search for other papers by M. V. Rudko in
Current site
Google Scholar
PubMed Close
,
I. V. Kamenkovich Department of Ocean Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

Search for other papers by I. V. Kamenkovich in
Current site
Google Scholar
PubMed Close
, and
D. S. Nolan Department of Atmospheric Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

Search for other papers by D. S. Nolan in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Nov 2016
DOI:
https://doi.org/10.1175/JPO-D-16-0067.1
Page(s):
3245–3262
Restricted access

Abstract

This paper explores stability of and transport by baroclinic vortices on the β plane using a two-layer, quasigeostrophic model. The study adapts a wave–mean flow formalism and examines interactions between the axisymmetric flow (“the vortex”) and residuals (“the waves”). Unlike baroclinically unstable vortices on the f plane, such vortices on the β plane can be also vulnerable to barotropic instability as revealed by the globally integrated energy balance analysis. The spatial structure of energy fluxes shows the energy leakage inside the vortex core when its breakdown occurs. Mixing by stable and unstable vortical flows is quantified through the computation of finite-time Lyapunov exponent (FTLE) maps. Depending on the strength of wave radiation, the upper-layer FTLE maps of stable vortices show either an annulus or volute ring of vigorous mixing inside the vortex interior. This ring region is disrupted when the vortex becomes unstable. Both stable and unstable vortices show the wavy patterns of FTLE in the near and far fields. Despite the fact that the initial vortex resides in the top layer only, significant FTLE patterns are observed in the deep layer at later times. Lagrangian analysis of the vortex-induced change of large-scale tracer gradient demonstrates significant effects of vortex instability in the top layer and the importance of the wavelike anomalies in the bottom layer.

Denotes Open Access content.

Corresponding author address: M. V. Rudko, Department of Ocean Sciences, RSMAS, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. E-mail: mrudko@rsmas.miami.edu.

Abstract

This paper explores stability of and transport by baroclinic vortices on the β plane using a two-layer, quasigeostrophic model. The study adapts a wave–mean flow formalism and examines interactions between the axisymmetric flow (“the vortex”) and residuals (“the waves”). Unlike baroclinically unstable vortices on the f plane, such vortices on the β plane can be also vulnerable to barotropic instability as revealed by the globally integrated energy balance analysis. The spatial structure of energy fluxes shows the energy leakage inside the vortex core when its breakdown occurs. Mixing by stable and unstable vortical flows is quantified through the computation of finite-time Lyapunov exponent (FTLE) maps. Depending on the strength of wave radiation, the upper-layer FTLE maps of stable vortices show either an annulus or volute ring of vigorous mixing inside the vortex interior. This ring region is disrupted when the vortex becomes unstable. Both stable and unstable vortices show the wavy patterns of FTLE in the near and far fields. Despite the fact that the initial vortex resides in the top layer only, significant FTLE patterns are observed in the deep layer at later times. Lagrangian analysis of the vortex-induced change of large-scale tracer gradient demonstrates significant effects of vortex instability in the top layer and the importance of the wavelike anomalies in the bottom layer.

Denotes Open Access content.

Corresponding author address: M. V. Rudko, Department of Ocean Sciences, RSMAS, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149. E-mail: mrudko@rsmas.miami.edu.
Save
Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Beal, L. M., and Coauthors, 2011: On the role of the Agulhas system in ocean circulation and climate. Nature, 472, 429–436, doi:10.1038/nature09983.

    • Search Google Scholar
    • Export Citation

  • Benilov, E. S., 1999: On the advection of tracer by eddies on the beta-plane: A numerical study. Nonlinear Processes Geophys., 6, 67–77, doi:10.5194/npg-6-67-1999.

    • 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, doi:10.1017/S0022112003007547.

    • Search Google Scholar
    • Export Citation

  • Benilov, E. S., and J. D. Flanagan, 2008: The effect of ageostrophy on the stability of vortices in a two-layer ocean. Ocean Modell., 23, 49–58, doi:10.1016/j.ocemod.2008.03.004.

