Effective Eddy Diffusivities Inferred from a Point Release Tracer in an Eddy-Resolving Ocean Model

Mei-Man Lee National Oceanography Centre, Southampton, Southampton, United Kingdom

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A. J. George Nurser National Oceanography Centre, Southampton, Southampton, United Kingdom

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Andrew C. Coward National Oceanography Centre, Southampton, Southampton, United Kingdom

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Beverly A. de Cuevas National Oceanography Centre, Southampton, Southampton, United Kingdom

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Abstract

This study uses tracer experiments in a global eddy-resolving ocean model to examine two diagnostic methods for inferring effective eddy isopycnic diffusivity from point release tracers. The first method is based on the growth rate of the area occupied by the tracers (the equivalent variance). During the period when tracer dispersion is dominated by stirring, the equivalent variance is found to increase at a rate between the second power law (for a pure shearing flow regime) and the exponential law (for a pure stretching flow regime). The second method is based on the length of the tracer contours. In the framework of equivalent radius, the two methods of inferring eddy diffusivity can be understood as two different averagings over the tracer patch. Over a shorter period of tracer dispersion the two methods give different eddy diffusivities, and only over a longer time when tracer dispersion approaches the final stage of diffusion do they give a similar value of diffusivity. A new diagnostic quantity called stirring efficiency is introduced to indicate different flow regimes by measuring the efficiency of stirring against mixing. The new diagnostic quantity has the advantage that it can be calculated directly from the gradients of tracer distribution without needing to estimate strain rate or background diffusivity.

Corresponding author address: Mei-Man Lee, National Oceanography Centre, Southampton, Empress Dock, European Way, Southampton SO14 3ZH, United Kingdom. Email: mmlee@noc.soton.ac.uk

Abstract

This study uses tracer experiments in a global eddy-resolving ocean model to examine two diagnostic methods for inferring effective eddy isopycnic diffusivity from point release tracers. The first method is based on the growth rate of the area occupied by the tracers (the equivalent variance). During the period when tracer dispersion is dominated by stirring, the equivalent variance is found to increase at a rate between the second power law (for a pure shearing flow regime) and the exponential law (for a pure stretching flow regime). The second method is based on the length of the tracer contours. In the framework of equivalent radius, the two methods of inferring eddy diffusivity can be understood as two different averagings over the tracer patch. Over a shorter period of tracer dispersion the two methods give different eddy diffusivities, and only over a longer time when tracer dispersion approaches the final stage of diffusion do they give a similar value of diffusivity. A new diagnostic quantity called stirring efficiency is introduced to indicate different flow regimes by measuring the efficiency of stirring against mixing. The new diagnostic quantity has the advantage that it can be calculated directly from the gradients of tracer distribution without needing to estimate strain rate or background diffusivity.

Corresponding author address: Mei-Man Lee, National Oceanography Centre, Southampton, Empress Dock, European Way, Southampton SO14 3ZH, United Kingdom. Email: mmlee@noc.soton.ac.uk

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  • Allen, D. R., and N. Nakamura, 2001: A seasonal climatology of effective diffusivity in the stratosphere. J. Geophys. Res., 106 , 79177935.

    • Search Google Scholar
    • Export Citation
  • 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
  • Garrett, C., 1983: On the initial streakiness of a dispersing tracer in two- and three-dimensional turbulence. Dyn. Atmos. Oceans, 7 , 265277.

    • Search Google Scholar
    • Export Citation
  • Garrett, C., 2006: Turbulent dispersion in the ocean. Prog. Oceanogr., 70 , 113125.

  • Joseph, J., and H. Sender, 1958: Über die horizontale Diffusion im Meere. Dtsch. Hydrogr. Z., 11 , 4977.

  • Ledwell, J. R., A. J. Watson, and C. S. Law, 1998: Mixing of a tracer in the pycnocline. J. Geophys. Res., 103 , 2149921529.

  • Ledwell, J. R., E. T. Montgomery, K. L. Polzin, L. C. St. Laurent, R. W. Schmitt, and J. M. Toole, 2000: Evidence for enhanced mixing over rough topography in the abyssal ocean. Nature, 403 , 179182.

    • Search Google Scholar
    • Export Citation
  • Lee, M-M., A. C. Coward, and A. J. G. Nurser, 2002: Spurious diapycnal mixing of the deep waters in an eddy-permitting global ocean model. J. Phys. Oceanogr., 32 , 15221535.

    • 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
  • Nakamura, N., 1995: Modified Lagrangian-mean diagnostics of the stratospheric polar vortices. Part I: Formulation and analysis of GFDL SKYHI GCM. J. Atmos. Sci., 52 , 20962108.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., 1996: Two-dimensional mixing, edge formation and permeability diagnosed in an area coordinate. J. Atmos. Sci., 53 , 15241537.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., and J. Ma, 1997: Modified Lagrangian-mean diagnostics of the stratospheric polar vortices, 2, Nitrous oxide and seasonal barrier migration in the cryogenic limb array etalon spectrometer and SKYHI general circulation model. J. Geophys. Res., 102 , 2572125735.

    • Search Google Scholar
    • Export Citation
  • Novikov, E. A., 1958: Concerning a turbulent diffusion in a stream with a transverse gradient of velocity. J. Appl. Math. Mech., 22 , 576579.

    • Search Google Scholar
    • Export Citation
  • Okubo, A., 1966: A note on horizontal diffusion from an instantaneous source in a nonuniform flow. J. Oceanogr. Soc. Japan, 22 , 3540.

    • Search Google Scholar
    • Export Citation
  • Okubo, A., 1968: Some remarks on the importance of the “shear effect” on horizontal diffusion. J. Oceanogr. Soc. Japan, 24 , 6069.

    • Search Google Scholar
    • Export Citation
  • Okubo, A., 1971: Oceanic diffusion diagrams. Deep-Sea Res., 18 , 789802.

  • Sanderson, B. G., and A. Okubo, 1986: An analytical calculation of two-dimensional dispersion. J. Oceanogr. Soc. Japan, 42 , 139153.

  • Schmitt, R. W., J. R. Ledwell, E. T. Montgomery, K. L. Polzin, and J. M. Toole, 2005: Enhanced diapycnal mixing by salt fingers in the thermocline of the tropical Atlantic. Science, 308 , 685688.

    • Search Google Scholar
    • Export Citation
  • Shuckburgh, E., and P. Haynes, 2003: Diagnosing transport and mixing using a tracer-based coordinate system. Phys. Fluids, 15 , 33423357.

    • Search Google Scholar
    • Export Citation
  • Sundermeyer, M. A., and J. F. Price, 1998: Lateral mixing and the North Atlantic Tracer Release Experiment: Observations and numerical simulations of Lagrangian particles and a passive tracer. J. Geophys. Res., 103 , 2148121497.

    • Search Google Scholar
    • Export Citation
  • Townsend, A. A., 1951: The diffusion of heat spots in isotropic turbulence. Proc. Roy. Soc. London, 209A , 418430.

  • Watson, A. J., and Coauthors, 1999: Mixing and convection in the Greenland Sea from a tracer-release experiment. Nature, 401 , 902904.

    • Search Google Scholar
    • Export Citation
  • Webb, D. J., B. A. de Cuevas, and C. S. Richmond, 1998: Improved advection schemes for ocean models. J. Atmos. Oceanic Technol., 15 , 11711187.

    • Search Google Scholar
    • Export Citation
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