Skip to main content

Three-Dimensional Residual-Mean Theory

  • Chapter
Ocean Modeling and Parameterization

Part of the book series: NATO Science Series ((ASIC,volume 516))

Abstract

Mesoscale eddies act to mix fluid parcels in a way that is highly constrained by the stratified nature of the fluid. The residual-mean theory provides the link between the different views that are apparent from averaging these turbulent flow fields in height coordinates and in density coordinates. It reduces the parameterization problem from three dimensions to two dimensions and it shows how the eddy fluxes are skew-symmetric in height coordinates so that the total advection velocity can be adiabatic.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Andrews, D. G. and M. E. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the zonal mean acceleration. J. Atmos. Sci., 33 2031–2048.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bleck, R., C. Rooth, D. Hu and L. Smith, 1992, Salinity-driven thermocline transients in a wind-and thermohaline-forced isopycnic coordinate model of the North Atlantic. J. Phys. Oceanogr., 22 1486–1505.

    Article  Google Scholar 

  • Danabasoglu, G. and J. C. McWilliams, 1995: Sensitivity of the global ocean circulation to parameterization of mesoscale tracer transports. J. Climate, 8 2967–2987.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Griffies, S. M., 1998: The Gent-McWilliams skew-flux. Submitted to J. Phys. Oceanogr.

    Google Scholar 

  • Griffies, S. M., A. Gnanadesikan, R. C. Pacanowski, V. Larichev, J. K. Dukowicz, and R. D. Smith, 1998: Isoneutral diffusion in a z-coordinate ocean model. Submitted to J. Phys. Oceanogr.

    Google Scholar 

  • Hirst, A. C., H. B. Gordon and S. P. O’Farrell, 1996: Global warming in a coupled climate model including oceanic eddy-induced advection. Geophys. Res. Lett., 23 3361–3364.

    Article  Google Scholar 

  • Hirst, A. C. and T. J. McDougall, 1996: Deep water properties and surface buoyancy flux as simulated by a z-coordinate model including eddy-induced advection. J. Phys. Oceanogr., 26 1320–1343.

    Article  Google Scholar 

  • Hirst, A. C. and T. J. McDougall, 1998: Meridional overturning and dianeutral motion in a z-coordinate ocean model including eddy-induced advection. J. Phys. Oceanogr., in press.

    Google Scholar 

  • Killworth, P. D., 1998: On the parameterization of eddy transfer. Part I: Theory. J. Mar. Res., 55 1171–1197.

    Article  Google Scholar 

  • Large, W. G., G. Danabasoglu, S. C. Doney, and J. C. McWilliams, 1997: Sensitivity to surface forcing and boundary layer mixing in a global ocean model: Annual-mean climatology. J. Phys. Oceanogr., 27 2418–2447.

    Article  Google Scholar 

  • Lozier, M. S., M. S. McCartney, and W. B. Owens, 1994: Anomalous anomalies in averaged hydrographic data. J. Phys. Oceanogr., 24 2624–2638.

    Article  Google Scholar 

  • Marshall, J. and G. Shutts, 1981: A note on rotational and divergent eddy fluxes. J. Phys. Oceanogr., 11,1677–1680.

    Article  Google Scholar 

  • McDougall, T. J., 1995: The influence of ocean mixing on the absolute velocity vector. J. Phys. Oceanogr., 25 705–725.

    Article  Google Scholar 

  • McDougall, T. J. and P. C. McIntosh, 1996: The temporal-residual-mean velocity. Part I: Derivation and the scalar conservation equations. J. Phys. Oceanogr., 26 2653–2665.

    Article  Google Scholar 

  • McDougall, T. J. and P. C. McIntosh, 1998a: A residual-mean circulation suitable for unsteady flows. Submitted to J. Phys. Oceanogr.

    Google Scholar 

  • McDougall, T. J. and P. C. McIntosh, 1998b: The temporal-residual-mean velocity. Part II: Isopycnal interpretation. Submitted to J. Phys. Oceanogr.

    Google Scholar 

  • McIntosh, P. C. and T. J. McDougall, 1996: Isopycnal averaging and the residual mean circulation. J. Phys. Oceanogr., 26 1655–1660.

    Article  Google Scholar 

  • Plumb, R. A, 1979: Eddy fluxes of conserved quantities by small-amplitude waves. J. Atmos. Sci., 36 1699–1704.

    Article  Google Scholar 

  • Plumb, R. A. and J. D. Mahlman, 1987: The zonally-average transport characteristics of the GFDL general circulation/transport model. J. Atmos. Sci., 44 298–327.

    Article  Google Scholar 

  • Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12 1154–1158.

    Article  Google Scholar 

  • Rintoul, S. R., and C. Wunsch, 1991: Mass, heat, oxygen and nutrient fluxes and budgets in the North Atlantic Ocean. Deep-Sea Res., 38(Suppl. 1), S355 - S377.

    Article  Google Scholar 

  • Tréguier, A. M., 1998: Evaluating eddy mixing coefficients from eddy resolving ocean models: A case study. Submitted to J. Marine. Res.

    Google Scholar 

  • Tréguier, A. M., I. M. Held, and V. D. Larichev, 1997: Parameterization of quasigeostrophic eddies in primitive equation ocean models. J. Phys. Oceanogr., 27 567–580.

    Article  Google Scholar 

  • Visbeck, M., J. Marshall, T. Haine and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27 381–402.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

McDougall, T.J. (1998). Three-Dimensional Residual-Mean Theory. In: Chassignet, E.P., Verron, J. (eds) Ocean Modeling and Parameterization. NATO Science Series, vol 516. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5096-5_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5096-5_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5229-7

  • Online ISBN: 978-94-011-5096-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics