• Balmforth, N., , S. L. Smith, , and W. Young, 1998: Dynamics of interfaces and layers in a stratified turbulent fluid. J. Fluid Mech, 355 , 329358.

    • Search Google Scholar
    • Export Citation
  • Batchelor, G. K., 1959: Small-scale variation of convected quantities like temperature in turbulent fluid. J. Fluid Mech, 5 , 113133.

  • Broadwell, J., , and R. Breidenthal, 1982: A simple model of mixing and chemical reaction in a turbulent shear layer. J. Fluid Mech, 125 , 397410.

    • Search Google Scholar
    • Export Citation
  • Caldwell, D., 1983: Oceanic turbulence: Big bangs or continuous creation? J. Geophys. Res, 88 , 75437550.

  • Caulfield, C., , and W. Peltier, 2000: Anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech, 413 , 147.

    • Search Google Scholar
    • Export Citation
  • DeSilva, I., , H. Fernando, , F. Eaton, , and D. Hebert, 1996: Evolution of Kelvin–Helmholtz billows in nature and laboratory. Earth Planet. Sci. Lett, 143 , 217231.

    • Search Google Scholar
    • Export Citation
  • Dillon, T., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov scales. J. Geophys. Res, 87 , 96019613.

  • Gargett, A. E., 1988: The scaling of turbulence in the presence of stable stratification. J. Geophys. Res, 93 , 50215036.

  • Gargett, A. E., , and J. Moum, 1995: Mixing efficiencies in turbulent tidal fronts: Results from direct and indirect measurements of density flux. J. Phys. Oceanogr, 25 , 25832608.

    • Search Google Scholar
    • Export Citation
  • Gargett, A. E., , T. Osborn, , and P. Nasmyth, 1984: Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech, 144 , 231280.

    • Search Google Scholar
    • Export Citation
  • Gibson, C., 1980: Fossil temperature, salinity and vorticity turbulence in the ocean. Marine Turbulence, J. Nihoul, Ed., Elsevier, 221–257.

    • Search Google Scholar
    • Export Citation
  • Gregg, M. C., 1987: Diapycnal mixing in the thermocline: A review. J. Geophys. Res, 92 , (C5). 52495286.

  • Hazel, P., 1972: Numerical studies of the stability of inviscid parallel shear flows. J. Fluid Mech, 51 , 3962.

  • Hebert, D., , and J. Moum, 1994: Decay of a near-inertial wave. J. Phys. Oceanogr, 24 , 23342351.

  • Hebert, D., , J. Moum, , C. Paulson, , and D. Caldwell, 1992: Turbulence and internal waves at the equator. Part II: Details of a single event. J. Phys. Oceanogr, 22 , 13461356.

    • Search Google Scholar
    • Export Citation
  • Hinze, J., 1975: Turbulence. 2d ed. McGraw-Hill, 790 pp.

  • Ivey, G., , and J. Imberger, 1991: On the nature of turbulence in a stratified fluid. Part I: The energetics of mixing. J. Phys. Oceanogr, 21 , 650658.

    • Search Google Scholar
    • Export Citation
  • Klaassen, G., , and W. Peltier, 1991: The influence of stratification on secondary instability in free shear layers. J. Fluid Mech, 227 , 71106.

    • Search Google Scholar
    • Export Citation
  • Lien, R-C., , D. Caldwell, , M. Gregg, , and J. Moum, 1995: Turbulence variability at the equator in the central Pacific at the beginning of the 1991–1993 El Nino. J. Geophys. Res, 100 , (C4). 68816898.

    • Search Google Scholar
    • Export Citation
  • McEwan, A., 1983: Internal mixing in stratified fluids. J. Fluid Mech, 128 , 5980.

  • Moum, J. N., 1990: Profiler measurements of vertical velocity microstructure in the ocean. J. Atmos. Oceanic Technol, 7 , 323333.

  • Moum, J. N., 1996a: Efficiency of mixing in the main thermocline. J. Geophys. Res, 101 , (C5). 12 05712 069.

  • Moum, J. N., 1996b: Energy-containing scales of turbulence in the ocean thermocline. J. Geophys. Res, 101 , (C6). 14 09514 109.

  • Oakey, N., 1982: Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements. J. Phys. Oceanogr, 12 , 256271.

    • Search Google Scholar
    • Export Citation
  • Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr, 10 , 8389.

  • Osborn, T. R., , and C. S. Cox, 1972: Oceanic fine structure. Geophys. Fluid Dyn, 3 , 321345.

  • Peters, H., , M. Gregg, , and J. O'Toole, 1988: On the parameterization of equatorial turbulence. J. Geophys. Res, 93 , 11991218.

  • Phillips, O., 1972: Turbulence in a strongly stratified fluid: Is it unstable? Deep-Sea Res, 19 , 7981.

  • Posmentier, E., 1977: The generation of salinity finestructure by vertical diffusion. J. Phys. Oceanogr, 7 , 298300.

  • Ruddick, B., , T. McDougall, , and J. Turner, 1989: The formation of layers in a uniformly stirred density gradient. Deep-Sea Res, 36 , 579609.

    • Search Google Scholar
    • Export Citation
  • Ruddick, B., , D. Walsh, , and N. Oakey, 1997: Variations in apparent mixing efficiency in the North Atlantic Central Water. J. Phys. Oceanogr, 27 , 25892605.

