• Argo, 2000: Argo float data and metadata from Global Data Assembly Centre (Argo GDAC). SEANOE, accessed 16 July 2020, https://doi.org/10.17882/42182.

    • Crossref
    • Export Citation
  • American Meteorological Society, 2020: Symmetric instability. Glossary of Meteorology, http://glossary.ametsoc.org/wiki/symmetric_instability.

  • Bachman, S. D., and J. R. Taylor, 2014: Modelling of partially-resolved oceanic symmetric instability. Ocean Modell., 82, 1527, https://doi.org/10.1016/j.ocemod.2014.07.006.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bower, A., and et al. , 2019: Lagrangian views of the pathways of the Atlantic meridional overturning circulation. J. Geophys. Res. Oceans, 124, 53135335, https://doi.org/10.1029/2019JC015014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brannigan, L., 2016: Intense submesoscale upwelling in anticyclonic eddies. Geophys. Res. Lett., 43, 33603369, https://doi.org/10.1002/2016GL067926.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bryden, H. L., W. E. Johns, B. A. King, G. McCarthy, E. L. McDonagh, B. I. Moat, and D. A. Smeed, 2020: Reduction in ocean heat transport at 26°N since 2008 cools the eastern subpolar gyre of the North Atlantic Ocean. J. Climate, 33, 16771689, https://doi.org/10.1175/JCLI-D-19-0323.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buckley, M. W., and J. Marshall, 2016: Observations, inferences, and mechanisms of the Atlantic meridional overturning circulation: A review. Rev. Geophys., 54, 563, https://doi.org/10.1002/2015RG000493.

    • Crossref
    • 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, https://doi.org/10.1029/2010JC006575.

    • Search Google Scholar
    • Export Citation
  • Eden, G., and J. Willebrand, 1999: Neutral density revisited. Deep-Sea Res. II, 46, 3354, https://doi.org/10.1016/S0967-0645(98)00113-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Edwards, C. A., and J. Pedlosky, 1998a: Dynamics of nonlinear cross-equatorial flow. Part I: Potential vorticity transformation. J. Phys. Oceanogr., 28, 23822406, https://doi.org/10.1175/1520-0485(1998)028<2382:DONCEF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Edwards, C. A., and J. Pedlosky, 1998b: Dynamics of nonlinear cross-equatorial flow. Part II: The tropically enhanced instability of the western boundary current. J. Phys. Oceanogr., 28, 24072417, https://doi.org/10.1175/1520-0485(1998)028<2407:DONCEF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fonseca, C. A., G. J. Goni, W. E. Johns, and E. J. Campos, 2004: Investigation of the North Brazil Current retroflection and North Equatorial Countercurrent variability. Geophys. Res. Lett., 31, L21304, https://doi.org/10.1029/2004GL020054.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goes, M. P., D. P. Marshall, and I. Wainer, 2009: Eddy formation in the tropical Atlantic induced by abrupt changes in the meridional overturning circulation. J. Phys. Oceanogr., 39, 30213031, https://doi.org/10.1175/2009JPO4004.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goldsworth, F. W., D. P. Marshall, and H. L. Johnson, 2021: GitHub repository for “Symmetric instability in cross equatorial western boundary currents.” Zenodo, https://doi.org/10.5281/zenodo.4650332.

    • Crossref
    • Export Citation
  • Griffies, S. M., and R. W. Hallberg, 2000: Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models. Mon. Wea. Rev., 128, 29352946, https://doi.org/10.1175/1520-0493(2000)128<2935:BFWASL>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Griffiths, S. D., 2003a: Nonlinear vertical scale selection in equatorial inertial instability. J. Atmos. Sci., 60, 977990, https://doi.org/10.1175/1520-0469(2003)060<0977:NVSSIE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Griffiths, S. D., 2003b: The nonlinear evolution of zonally symmetric equatorial inertial instability. J. Fluid Mech., 474, 245273, https://doi.org/10.1017/S0022112002002586.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Haine, T. W. N., and J. Marshall, 1998: Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr., 28, 634658, https://doi.org/10.1175/1520-0485(1998)028<0634:GSABIO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holton, J. R., and G. J. Hakim, 2013: Mesoscale circulations. An Introduction to Dynamic Meteorology, Elsevier, 279–323, https://doi.org/10.1016/B978-0-12-384866-6.00009-X.

