Editorial Type:
Article
Article Type:
Research Article

Eddy Cancellation of the Ekman Cell in Subtropical Gyres

Edward W. Doddridge Department of Physics, University of Oxford, Oxford, United Kingdom

Search for other papers by Edward W. Doddridge in
Current site
Google Scholar
PubMed Close
,
David P. Marshall Department of Physics, University of Oxford, Oxford, United Kingdom

Search for other papers by David P. Marshall in
Current site
Google Scholar
PubMed Close
, and
Andrew McC. Hogg Research School of Earth Sciences, and the ARC Centre of Excellence for Climate System Science, The Australian National University, Acton, Australian Capital Territory, Australia.

Search for other papers by Andrew McC. Hogg in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Oct 2016
DOI:
https://doi.org/10.1175/JPO-D-16-0097.1
Page(s):
2995–3010
Restricted access

Abstract

The presence of large-scale Ekman pumping associated with the climatological wind stress curl is the textbook explanation for low biological activity in the subtropical gyres. Using an idealized, eddy-resolving model, it is shown that Eulerian-mean Ekman pumping may be opposed by an eddy-driven circulation, analogous to the way in which the atmospheric Ferrel cell and the Southern Ocean Deacon cell are opposed by eddy-driven circulations. Lagrangian particle tracking, potential vorticity fluxes, and depth–density streamfunctions are used to show that, in the model, the rectified effect of eddies acts to largely cancel the Eulerian-mean Ekman downwelling. To distinguish this effect from eddy compensation, it is proposed that the suppression of Eulerian-mean downwelling by eddies be called “eddy cancellation.”

Denotes Open Access content.

This article is licensed under a Creative Commons Attribution 4.0 license.

Corresponding author address: Edward W. Doddridge, Atmospheric, Oceanic, and Planetary Physics, Parks Road, Oxford OX1 3PU, United Kingdom. E-mail: edward.doddridge@physics.ox.ac.uk

Abstract

The presence of large-scale Ekman pumping associated with the climatological wind stress curl is the textbook explanation for low biological activity in the subtropical gyres. Using an idealized, eddy-resolving model, it is shown that Eulerian-mean Ekman pumping may be opposed by an eddy-driven circulation, analogous to the way in which the atmospheric Ferrel cell and the Southern Ocean Deacon cell are opposed by eddy-driven circulations. Lagrangian particle tracking, potential vorticity fluxes, and depth–density streamfunctions are used to show that, in the model, the rectified effect of eddies acts to largely cancel the Eulerian-mean Ekman downwelling. To distinguish this effect from eddy compensation, it is proposed that the suppression of Eulerian-mean downwelling by eddies be called “eddy cancellation.”

Denotes Open Access content.

This article is licensed under a Creative Commons Attribution 4.0 license.

Corresponding author address: Edward W. Doddridge, Atmospheric, Oceanic, and Planetary Physics, Parks Road, Oxford OX1 3PU, United Kingdom. E-mail: edward.doddridge@physics.ox.ac.uk
Save
Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Abernathey, R., J. C. Marshall, and D. Ferreira, 2011: The dependence of Southern Ocean meridional overturning on wind stress. J. Phys. Oceanogr., 41, 2261–2278, doi:10.1175/JPO-D-11-023.1.

    • Search Google Scholar
    • Export Citation

  • Andrews, D. G., and M. E. McIntyre, 1978a: An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech., 89, 609–646, doi:10.1017/S0022112078002773.

    • Search Google Scholar
    • Export Citation

  • Andrews, D. G., and M. E. McIntyre, 1978b: On wave-action and its relatives. J. Fluid Mech., 89, 647–664, doi:10.1017/S0022112078002785.

    • Search Google Scholar
    • Export Citation

  • Chassignet, E. P., and D. P. Marshall, 2008: Gulf Stream separation in numerical ocean models. Ocean Modeling in an Eddying Regime, Geophys. Monogr., Vol. 177, Amer. Geophys. Union, 39–61, doi:10.1029/GM177.

  • Danabasoglu, G., J. C. McWilliams, and P. R. Gent, 1994: The role of mesoscale tracer transports in the global ocean circulation. Science, 264, 1123–1126, doi:10.1126/science.264.5162.1123.