    • Search Google Scholar
    • Export Citation

  • Berloff, P., S. Karabasov, J. T. Farrar, and I. Kamenkovich, 2011: On latency of multiple zonal jets in the oceans. J. Fluid Mech., 686, 534–567, doi:10.1017/jfm.2011.345.

    • Search Google Scholar
    • Export Citation

  • Castelão, G. P., and W. E. Johns, 2011: Sea surface structure of North Brazil Current rings derived from shipboard and moored acoustic Doppler current profiler observations. J. Geophys. Res., 116, C01010, doi:10.1029/2010JC006575.

    • 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, 167–216, doi:10.1016/j.pocean.2011.01.002.

    • Search Google Scholar
    • Export Citation

  • Dewar, W. K., and G. R. Flierl, 1985: Particle trajectories and simple models of transport in coherent vortices. Dyn. Atmos. Oceans, 9, 215–252, doi:10.1016/0377-0265(85)90021-1.

    • Search Google Scholar
    • Export Citation

  • Dewar, W. K., and P. D. Killworth, 1995: On the stability of oceanic rings. J. Phys. Oceanogr., 25, 1467–1487, doi:10.1175/1520-0485(1995)025<1467:OTSOOR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Dewar, W. K., P. D. Killworth, and J. R. Blundell, 1999: Primitive-equation instability of wide oceanic rings. Part II: Numerical studies of ring stability. J. Phys. Oceanogr., 29, 1744–1758, doi:10.1175/1520-0485(1999)029<1744:PEIOWO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Dong, C., J. C. McWilliams, Y. Liu, and D. Chen, 2014: Global heat and salt transports by eddy movement. Nat. Commun., 5, 3294, doi:10.1038/ncomms4294.

    • Search Google Scholar
    • Export Citation

  • Farrell, B. F., and P. J. Ioannou, 1996: Generalized stability theory. Part II: Nonautonomous operators. J. Atmos. Sci., 53, 2041–2053, doi:10.1175/1520-0469(1996)053<2041:GSTPIN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Fiorino, M., and R. L. Elsberry, 1989: Some aspects of vortex structure related to tropical cyclone motion. J. Atmos. Sci., 46, 975–990, doi:10.1175/1520-0469(1989)046<0975:SAOVSR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Flierl, G. R., 1977: The application of linear quasigeostrophic dynamics to Gulf Stream rings. J. Phys. Oceanogr., 7, 365–379, doi:10.1175/1520-0485(1977)007<0365:TAOLQD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Flierl, G. R., 1988: On the instability of geostrophic vortices. J. Fluid Mech., 197, 349–388, doi:10.1017/S0022112088003283.

  • Flohr, P., and J. C. Vassilicos, 1997: Accelerated scalar dissipation in a vortex. J. Fluid Mech., 348, 295–317, doi:10.1017/S0022112097006927.

    • Search Google Scholar
    • Export Citation

  • Garraffo, Z. D., W. E. Johns, E. P. Chassignet, and G. Goni, 2003: North Brazil Current rings and transport of southern waters in a high resolution numerical simulation of the North Atlantic. Interhemispheric Water Exchange in the Atlantic Ocean, G. J. Goni and P. Malanotte-Rizzoli, Eds., Elsevier Oceanography Series, Vol. 68, 375–409, doi:10.1016/S0422-9894(03)80155-1.

  • Griffiths, R. W., and P. F. Linden, 1981: The stability of vortices in a rotating, stratified fluid. J. Fluid Mech., 105, 283–316, doi:10.1017/S0022112081003212.

    • Search Google Scholar
    • Export Citation

  • Haller, G., 2001: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Physica D, 149, 248–277, doi:10.1016/S0167-2789(00)00199-8.

    • Search Google Scholar
    • Export Citation

  • Helfrich, K. R., and U. W. Send, 1988: Finite-amplitude evolution of two-layer geostrophic vortices. J. Fluid Mech., 197, 331–348, doi:10.1017/S0022112088003271.