    • Crossref
    • Export Citation
  • Hoskins, B. J., 1974: The role of potential vorticity in symmetric stability and instability. Quart. J. Roy. Meteor. Soc., 100, 480482, https://doi.org/10.1002/qj.49710042520.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hua, B. L., D. W. Moore, and S. Le Gentil, 1997: Inertial nonlinear equilibration of equatorial flows. J. Fluid Mech., 331, 345371, https://doi.org/10.1017/S0022112096004016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jackson, L. C., R. Kahana, T. Graham, M. A. Ringer, T. Woollings, J. V. Mecking, and R. A. Wood, 2015: Global and European climate impacts of a slowdown of the AMOC in a high resolution GCM. Climate Dyn., 45, 32993316, https://doi.org/10.1007/s00382-015-2540-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jochum, M., and P. Malanotte-Rizzoli, 2003: On the generation of North Brazil Current rings. J. Mar. Res., 61, 147173, https://doi.org/10.1357/002224003322005050.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Johns, W. E., T. N. Lee, R. C. Beardsley, J. Candela, R. Limeburner, and B. Castro, 1998: Annual cycle and variability of the North Brazil current. J. Phys. Oceanogr., 28, 103128, https://doi.org/10.1175/1520-0485(1998)028<0103:ACAVOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Joshi, M., 1994: Orographic influences in the atmosphere of Mars. Ph.D. thesis, University of Oxford, 185 pp.

  • Killworth, P. D., 1991: Cross-equatorial geostrophic adjustment. J. Phys. Oceanogr., 21, 15811601, https://doi.org/10.1175/1520-0485(1991)021<1581:CEGA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kloosterziel, R. C., G. F. Carnevale, and P. Orlandi, 2017: Equatorial inertial instability with full Coriolis force. J. Fluid Mech., 825, 69108, https://doi.org/10.1017/jfm.2017.377.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, D. P., and H. R. Pillar, 2011: Momentum balance of the wind-driven and meridional overturning circulation. J. Phys. Oceanogr., 41, 960978, https://doi.org/10.1175/2010JPO4528.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 57535766, https://doi.org/10.1029/96JC02775.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Plougonven, R., and V. Zeitlin, 2009: Nonlinear development of inertial instability in a barotropic shear. Phys. Fluids, 21, 106601, https://doi.org/10.1063/1.3242283.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Prather, M. J., 1986: Numerical advection by conservation of second-order moments. J. Geophys. Res., 91, 6671, https://doi.org/10.1029/JD091iD06p06671.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ribstein, B. V. Zeitlin, and A. S. Tissier, 2014: Barotropic, baroclinic, and inertial instabilities of the easterly Gaussian jet on the equatorial β-plane in rotating shallow water model. Phys. Fluids, 26, 056605, https://doi.org/10.1063/1.4875030.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rodwell, M. J., and B. J. Hoskins, 1995: A model of the Asian summer monsoon. Part II: Cross-equatorial flow and PV behavior. J. Atmos. Sci., 52, 13411356, https://doi.org/10.1175/1520-0469(1995)052<1341:AMOTAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schott, F., J. Fischer, J. Reppin, and U. Send, 1993: On mean and seasonal currents and transports at the western boundary of the equatorial Atlantic. J. Geophys. Res., 98, 14353, https://doi.org/10.1029/93JC01287.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Mon. Wea. Rev., 91, 99164, https://doi.org/10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Srokosz, M., M. Baringer, H. Bryden, S. Cunningham, T. Delworth, S. Lozier, J. Marotzke, and R. Sutton, 2012: Past, present, and future changes in the Atlantic meridional overturning circulation. Bull. Amer. Meteor. Soc., 93, 16631676, https://doi.org/10.1175/BAMS-D-11-00151.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stewart, A. L., and P. J. Dellar, 2011: The rôle of the complete Coriolis force in cross-equatorial flow of abyssal ocean currents. Ocean Modell., 38, 187202, https://doi.org/10.1016/j.ocemod.2011.03.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stone, P. H., 1966: On non-geostrophic baroclinic stability. J. Atmos. Sci., 23, 390400, https://doi.org/10.1175/1520-0469(1966)023<0390:ONGBS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Talley, L. D., G. L. Pickard, W. J. Emery, and J. H. Swift, 2011: Atlantic Ocean. Descriptive Physical Oceanography, Elsevier, 245–301, https://doi.org/10.1016/B978-0-7506-4552-2.10009-5.

    • Crossref
    • Export Citation
  • Taylor, J. R., and R. Ferrari, 2009: On the equilibration of a symmetrically unstable front via a secondary shear instability. J. Fluid Mech., 622, 103113, https://doi.org/10.1017/S0022112008005272.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thomas, L. N., J. R. Taylor, R. Ferrari, and T. M. Joyce, 2013: Symmetric instability in the Gulf Stream. Deep-Sea Res. II, 91, 96110, https://doi.org/10.1016/j.dsr2.2013.02.025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vianna, M., and V. de Menezes, 2003: A seasonal and interannual study of the western equatorial Atlantic upper thermocline circulation variability. Interhemispheric Water Exchange in the Atlantic Ocean, G. Goni and P. Malanotte-Rizzoli, Eds., Elsevier Oceanography Series, Vol. 68, Elsevier, 137–173, https://doi.org/10.1016/S0422-9894(03)80145-9.