    • Search Google Scholar
    • Export Citation

  • Döös, K., and D. Webb, 1994: The Deacon cell and the other meridional cells of the Southern Ocean. J. Phys. Oceanogr., 24, 429–442, doi:10.1175/1520-0485(1994)024<0429:TDCATO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Dufour, C. O., J. Le Sommer, J. D. Zika, M. Gehlen, J. C. Orr, P. Mathiot, and B. Barnier, 2012: Standing and transient eddies in the response of the Southern Ocean meridional overturning to the southern annular mode. J. Climate, 25, 6958–6974, doi:10.1175/JCLI-D-11-00309.1.

    • Search Google Scholar
    • Export Citation

  • Dunkerton, T., 1978: On the mean meridional mass motions of the stratosphere and mesosphere. J. Atmos. Sci., 35, 2325–2333, doi:10.1175/1520-0469(1978)035<2325:OTMMMM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Dunkerton, T., 1980: A Lagrangian mean theory of wave, mean-flow interaction with applications to nonacceleration and its breakdown. Rev. Geophys., 18, 387–400, doi:10.1029/RG018i002p00387.

    • Search Google Scholar
    • Export Citation

  • Ertel, H., 1942: Ein neuer hydrodynamischer Erhaltungssatz. Naturwissenschaften, 30, 543–544, doi:10.1007/BF01475602.

  • Follows, M. J., and J. C. Marshall, 1996: On models of bomb 14C in the North Atlantic. J. Geophys. Res., 101, 22 577–22 582, doi:10.1029/96JC01698.

    • Search Google Scholar
    • Export Citation

  • Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25, 463–474, doi:10.1175/1520-0485(1995)025<0463:PEITTI>2.0.CO;2.

    • Search Google Scholar
    • 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, 2935–2946, doi:10.1175/1520-0493(2000)128<2935:BFWASL>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Griffies, S. M., and Coauthors, 2015: Impacts on ocean heat from transient mesoscale eddies in a hierarchy of climate models. J. Climate, 28, 952–977, doi:10.1175/JCLI-D-14-00353.1.

    • Search Google Scholar
    • Export Citation

  • Hallberg, R., and A. Gnanadesikan, 2006: The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: Results from the Modeling Eddies in the Southern Ocean (MESO) project. J. Phys. Oceanogr., 36, 2232–2252, doi:10.1175/JPO2980.1.

    • Search Google Scholar
    • Export Citation

  • Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and frictional or other forces. J. Atmos. Sci., 44, 828–841, doi:10.1175/1520-0469(1987)044<0828:OTEOVA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Haynes, P. H., and M. E. McIntyre, 1990: On the conservation and impermeability theorems for potential vorticity. J. Atmos. Sci., 47, 2021–2031, doi:10.1175/1520-0469(1990)047<2021:OTCAIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Henning, C. C., and G. K. Vallis, 2004: The effects of mesoscale eddies on the main subtropical thermocline. J. Phys. Oceanogr., 34, 2428–2443, doi:10.1175/JPO2639.1.

    • Search Google Scholar
    • Export Citation

  • Henning, C. C., and G. K. Vallis, 2005: The effects of mesoscale eddies on the stratification and transport of an ocean with a circumpolar channel. J. Phys. Oceanogr., 35, 880–896, doi:10.1175/JPO2727.1.

    • Search Google Scholar
    • Export Citation

  • Hill, C., D. Ferreira, J. M. Campin, J. Marshall, R. Abernathey, and N. Barrier, 2012: Controlling spurious diapycnal mixing in eddy-resolving height-coordinate ocean models—Insights from virtual deliberate tracer release experiments. Ocean Modell., 45–46, 14–26, doi:10.1016/j.ocemod.2011.12.001.

    • Search Google Scholar
    • Export Citation

  • Hirst, A. C., D. R. Jackett, and T. J. McDougall, 1996: The meridional overturning cells of a World Ocean model in neutral density coordinates. J. Phys. Oceanogr., 26, 775–791, doi:10.1175/1520-0485(1996)026<0775:TMOCOA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Jenkins, W. J., and S. C. Doney, 2003: The subtropical nutrient spiral. Global Biogeochem. Cycles, 17, 1110, doi:10.1029/2003GB002085.

  • Kähler, P., A. Oschlies, H. Dietze, and W. Koeve, 2009: Oxygen, carbon, and nutrients in the oligotrophic eastern subtropical North Atlantic. Biogeosci. Discuss., 6, 8923–8960, doi:10.5194/bgd-6-8923-2009.

