A Conjecture on the Role of Bottom-Enhanced Diapycnal Mixing in the Parameterization of Geostrophic Eddies

David P. Marshall Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, United Kingdom

Search for other papers by David P. Marshall in
Current site
Google Scholar
PubMed
Close
and
Alberto C. Naveira Garabato National Oceanography Centre, Southampton, Southampton, United Kingdom

Search for other papers by Alberto C. Naveira Garabato in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The parameterization of geostrophic eddies represents a large sink of energy in most ocean models, yet the ultimate fate of this eddy energy in the ocean remains unclear. The authors conjecture that a significant fraction of the eddy energy may be transferred to internal lee waves and oscillations over rough bottom topography, leading to bottom-enhanced diapycnal mixing. A range of circumstantial evidence in support of this conjecture is presented and discussed. The authors further propose a modification to the Gent and McWilliams eddy parameterization to account for the bottom-enhanced diapycnal mixing.

Corresponding author address: David Marshall, Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom. Email: marshall@atm.ox.ac.uk

Abstract

The parameterization of geostrophic eddies represents a large sink of energy in most ocean models, yet the ultimate fate of this eddy energy in the ocean remains unclear. The authors conjecture that a significant fraction of the eddy energy may be transferred to internal lee waves and oscillations over rough bottom topography, leading to bottom-enhanced diapycnal mixing. A range of circumstantial evidence in support of this conjecture is presented and discussed. The authors further propose a modification to the Gent and McWilliams eddy parameterization to account for the bottom-enhanced diapycnal mixing.

Corresponding author address: David Marshall, Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom. Email: marshall@atm.ox.ac.uk

Save
  • Adcock, S. T., and D. P. Marshall, 2000: Interactions between geostrophic eddies and the mean circulation over large-scale bottom topography. J. Phys. Oceanogr., 30 , 3223–3238.

    • Search Google Scholar
    • Export Citation
  • Aguilar, D. A., and B. R. Sutherland, 2006: Internal wave generation from rough topography. Phys. Fluids, 18 .066 603, doi:10.1063/1.2214538.

    • Search Google Scholar
    • Export Citation
  • Arbic, B. K., and G. R. Flierl, 2004: Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom Ekman friction: Application to midocean eddies. J. Phys. Oceanogr., 34 , 2257–2273.

    • Search Google Scholar
    • Export Citation
  • Bretherton, F. B., and D. Haidvogel, 1976: Two-dimensional turbulence over topography. J. Fluid Mech., 78 , 129–154.

  • Chapman, D. C., and D. B. Haidvogel, 1993: Generation of internal lee waves trapped over a tall isolated seamount. Geophys. Astrophys. Fluid Dyn., 69 , 33–54.

    • Search Google Scholar
    • Export Citation
  • Danabasoglu, G., and J. C. McWilliams, 1995: Sensitivity of the global ocean circulation to parameterizations of mesoscale tracer transports. J. Climate, 8 , 2967–2987.

    • Search Google Scholar
    • Export Citation
  • 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.

    • Search Google Scholar
    • Export Citation
  • Dewar, W. K., and P. D. Killworth, 1995: Do fast gravity waves interact with geostrophic motions? Deep-Sea Res., 42 , 1063–1081.

  • Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20 , 150–155.

  • 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.

    • Search Google Scholar
    • Export Citation
  • Gille, S. T., M. M. Yale, and D. T. Sandwell, 2000: Global correlation of mesoscale ocean variability with seafloor roughness. Geophys. Res. Lett., 27 , 1251–1254.

    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1987: Diapycnal mixing in the thermocline: A review. J. Geophys. Res., 92 , 5249–5286.

  • Griffies, S. M., R. Pacanowski, and R. Hallberg, 2000: Spurious diapycnal mixing associated with advection in a Z-coordinate ocean model. Mon. Wea. Rev., 128 , 538–564.

    • Search Google Scholar
    • Export Citation
  • Huang, R. X., and W. Wang, 2003: Gravitational potential energy sinks in the oceans. From Stirring to Mixing in a Stratified Ocean: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 239–247.

    • Search Google Scholar
    • Export Citation
  • Hughes, C. W., and B. A. de Cuevas, 2001: Why western boundary currents in realistic oceans are inviscid: A link between form stress and bottom pressure torque. J. Phys. Oceanogr., 31 , 2871–2885.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., E. Firing, J. M. Hummon, T. K. Chereskin, and A. M. Thurnherr, 2006: Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J. Phys. Oceanogr., 36 , 1553–1576.

    • Search Google Scholar
    • Export Citation
  • Ledwell, J. R., A. J. Watson, and C. S. Law, 1998: Mixing of a tracer in the pycnocline. J. Geophys. Res., 103 , 21499–21529.

  • MacCready, P., G. Pawlak, K. Edwards, and R. McCabe, 2003: Form drag on ocean flows. From Stirring to Mixing in a Stratified Ocean: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 119–130.

    • Search Google Scholar
    • Export Citation
  • Maximenko, N. A., B. Bang, and H. Sasaki, 2005: Observational evidence of alternating zonal jets in the world ocean. Geophys. Res. Lett., 32 .L12607, doi:10.1029/2005GL022728.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., and I. Yavneh, 1998: Fluctuation growth and instability associated with a singularity of the balance equations. Phys. Fluids, 10 , 2587–2596.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., I. Yavneh, M. J. P. Cullen, and P. R. Gent, 1998: The breakdown of large-scale flows in rotating, stratified fluids. Phys. Fluids, 10 , 3178–3184.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., M. J. Molemaker, and I. Yavneh, 2001: From stirring to mixing of momentum: Cascades from balanced flows to dissipation in the oceanic interior. Near-Boundary Processes and Their Parameterization: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, Honolulu, HI, University of Hawaii at Manoa, 59–66.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2000: Instability and equilibration of centrifugally-stable stratified Taylor-Couette flow. Phys. Rev. Lett., 86 , 5270–5273.

    • Search Google Scholar
    • Export Citation
  • Molemaker, M. J., J. C. McWilliams, and I. Yavneh, 2005: Baroclinic instability and loss of balance. J. Phys. Oceanogr., 35 , 1505–1517.

    • Search Google Scholar
    • Export Citation
  • Naveira Garabato, A. C., K. L. Polzin, B. A. King, K. J. Heywood, and M. Visbeck, 2004: Widespread intense turbulent mixing in the Southern Ocean. Science, 303 , 210–213.

    • Search Google Scholar
    • Export Citation
  • Naveira Garabato, A. C., D. P. Stevens, A. J. Watson, and W. Roether, 2007: Short-circuiting of the overturning circulation in the Antarctic Circumpolar Current. Nature, 447 , 194–197.

    • Search Google Scholar
    • Export Citation
  • Pain, C. C., and Coauthors, 2005: Three-dimensional unstructured mesh ocean modelling. Ocean Modell., 10 , 5–33.

  • Polzin, K. L., and E. Firing, 1997: Estimates of diapycnal mixing using LADCP and CTD data from 18S. International WOCE Newsletter, No. 29, WOCE International Project Office, Southampton, United Kingdom, 39–42.

    • Search Google Scholar
    • Export Citation
  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69 , 417–443.

  • Richards, K. J., N. A. Maximenko, F. O. Bryan, and H. Sasaki, 2006: Zonal jets in the Pacific Ocean. Geophys. Res. Lett., 33 .L03605, doi:10.1029/2005GL024645.

    • Search Google Scholar
    • Export Citation
  • Roberts, M., and D. Marshall, 1998: Do we require adiabatic dissipation schemes in eddy-resolving ocean models? J. Phys. Oceanogr., 28 , 2050–2063.

    • Search Google Scholar
    • Export Citation
  • Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 400 pp.

  • Scott, R. B., and F. Wang, 2005: Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J. Phys. Oceanogr., 35 , 1650–1666.

    • Search Google Scholar
    • Export Citation
  • Scott, R. B., and B. K. Arbic, 2007: Spectral energy fluxes in geostrophic turbulence: Implications for ocean energetics. J. Phys. Oceanogr., 37 , 673–688.

    • Search Google Scholar
    • Export Citation
  • Shcherbina, A., L. D. Talley, E. Firing, and P. Hacker, 2003: Near-surface frontal zone trapping and deep upward propagation of internal wave energy in the Japan/East Sea. J. Phys. Oceanogr., 33 , 900–912.

    • Search Google Scholar
    • Export Citation
  • Sloyan, B. M., 2005: Spatial variability of mixing in the Southern Ocean. Geophys. Res. Lett., 32 .L18603, doi:10.1029/2005GL023568.

  • Tandon, A., and C. Garrett, 1996: On a recent parameterization of mesoscale eddies. J. Phys. Oceanogr., 26 , 406–411.

  • Theiss, J., 2004: Equatorward energy cascade, critical latitude, and the predominance of cyclonic vortices in geostrophic turbulence. J. Phys. Oceanogr., 34 , 1633–1678.

    • Search Google Scholar
    • Export Citation
  • Treguier, A. M., and B. L. Hua, 1988: Influence of bottom topography on stratified quasi-geostrophic turbulence in the ocean. Geophys. Astrophys. Fluid Dyn., 43 , 265–305.

    • Search Google Scholar
    • Export Citation
  • Visbeck, M., J. Marshall, T. Haine, and M. Spall, 1997: On the specification of eddy transfer coefficients in coarse resolution ocean circulation models. J. Phys. Oceanogr., 27 , 381–402.

    • Search Google Scholar
    • Export Citation
  • Walter, M., C. Mertens, and M. Rhein, 2005: Mixing estimates from a large-scale hydro-graphic survey in the North Atlantic. Geophys. Res. Lett., 32 .L13605, doi:10.1029/2005GL022471.

    • Search Google Scholar
    • Export Citation
  • Watson, A. J., and A. C. Naveira Garabato, 2006: The role of Southern Ocean mixing and upwelling in glacial–interglacial atmospheric CO2 change. Tellus, 58B , 73–87.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1998: The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr., 28 , 2332–2340.

  • Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36 , 281–314.

    • Search Google Scholar
    • Export Citation
  • Yavneh, I., J. C. McWilliams, and M. J. Molemaker, 2001: Non-axisymmetric instability of centrifugally stable, stratified Taylor-Couette flow. J. Fluid Mech., 448 , 1–21.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 912 694 173
PDF Downloads 151 35 4