Comparison of the Effect of Parameterized Eddy Fluxes of Thickness and Potential Vorticity

V. O. Ivchenko Alfred-Wegener-Institute for Polar and Marine Research, Bremerhaven, Germany

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S. Danilov Alfred-Wegener-Institute for Polar and Marine Research, Bremerhaven, Germany

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J. Schröter Alfred-Wegener-Institute for Polar and Marine Research, Bremerhaven, Germany

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Abstract

Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent–McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.

Corresponding author address: V. O. Ivchenko, Alfred Wegener Institute for Polar and Marine Research, Bussestrasse 24, D-27570, Bremerhaven, Germany. E-mail: vladimir.ivchenko@awi.de

Abstract

Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent–McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.

Corresponding author address: V. O. Ivchenko, Alfred Wegener Institute for Polar and Marine Research, Bussestrasse 24, D-27570, Bremerhaven, Germany. E-mail: vladimir.ivchenko@awi.de
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  • Bretherton, F. S., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc., 92, 325334, doi:10.1002/qj.49709239302.

    • 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, 11231126, doi:10.1126/science.264.5162.1123.

    • Search Google Scholar
    • Export Citation
  • Danilov, S., and D. Gurarie, 2002: Rhines scale and spectra of the β-plane turbulence with bottom drag. Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 65, 067301, doi:10.1103/PhysRevE.65.067301.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D. G., and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Philips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65, 855874, doi:10.1175/2007JAS2227.1.

    • Search Google Scholar
    • Export Citation
  • Eden, C., 2010: Parameterising meso-scale eddy momentum fluxes based on potential vorticity mixing and a gauge term. Ocean Modell., 32, 5871, doi:10.1016/j.ocemod.2009.10.008.

    • Search Google Scholar
    • Export Citation
  • Eden, C., and R. J. Greatbatch, 2008: Towards a mesoscale eddy closure. Ocean Modell., 20, 223239, doi:10.1016/j.ocemod.2007.09.002.

  • Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150155, doi:10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Green, J. S. A., 1970: Transfer properties of the large-scale eddies and the general circulation of the atmosphere. Quart. J. Roy. Meteor. Soc., 96, 157185, doi:10.1002/qj.49709640802.

    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton University Press, 518 pp.

  • Harrison, D. E., 1978: On the diffusion parameterization of mesoscale eddy effects from a numerical ocean experiment. J. Phys. Oceanogr., 8, 913918, doi:10.1175/1520-0485(1978)008<0913:OTDPOM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • 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, 13201343, doi:10.1175/1520-0485(1996)026<1320:DWPASB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Holland, W. R., 1978: The role of mesoscale eddies in the general circulation of the ocean—Numerical experiments using a wind-driven quasi-geostrophic model. J. Phys. Oceanogr., 8, 363392, doi:10.1175/1520-0485(1978)008<0363:TROMEI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., 1984: Parameterization of the eddy fluxes of the quasi-geostrophic potential vorticity in zonal flows. Dokl. Akad. Nauk USSR, 277, 972976.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., 1987: Influence of bottom topography on the eddy transfer coefficient. Izv. Akad. Nauk USSR, Atmos. Ocean Phys.,23, 200208.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., K. J. Richards, and D. P. Stevens, 1996: The dynamics of the Antarctic Circumpolar Current. J. Phys. Oceanogr., 26, 753774, doi:10.1175/1520-0485(1996)026<0753:TDOTAC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., K. J. Richards, B. Sinha, and J.-O. Wolff, 1997: Parameterization of mesoscale eddy fluxes in zonal ocean flows. J. Mar. Res., 55, 11271162, doi:10.1357/0022240973224076.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., S. Danilov, and D. Olbers, 2008: Eddies in numerical models of the Southern Ocean. Ocean Modeling in an Eddying Regime, Geophys. Monogr., Vol. 177, Amer. Geophys. Union, 177–198, doi:10.1029/177GM13.

  • Ivchenko, V. O., B. Sinha, V. B. Zalesny, R. Marsh, and A. T. Blaker, 2013: Influence of bottom topography on integral constraints in zonal flows with parameterized potential vorticity fluxes. J. Phys. Oceanogr., 43, 311323, doi:10.1175/JPO-D-12-0126.1.

    • Search Google Scholar
    • Export Citation
  • Ivchenko, V. O., S. Danilov, B. Sinha, and J. Schroeter, 2014: Integral constraints for momentum and energy in zonal flows with parameterized potential vorticity fluxes: Governing parameters. J. Phys. Oceanogr., 44, 922943, doi:10.1175/JPO-D-13-0173.1.