    • Search Google Scholar
    • Export Citation

  • Karoly, D., P. McIntosh, P. Berrisford, T. McDougall, and A. Hirst, 1997: Similarities of the Deacon cell in the Southern Ocean and Ferrel cells in the atmosphere. Quart. J. Roy. Meteor. Soc., 123, 519–526, doi:10.1002/qj.49712353813.

    • Search Google Scholar
    • Export Citation

  • Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary-layer parameterization. Rev. Geophys., 32, 363–403, doi:10.1029/94RG01872.

    • Search Google Scholar
    • Export Citation

  • Lee, M.-M., and R. G. Williams, 2000: The role of eddies in the isopycnic transfer of nutrients and their impact on biological production. J. Mar. Res., 58, 895–917, doi:10.1357/002224000763485746.

    • Search Google Scholar
    • Export Citation

  • Lee, M.-M., D. P. Marshall, and R. G. Williams, 1997: On the eddy transfer of tracers: Advective or diffusive? J. Mar. Res., 55, 483–505, doi:10.1357/0022240973224346.

    • Search Google Scholar
    • Export Citation

  • Maddison, J. R., and D. P. Marshall, 2013: The Eliassen–Palm flux tensor. J. Fluid Mech., 729, 69–102, doi:10.1017/jfm.2013.259.

  • Marshall, D. P., 1997: Subduction of water masses in an eddying ocean. J. Mar. Res., 55, 201–222, doi:10.1357/0022240973224373.

  • Marshall, D. P., 2000: Vertical fluxes of potential vorticity and the structure of the thermocline. J. Phys. Oceanogr., 30, 3102–3112, doi:10.1175/1520-0485(2000)030<3102:VFOPVA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Marshall, J. C., and T. Radko, 2003: Residual-mean solutions for the Antarctic Circumpolar Current and its associated overturning circulation. J. Phys. Oceanogr., 33, 2341–2354, doi:10.1175/1520-0485(2003)033<2341:RSFTAC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Marshall, J. C., 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. Ocean., 102, 5753–5766, doi:10.1029/96JC02775.

    • Search Google Scholar
    • Export Citation

  • Marshall, J. C., H. Jones, R. Karsten, and R. Wardle, 2002: Can eddies set ocean stratification? J. Phys. Oceanogr., 32, 26–38, doi:10.1175/1520-0485(2002)032<0026:CESOS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • McDougall, T. J., 1987: Neutral surfaces. J. Phys. Oceanogr., 17, 1950–1964, doi:10.1175/1520-0485(1987)017<1950:NS>2.0.CO;2.

  • McGillicuddy, D. J., Jr., 2016: Mechanisms of physical-biological-biogeochemical interaction at the oceanic mesoscale. Annu. Rev. Mar. Sci., 8, 125–159, doi:10.1146/annurev-marine-010814-015606.

    • Search Google Scholar
    • Export Citation

  • McGillicuddy, D. J., Jr., and Coauthors, 1998: Influence of mesoscale eddies on new production in the Sargasso Sea. Nature, 394, 263–266, doi:10.1038/28367.

    • Search Google Scholar
    • Export Citation

  • McGillicuddy, D. J., Jr., L. A. Anderson, S. C. Doney, and M. E. Maltrud, 2003: Eddy-driven sources and sinks of nutrients in the upper ocean: Results from a 0.1° resolution model of the North Atlantic. Global Biogeochem. Cycles, 17, 1035, doi:10.1029/2002GB001987.

    • Search Google Scholar
    • Export Citation

  • Morrison, A. K., and A. M. Hogg, 2013: On the relationship between Southern Ocean overturning and ACC transport. J. Phys. Oceanogr., 43, 140–148, doi:10.1175/JPO-D-12-057.1.

    • Search Google Scholar
    • Export Citation

  • Munday, D. R., H. L. Johnson, and D. P. Marshall, 2013: Eddy saturation of equilibrated circumpolar currents. J. Phys. Oceanogr., 43, 507–532, doi:10.1175/JPO-D-12-095.1.

    • Search Google Scholar
    • Export Citation

  • Najjar, R. G., and R. F. Keeling, 2000: Mean annual cycle of the air-sea oxygen flux: A global view. Global Biogeochem. Cycles, 14, 573–584, doi:10.1029/1999GB900086.

    • Search Google Scholar
    • Export Citation

  • Nurser, A. J. G., and M.-M. Lee, 2004: Isopycnal averaging at constant height. Part II: Relating to the residual streamfunction in Eulerian space. J. Phys. Oceanogr., 34, 2740–2755, doi:10.1175/JPO2650.1.