    • Search Google Scholar
    • Export Citation
  • Scinocca, J., 1995: The mixing of mass and momentum by Kelvin–Helmholtz billows. J. Atmos. Sci, 52 , 25092530.

  • Smyth, W., 1999: Dissipation range geometry and scalar spectra in sheared, stratified turbulence. J. Fluid Mech, 401 , 209242.

  • Smyth, W., , and W. Peltier, 1989: The transition between Kelvin–Helmholtz and Holmboe instability: An investigation of the overreflection hypothesis. J. Atmos. Sci, 46 , 36983720.

    • Search Google Scholar
    • Export Citation
  • Smyth, W., , and W. Peltier, 1993: Two-dimensional turbulence in homogeneous and stratified shear layers. Geophys. Astrophys. Fluid Dyn, 69 , 132.

    • Search Google Scholar
    • Export Citation
  • Smyth, W., , and J. Moum, 2000a: Anisotropy of turbulence in stably stratified mixing layers. Phys. Fluids, 12 , 13431362.

  • Smyth, W., , and J. Moum, 2000b: Length scales of turbulence in stably stratified mixing layers. Phys. Fluids, 12 , 13271342.

  • Smyth, W., , D. Hebert, , and J. Moum, 1996: Local ocean response to a multiphase westerly wind-burst. Part 2: Thermal and freshwater responses. J. Geophys. Res, 101 , 22 49522 512.

    • Search Google Scholar
    • Export Citation
  • Staquet, C., 2000: Mixing in a stably stratified shear layer: Two- and three-dimensional numerical experiments. Fluid. Dyn. Res., 27, 367–404.

    • Search Google Scholar
    • Export Citation
  • Tennekes, H., , and J. Lumley, 1972: A First Course in Turbulence. The MIT Press, 300 pp.

  • Thorpe, S., 1977: Turbulence and mixing in a Scottish loch. Philos. Trans. Roy. Soc. London, A286 , 125181.

  • Werne, J., , and D. Fritts, 1999: Stratified shear turbulence: Evolution and statistics. Geophys. Res. Lett, 26 , 439442.

  • Wijesekera, H., , and T. Dillon, 1997: Shannon entropy as an indicator of age for turbulent overturns in the oceanic thermocline. J. Geophys. Res, 102 , (C2). 32793291.

    • Search Google Scholar
    • Export Citation
  • Wijesekera, H., , T. Dillon, , and L. Padman, 1993: Some statistical and dynamical properties of turbulence in the ocean pycnocline. J. Geophys. Res, 98 , 22 66522 679.

    • Search Google Scholar
    • Export Citation
  • Winters, K., , P. Lombard, , J. Riley, , and E. A. D'Asaro, 1995: Available potential energy and mixing in density-stratified fluids. J. Fluid. Mech, 289 , 115128.

    • Search Google Scholar
    • Export Citation
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The Efficiency of Mixing in Turbulent Patches: Inferences from Direct Simulations and Microstructure Observations

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  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
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Abstract

The time evolution of mixing in turbulent overturns is investigated using a combination of direct numerical simulations (DNS) and microstructure profiles obtained during two field experiments. The focus is on the flux coefficient Γ, the ratio of the turbulent buoyancy flux to the turbulent kinetic energy dissipation rate ϵ. In observational oceanography, a constant value Γ = 0.2 is often used to infer the buoyancy flux and the turbulent diffusivity from measured ϵ. In the simulations, the value of Γ changes by more than an order of magnitude over the life of a turbulent overturn, suggesting that the use of a constant value for Γ is an oversimplification. To account for the time dependence of Γ in the interpretation of ocean turbulence data, a way to assess the evolutionary stage at which a given turbulent event was sampled is required. The ratio of the Ozmidov scale LO to the Thorpe scale LT is found to increase monotonically with time in the simulated flows, and therefore may provide the needed time indicator. From the DNS results, a simple parameterization of Γ in terms of LO/LT is found. Applied to observational data, this parameterization leads to a 50%–60% increase in median estimates of turbulent diffusivity, suggesting a potential reassessment of turbulent diffusivity in weakly and intermittently turbulent regimes such as the ocean interior.

Corresponding author address: Dr. William D. Smyth, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331. Email: smyth@oce.orst.edu

Abstract

The time evolution of mixing in turbulent overturns is investigated using a combination of direct numerical simulations (DNS) and microstructure profiles obtained during two field experiments. The focus is on the flux coefficient Γ, the ratio of the turbulent buoyancy flux to the turbulent kinetic energy dissipation rate ϵ. In observational oceanography, a constant value Γ = 0.2 is often used to infer the buoyancy flux and the turbulent diffusivity from measured ϵ. In the simulations, the value of Γ changes by more than an order of magnitude over the life of a turbulent overturn, suggesting that the use of a constant value for Γ is an oversimplification. To account for the time dependence of Γ in the interpretation of ocean turbulence data, a way to assess the evolutionary stage at which a given turbulent event was sampled is required. The ratio of the Ozmidov scale LO to the Thorpe scale LT is found to increase monotonically with time in the simulated flows, and therefore may provide the needed time indicator. From the DNS results, a simple parameterization of Γ in terms of LO/LT is found. Applied to observational data, this parameterization leads to a 50%–60% increase in median estimates of turbulent diffusivity, suggesting a potential reassessment of turbulent diffusivity in weakly and intermittently turbulent regimes such as the ocean interior.

Corresponding author address: Dr. William D. Smyth, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331. Email: smyth@oce.orst.edu

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