    • Crossref
    • Export Citation
  • Walin, G., 1982: On the relation between sea-surface heat flow and thermal circulation in the ocean. Tellus, 34, 187195, https://doi.org/10.3402/tellusa.v34i2.10801.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Williams, R. G., and M. J. Follows, 2011: Ocean Dynamics and the Carbon Cycle. Cambridge University Press, 434 pp.

  • Yankovsky, E., and S. Legg, 2019: Symmetric and baroclinic instability in dense shelf overflows. J. Phys. Oceanogr., 49, 3961, https://doi.org/10.1175/JPO-D-18-0072.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zeitlin, V., 2018: Symmetric instability drastically changes upon inclusion of the full Coriolis force. Phys. Fluids, 30, 061701, https://doi.org/10.1063/1.5031099.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Symmetric Instability in Cross-Equatorial Western Boundary Currents

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  • 1 a Department of Physics, University of Oxford, Oxford, United Kingdom
  • | 2 b Oxford NERC Environmental Research DTP, University of Oxford, Oxford, United Kingdom
  • | 3 c Department of Earth Sciences, University of Oxford, Oxford, United Kingdom
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Abstract

The upper limb of the Atlantic meridional overturning circulation draws waters with negative potential vorticity from the Southern Hemisphere into the Northern Hemisphere. The North Brazil Current is one of the cross-equatorial pathways in which this occurs: upon crossing the equator, fluid parcels must modify their potential vorticity to render them stable to symmetric instability and to merge smoothly with the ocean interior. In this work a linear stability analysis is performed on an idealized western boundary current, dynamically similar to the North Brazil Current, to identify features that are indicative of symmetric instability. Simple two-dimensional numerical models are used to verify the results of the stability analysis. The two-dimensional models and linear stability theory show that symmetric instability in meridional flows does not change when the nontraditional component of the Coriolis force is included, unlike in zonal flows. Idealized three-dimensional numerical models show anticyclonic barotropic eddies being spun off as the western boundary current crosses the equator. These eddies become symmetrically unstable a few degrees north of the equator, and their PV is set to zero through the action of the instability. The instability is found to have a clear fingerprint in the spatial Fourier transform of the vertical kinetic energy. An analysis of the water mass formation rates suggest that symmetric instability has a minimal effect on water mass transformation in the model calculations; however, this may be the result of unresolved dynamics, such as secondary Kelvin–Helmholtz instabilities, which are important in diabatic transformation.

Significance Statement

The Atlantic meridional overturning circulation includes an ocean current that transports heat, carbon, and other climatically important tracers from the Southern Hemisphere into the Northern Hemisphere. Theoretical considerations suggest that this current may become unstable through the so-called “symmetric instability” upon crossing the equator. In this study, a hierarchy of models is used to investigate how symmetric instability might manifest itself if excited in cross-equatorial flows. We find that when the instability is excited, it generates stacked overturning cells which reorganize the current to make it neutrally stable to symmetric instability. We hypothesize this process could be occurring in the ocean off the coast of Brazil.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-20-0273.s1.

© 2021 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: Fraser W. Goldsworth, frasergocean@gmail.com

Abstract

The upper limb of the Atlantic meridional overturning circulation draws waters with negative potential vorticity from the Southern Hemisphere into the Northern Hemisphere. The North Brazil Current is one of the cross-equatorial pathways in which this occurs: upon crossing the equator, fluid parcels must modify their potential vorticity to render them stable to symmetric instability and to merge smoothly with the ocean interior. In this work a linear stability analysis is performed on an idealized western boundary current, dynamically similar to the North Brazil Current, to identify features that are indicative of symmetric instability. Simple two-dimensional numerical models are used to verify the results of the stability analysis. The two-dimensional models and linear stability theory show that symmetric instability in meridional flows does not change when the nontraditional component of the Coriolis force is included, unlike in zonal flows. Idealized three-dimensional numerical models show anticyclonic barotropic eddies being spun off as the western boundary current crosses the equator. These eddies become symmetrically unstable a few degrees north of the equator, and their PV is set to zero through the action of the instability. The instability is found to have a clear fingerprint in the spatial Fourier transform of the vertical kinetic energy. An analysis of the water mass formation rates suggest that symmetric instability has a minimal effect on water mass transformation in the model calculations; however, this may be the result of unresolved dynamics, such as secondary Kelvin–Helmholtz instabilities, which are important in diabatic transformation.

Significance Statement

The Atlantic meridional overturning circulation includes an ocean current that transports heat, carbon, and other climatically important tracers from the Southern Hemisphere into the Northern Hemisphere. Theoretical considerations suggest that this current may become unstable through the so-called “symmetric instability” upon crossing the equator. In this study, a hierarchy of models is used to investigate how symmetric instability might manifest itself if excited in cross-equatorial flows. We find that when the instability is excited, it generates stacked overturning cells which reorganize the current to make it neutrally stable to symmetric instability. We hypothesize this process could be occurring in the ocean off the coast of Brazil.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-20-0273.s1.

© 2021 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: Fraser W. Goldsworth, frasergocean@gmail.com

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