    • Search Google Scholar
    • Export Citation
  • Kamenkovich, V. M., M. N. Koshlyakov, and A. S. Monin, 1986: Synoptic Eddies in the Ocean. D. Reidel Publishing Company, 433 pp.

  • Killworth, P. D., 1992: An equivalent barotropic mode in the Fine Resolution Antarctic Model. J. Phys. Oceanogr., 22, 13791387, doi:10.1175/1520-0485(1992)022<1379:AEBMIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Killworth, P. D., 1997: On the parameterization of eddy transfer. Part I. Theory. J. Mar. Res., 55, 11711197, doi:10.1357/0022240973224102.

    • Search Google Scholar
    • Export Citation
  • Krupitsky, A., V. M. Kamenkovich, N. Naik, and M. A. Cane, 1996: A linear equivalent barotropic model of the Antarctic Circumpolar Current with realistic coastlines and bottom topography. J. Phys. Oceanogr., 26, 18031824, doi:10.1175/1520-0485(1996)026<1803:ALEBMO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Marshall, D. P., and A. J. Adcroft, 2010: Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold’s first stability theorem. Ocean Modell., 32, 188204, doi:10.1016/j.ocemod.2010.02.001.

    • Search Google Scholar
    • Export Citation
  • Marshall, D. P., J. R. Maddison, and P. S. Berloff, 2012: A framework for parameterizing eddy potential vorticity fluxes. J. Phys. Oceanogr., 42, 539557, doi:10.1175/JPO-D-11-048.1.

    • Search Google Scholar
    • Export Citation
  • Marshall, J. C., 1981: On the parameterization of geostrophic eddies in the ocean. J. Phys. Oceanogr., 11, 257271, doi:10.1175/1520-0485(1981)011<0257:OTPOGE>2.0.CO;2.

    • 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 J. S. Chow, 1981: Equilibrium geostrophic turbulence. I: A reference solution in a beta plane channel. J. Phys. Oceanogr., 11, 921949, doi:10.1175/1520-0485(1981)011<0921:EGTIAR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • McWilliams, J. C., W. R. Holland, and J. S. Chow, 1978: A description of numerical Antarctic Circumpolar Currents. Dyn. Atmos. Oceans, 2, 213291, doi:10.1016/0377-0265(78)90018-0.

    • Search Google Scholar
    • Export Citation
  • Olbers, D., 2005: On the role of eddy mixing in the transport of zonal ocean currents. Marine Turbulence: Theories, Observations, and Models, H. Baumert, J. Simpson, and J. Sündermann, Eds., Cambridge University Press, 511–546.

  • Pedlosky, J., 1964: The stability of currents in the atmosphere and the ocean: Part I. J. Atmos. Sci., 21, 201219, doi:10.1175/1520-0469(1964)021<0201:TSOCIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rhines, P., 1975: Waves and turbulence on a β-plane. J. Fluid Mech., 69, 417443, doi:10.1017/S0022112075001504.

  • Ringler, T., and P. Gent, 2011: An eddy closure for potential vorticity. Ocean Modell., 39, 125134, doi:10.1016/j.ocemod.2011.02.003.

    • Search Google Scholar
    • Export Citation
  • Stevens, D. P., and V. O. Ivchenko, 1997: The zonal momentum balance in an eddy-resolving general-circulation model of the Southern Ocean. Quart. J. Roy. Meteor. Soc., 123, 929951, doi:10.1002/qj.49712354008.

    • 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, doi:10.1175/1520-0485(1997)027<0567:POQEIP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wardle, R., and J. Marshall, 2000: Representation of eddies in primitive equation models by a PV flux. J. Phys. Oceanogr., 30, 24812503, doi:10.1175/1520-0485(2000)030<2481:ROEIPE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Welander, P., 1973: Lateral friction in the ocean as an effect of potential vorticity mixing. Geophys. Fluid Dyn., 5, 173189, doi:10.1080/03091927308236114.

    • Search Google Scholar
    • Export Citation
  • Wolff, J.-O., E. Maier-Reimer, and D. J. Olbers, 1991: Wind-driven flow over topography in a zonal β-plane channel: A quasigeostrophic model of the Antarctic Circumpolar Current. J. Phys. Oceanogr., 21, 236264, doi:10.1175/1520-0485(1991)021<0236:WDFOTI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Wood, R. B., and M. E. McIntyre, 2010: A general theorem on angular-momentum changes due to potential vorticity mixing and on potential-energy changes due to buoyancy mixing. J. Atmos. Sci., 67, 12611274, doi:10.1175/2009JAS3293.1.

    • Search Google Scholar
    • Export Citation
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