• Boccaletti, G., , R. Ferrari, , and B. Fox-Kemper, 2007: Mixed layer instabilities and restratification. J. Phys. Oceanogr., 37 , 22282250.

    • Search Google Scholar
    • Export Citation
  • Canuto, V., , and M. S. Dubovikov, 2006: Dynamical model of mesoscales in z-coordinates. Ocean Modell., 11 , 123166.

  • Coward, A. C., , and B. A. de Cuevas, 2005: The OCCAM 66 level model: Physics, initial conditions and external forcing. SOC Internal Rep. 99, 58 pp.

    • Search Google Scholar
    • Export Citation
  • Eden, C., 2006: Thickness diffusivity in the Southern Ocean. Geophys. Res. Lett, 33 , L11606. doi:10.1029/2006GL026157.

  • Eden, C., , R. J. Greatbatch, , and D. Olbers, 2007a: Interpreting eddy fluxes. J. Phys. Oceanogr., 37 , 12821296.

  • Eden, C., , R. J. Greatbatch, , and J. Willebrand, 2007b: A diagnosis of thickness fluxes in an eddy-resolving model. J. Phys. Oceanogr, 37 , 727742.

    • Search Google Scholar
    • Export Citation
  • Ferrari, R. J., , J. C. McWilliams, , V. M. Canuto, , and M. Dubovikov, 2008: Parameterization of eddy fluxes near boundaries. J. Climate, 21 , 27702789.

    • Search Google Scholar
    • Export Citation
  • Ferreira, D., , J. Marshall, , and P. Heimbach, 2005: Estimating eddy stresses by fitting dynamics to observations using a residual-mean ocean circulation model and its adjoint. J. Phys. Oceanogr., 35 , 18911910.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., , and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20 , 150155.

  • Gille, S. T., , and R. E. Davis, 1999: The influence of mesoscale eddies on coarsely resolved density: An examination of subgrid-scale parameterization. J. Phys. Oceanogr., 29 , 11091123.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., , and T. Schneider, 1999: The surface branch of the zonally averaged mass transport circulation in the troposphere. J. Atmos. Sci., 56 , 16881697.

    • Search Google Scholar
    • Export Citation
  • Killworth, P. D., 1997: On the parameterization of eddy transfer. Part I: Theory. J. Mar. Res., 55 , 11711197.

  • Killworth, P. D., 2001: Boundary conditions on quasi-Stokes velocities in parameterizations. J. Phys. Oceanogr., 31 , 11321155.

  • Killworth, P. D., 2005: Parameterization of eddy effects on mixed layers and tracer transport: A linearized eddy perspective. J. Phys. Oceanogr., 35 , 17171725.

    • Search Google Scholar
    • Export Citation
  • Lee, M-M., , and A. Coward, 2003: Eddy mass transport for the Southern Ocean in an eddy-permitting global ocean model. Ocean Modell., 5 , 249266.

    • Search Google Scholar
    • Export Citation
  • Lee, M-M., , A. J. G. Nurser, , A. C. Coward, , and B. A. de Cuevas, 2007: Eddy advective and diffusive transports of heat and salt in the Southern Ocean. J. Phys. Oceanogr., 37 , 13761393.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., , E. Shuckburgh, , H. Jones, , and C. Hill, 2006: Estimates and implications of surface eddy diffusivity in the Southern Ocean derived from tracer transport. J. Phys. Oceanogr., 36 , 18061821.

    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., , and P. C. McIntosh, 2001: The temporal-residual-mean velocity. Part II: Isopycnal interpretation and the tracer and momentum equations. J. Phys. Oceanogr., 31 , 12221246.

    • Search Google Scholar
    • Export Citation
  • Nurser, A. 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 , 27402755.

    • Search Google Scholar
    • Export Citation
  • Plumb, R. A., , and R. Ferrari, 2005: Transformed Eulerian-mean theory. Part I: Nonquasigeostrophic theory for eddies on a zonal-mean flow. J. Phys. Oceanogr., 35 , 165174.

    • Search Google Scholar
    • Export Citation
  • Rix, N. H., , and J. Willebrand, 1996: Parameterization of mesoscale eddies as inferred from a high-resolution circulation model. J. Phys. Oceanogr., 26 , 22812285.

    • Search Google Scholar
    • Export Citation
  • Treguier, A. M., , I. M. Held, , and V. D. Larichev, 1997: Parameterization of quasigeostrophic eddies in primitive equation ocean models. J. Phys. Oceanogr., 27 , 567580.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 61 61 8
PDF Downloads 41 41 2

Estimating Bolus Velocities from Data—How Large Must They Be?

View More View Less
  • 1 National Oceanography Centre, Southampton, Southampton, United Kingdom
© Get Permissions
Restricted access

Abstract

This paper examines the representation of eddy fluxes by bolus velocities. In particular, it asks the following: 1) Can an arbitrary eddy flux divergence of density be represented accurately by a nondivergent bolus flux that satisfies the condition of no normal flow at boundaries? 2) If not, how close can such a representation come? 3) If such a representation can exist in some circumstances, what is the size of the smallest bolus velocity that fits the data?

The author finds, in agreement with earlier authors, that the answer to the first question is no, although under certain conditions, which include a modification to the eddy flux divergence, a bolus representation becomes possible. One such condition is when the eddy flux divergence is required to balance the time-mean flux divergence. The smallest bolus flow is easily found by solving a thickness-weighted Poisson equation on each density level. This problem is solved for the North Pacific using time-mean data from an eddy-permitting model. The minimum bolus flow is found to be very small at depth but larger than is usually assumed near the surface. The magnitude of this minimum flow is of order one-tenth of the mean flow. Similar but larger results are found for a coarse-resolution model.

* Deceased.

Corresponding author address: Jeff Blundell, National Oceanography Centre, Southampton, Empress Dock, Southampton SO14 3ZH, United Kingdom. Email: jeff@noc.soton.ac.uk.

Abstract

This paper examines the representation of eddy fluxes by bolus velocities. In particular, it asks the following: 1) Can an arbitrary eddy flux divergence of density be represented accurately by a nondivergent bolus flux that satisfies the condition of no normal flow at boundaries? 2) If not, how close can such a representation come? 3) If such a representation can exist in some circumstances, what is the size of the smallest bolus velocity that fits the data?

The author finds, in agreement with earlier authors, that the answer to the first question is no, although under certain conditions, which include a modification to the eddy flux divergence, a bolus representation becomes possible. One such condition is when the eddy flux divergence is required to balance the time-mean flux divergence. The smallest bolus flow is easily found by solving a thickness-weighted Poisson equation on each density level. This problem is solved for the North Pacific using time-mean data from an eddy-permitting model. The minimum bolus flow is found to be very small at depth but larger than is usually assumed near the surface. The magnitude of this minimum flow is of order one-tenth of the mean flow. Similar but larger results are found for a coarse-resolution model.

* Deceased.

Corresponding author address: Jeff Blundell, National Oceanography Centre, Southampton, Empress Dock, Southampton SO14 3ZH, United Kingdom. Email: jeff@noc.soton.ac.uk.

Save