    • Search Google Scholar
    • Export Citation

  • Oschlies, A., 2002: Nutrient supply to the surface waters of the North Atlantic: A model study. J. Geophys. Res., 107, 3046, doi:10.1029/2000JC000275.

    • Search Google Scholar
    • Export Citation

  • Palter, J. B., M. S. Lozier, and R. T. Barber, 2005: The effect of advection on the nutrient reservoir in the North Atlantic Subtropical Gyre. Nature, 437, 687–692, doi:10.1038/nature03969.

    • Search Google Scholar
    • Export Citation

  • Pennel, R., and I. Kamenkovich, 2014: On the factors controlling the eddy-induced transport in the Antarctic Circumpolar Current. J. Phys. Oceanogr., 44, 2127–2138, doi:10.1175/JPO-D-13-0256.1.

    • Search Google Scholar
    • Export Citation

  • Plumb, R. A., 1979: Eddy fluxes of conserved quantities by small-amplitude waves. J. Atmos. Sci., 36, 1699–1704, doi:10.1175/1520-0469(1979)036<1699:EFOCQB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Plumb, R. A., and J. D. Mahlman, 1987: The zonally averaged transport characteristics of the GFDL general circulation/transport model. J. Atmos. Sci., 44, 298–327, doi:10.1175/1520-0469(1987)044<0298:TZATCO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Polton, J. A., and D. P. Marshall, 2003: Understanding the structure of the subtropical thermocline. J. Phys. Oceanogr., 33, 1240–1249, doi:10.1175/1520-0485(2003)033<1240:UTSOTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Polton, J. A., and D. P. Marshall, 2007: Overturning cells in the Southern Ocean and subtropical gyres. Ocean Sci., 3, 17–30, doi:10.5194/os-3-17-2007.

    • Search Google Scholar
    • Export Citation

  • Prather, M. J., 1986: Numerical advection by conservation of second-order moments. J. Geophys. Res., 91, 6671–6681, doi:10.1029/JD091iD06p06671.

    • Search Google Scholar
    • Export Citation

  • Radko, T., and J. C. Marshall, 2004a: Eddy-induced diapycnal fluxes and their role in the maintenance of the thermocline. J. Phys. Oceanogr., 34, 372–383, doi:10.1175/1520-0485(2004)034<0372:EDFATR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Radko, T., and J. C. Marshall, 2004b: The leaky thermocline. J. Phys. Oceanogr., 34, 1648–1662, doi:10.1175/1520-0485(2004)034<1648:TLT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Schär, C., 1993: A generalization of Bernoulli’s theorem. J. Atmos. Sci., 50, 1437–1443, doi:10.1175/1520-0469(1993)050<1437:AGOBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Smagorinsky, J., 1963: General circulation experiments with the primitive equations. I. The basic experiment. Mon. Wea. Rev., 91, 99–164, doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2.

    • Search Google Scholar
    • Export Citation

  • Speer, K., S. R. Rintoul, and B. Sloyan, 2000: The diabatic Deacon cell. J. Phys. Oceanogr., 30, 3212–3222, doi:10.1175/1520-0485(2000)030<3212:TDDC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp.

  • Viebahn, J., and C. Eden, 2010: Towards the impact of eddies on the response of the Southern Ocean to climate change. Ocean Modell., 34, 150–165, doi:10.1016/j.ocemod.2010.05.005.

    • Search Google Scholar
    • Export Citation

  • Williams, R. G., and M. J. Follows, 1998: The Ekman transfer of nutrients and maintenance of new production over the North Atlantic. Deep-Sea Res. I, 45, 461–489, doi:10.1016/S0967-0637(97)00094-0.

    • Search Google Scholar
    • Export Citation

  • Williams, R. G., and M. J. Follows, 2011: Ocean Dynamics and the Carbon Cycle: Principles and Mechanisms. Cambridge University Press, 416 pp.

  • Xu, L., P. Li, Q. Liu, C. Liu, W. Gao, and S.-P. Xie, 2016: Observing mesoscale eddy effects on mode-water subduction and transport in the North Pacific. Nat. Commun., 7, 10505, doi:10.1038/ncomms10505.

    • Search Google Scholar
    • Export Citation

  • Young, W. R., 2012: An exact thickness-weighted average formulation of the Boussinesq equations. J. Phys. Oceanogr., 42, 692–707, doi:10.1175/JPO-D-11-0102.1.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1594 1012 81
PDF Downloads 505 100 6