    • Search Google Scholar
    • Export Citation

  • 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, doi:10.1175/1520-0485(1981)011<0987:IASOMR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Jochum, M., and P. Malanotte-Rizzoli, 2003: On the generation of North Brazil Current rings. J. Mar. Res., 61, 147–173, doi:10.1357/002224003322005050.

    • Search Google Scholar
    • Export Citation

  • Johns, W. E., R. J. Zantopp, and G. J. Goni, 2003: Cross-gyre transport by North Brazil Current rings. Interhemispheric Water Exchange in the Atlantic Ocean, G. J. Goni and P. Malanotte-Rizzoli, Eds., Elsevier Oceanography Series, Vol. 68, 411–441, doi:10.1016/S0422-9894(03)80156-3.

  • Karrasch, D., and G. Haller, 2013: Do finite-size Lyapunov exponents detect coherent structures? Chaos, 23, 043126, doi:10.1063/1.4837075.

    • Search Google Scholar
    • Export Citation

  • Katsman, C. A., P. C. F. Van der Vaart, H. A. Dijkstra, and W. P. M. de Ruijter, 2003: Stability of multilayer ocean vortices: A parameter study including realistic Gulf Stream and Agulhas rings. J. Phys. Oceanogr., 33, 1197–1218, doi:10.1175/1520-0485(2003)033<1197:SOMOVA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Lapeyre, G., 2002: Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence. Chaos, 12, 688–698, doi:10.1063/1.1499395.

    • Search Google Scholar
    • Export Citation

  • Lehahn, Y., F. d’Ovidio, M. Lévy, Y. Amitai, and E. Heifetz, 2011: Long range transport of a quasi isolated chlorophyll patch by an Agulhas ring. Geophys. Res. Lett., 38, L16610, doi:10.1029/2011GL048588.

    • Search Google Scholar
    • Export Citation

  • McWilliams, J. C., and G. R. Flierl, 1979: On the evolution of isolated, nonlinear vortices. J. Phys. Oceanogr., 9, 1155–1182, doi:10.1175/1520-0485(1979)009<1155:OTEOIN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • McWilliams, J. C., P. R. Gent, and N. J. Norton, 1986: The evolution of balanced, low-mode vortices on the β-plane. J. Phys. Oceanogr., 16, 838–855, doi:10.1175/1520-0485(1986)016<0838:TEOBLM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Olson, D. B., 1991: Rings in the ocean. Annu. Rev. Earth Planet. Sci., 19, 283–311, doi:10.1146/annurev.ea.19.050191.001435.

  • Ottino, J. M., 1989: The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press, 364 pp.

  • Pedlosky, J., 1982: Geophysical Fluid Dynamics. Springer-Verlag, 636 pp.

  • Provenzale, A., 1999: Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech., 31, 55–93, doi:10.1146/annurev.fluid.31.1.55.

    • Search Google Scholar
    • Export Citation

  • Reznik, G. M., and W. K. Dewar, 1994: An analytical theory of distributed axisymmetric barotropic vortices on the β-plane. J. Fluid Mech., 269, 301–321, doi:10.1017/S0022112094001576.

    • Search Google Scholar
    • Export Citation

  • Rhines, P. B., and W. R. Young, 1983: How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech., 133, 133–145, doi:10.1017/S0022112083001822.

    • Search Google Scholar
    • Export Citation

  • Schonten, M. W., W. P. M. de Ruijter, P. J. van Leeuwen, and J. R. E. Lutjeharms, 2000: Translation, decay and splitting of Agulhas rings in the southeastern Atlantic Ocean. J. Geophys. Res., 105, 21 913–21 925, doi:10.1029/1999JC000046.

    • Search Google Scholar
    • Export Citation

  • Thivolle-Cazat, E., J. Sommeria, and M. Galmiche, 2005: Baroclinic instability of two-layer vortices in laboratory experiments. J. Fluid Mech., 544, 69–97, doi:10.1017/S0022112005006531.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 650 239 74
PDF Downloads 303 75 3