Editorial Type:
Article
Article Type:
Research Article

A Global Model for the Diapycnal Diffusivity Induced by Internal Gravity Waves

Dirk Olbers Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany

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Carsten Eden Institut für Meereskunde, KlimaCampus, Universität Hamburg, Hamburg, Germany

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Print Publication:
01 Aug 2013
DOI:
https://doi.org/10.1175/JPO-D-12-0207.1
Page(s):
1759–1779
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Abstract

An energetically consistent model for the diapycnal diffusivity induced by breaking of internal gravity waves is proposed and tested in local and global settings. The model [Internal Wave Dissipation, Energy and Mixing (IDEMIX)] is based on the spectral radiation balance of the wave field, reduced by integration over the wavenumber space, which yields a set of balances for energy density variables in physical space. A further simplification results in a single partial differential equation for the total energy density of the wave field. The flux of energy to high vertical wavenumbers is parameterized by a functional derived from the wave–wave scattering integral of resonant wave triad interactions, which also forms the basis for estimates of dissipation rates and related diffusivities of ADCP and hydrography fine-structure data. In the current version of IDEMIX, the wave energy is forced by wind-driven near-inertial motions and baroclinic tides, radiating waves from the respective boundary layers at the surface and the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and diapycnal diffusivities in rough agreement to observational estimates. IDEMIX is ready for use as a mixing module in ocean circulation models and can be extended with more spectral components.

Corresponding author address: Carsten Eden, KlimaCampus, Universität Hamburg, Bundesstrasse 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de

Abstract

An energetically consistent model for the diapycnal diffusivity induced by breaking of internal gravity waves is proposed and tested in local and global settings. The model [Internal Wave Dissipation, Energy and Mixing (IDEMIX)] is based on the spectral radiation balance of the wave field, reduced by integration over the wavenumber space, which yields a set of balances for energy density variables in physical space. A further simplification results in a single partial differential equation for the total energy density of the wave field. The flux of energy to high vertical wavenumbers is parameterized by a functional derived from the wave–wave scattering integral of resonant wave triad interactions, which also forms the basis for estimates of dissipation rates and related diffusivities of ADCP and hydrography fine-structure data. In the current version of IDEMIX, the wave energy is forced by wind-driven near-inertial motions and baroclinic tides, radiating waves from the respective boundary layers at the surface and the bottom into the ocean interior. The model predicts plausible magnitudes and three-dimensional structures of internal wave energy, dissipation rates, and diapycnal diffusivities in rough agreement to observational estimates. IDEMIX is ready for use as a mixing module in ocean circulation models and can be extended with more spectral components.

Corresponding author address: Carsten Eden, KlimaCampus, Universität Hamburg, Bundesstrasse 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de
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  • Alford, M., 2001: Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer near-inertial motions. J. Phys. Oceanogr., 31, 2359–2368.

    • Search Google Scholar
    • Export Citation

  • Arbic, B., S. Garner, R. Hallberg, and H. Simmons, 2004: The accuracy of surface elevations in forward global barotropic and baroclinic tide models. Deep-Sea Res., 51, 3069–3101.

    • Search Google Scholar
    • Export Citation

  • Baines, P., 1982: On internal tide generation models. Deep-Sea Res., 29, 307–338.

  • Bell, T. H., 1975: Topographically generated internal waves in the open ocean. J. Geophys. Res., 80, 320–327.

  • Bryan, K., and L. Lewis, 1979: A water mass model of the world ocean. J. Geophys. Res., 84 (C5), 2503–2517.

  • Burchard, H., and H. Baumert, 1995: On the performance of a mixed-layer model based on the k-ϵ turbulence closure. J. Geophys. Res., 100 (C5), 8523–8540.

    • Search Google Scholar
    • Export Citation

  • Cairns, J. L., and G. O. Williams, 1976: Internal wave observations from a midwater float, 2. J. Geophys. Res., 81, 1943–1950.

  • Cummins, P., G. Holloway, and A. Gargett, 1990: Sensitivity of GFDL ocean general circulation model to a parameterization of vertical diffusion. J. Phys. Oceanogr., 20, 817–830.

    • Search Google Scholar
    • Export Citation

  • Eden, C., and R. J. Greatbatch, 2008: Diapycnal mixing by mesoscale eddies. Ocean Modell., 23, 113–120.

  • Eriksen, C. C., 1982: Observations of internal wave reflection off sloping bottoms. J. Geophys. Res., 87 (C1), 525–538.

  • Fu, L.-L., 1981: Observations and models of inertial waves in the deep ocean. Rev. Geophys. Space Phys., 19, 141–170.

  • Garrett, C., 2001: What is the near-inertial wave band and why is it different from the rest of the internal wave spectrum? J. Phys. Oceanogr., 31, 962–971.

    • Search Google Scholar
    • Export Citation

  • Garrett, C., and W. Munk, 1972: Space–time scales of internal waves. Geophys. Astrophys. Fluid Dyn., 3, 225–264.

  • Gaspar, P., Y. Gregoris, and J.-M. Lefevre, 1990: A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station PAPA and Long-Term Upper Ocean Study site. J. Geophys. Res., 95 (C9), 16 179–16 193.

    • Search Google Scholar
    • Export Citation

  • Gouretski, V., and K. Koltermann, 2004: WOCE global hydrographic climatology. Ber. BSH, 35, 1–52.

  • Gregg, M., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94 (C7), 9686–9698.

  • Gregg, M., T. Sanford, and D. Winkel, 2003: Reduced mixing from the breaking of internal waves in equatorial waters. Nature, 422, 513–515.

    • Search Google Scholar
    • Export Citation

  • Henyey, F., J. Wright, and S. Flatté, 1986: Energy and action flow through the internal wave field: An Eikonal approach. J. Geophys. Res., 91 (C7), 8487–8495.

    • Search Google Scholar
    • Export Citation

  • Jayne, S., 2009: The impact of abyssal mixing parameterizations in an ocean general circulation model. J. Phys. Oceanogr., 39, 1756–1775.

    • Search Google Scholar
    • Export Citation

  • Jayne, S., and L. St. Laurent, 2001: Parameterizing tidal dissipation over rough topography. Geophys. Res. Lett., 28, 811–814.

  • Jochum, M., B. Briegleb, G. Danabasoglu, W. Large, N. J. Norton, S. Jayne, M. Alford, and F. Bryan, 2012: The impact of oceanic near-inertial waves on climate. J. Climate,26, 2833–2844.

  • Käse, R., 1979: Calculations of the energy transfer by the wind to near-inertial waves. Deep-Sea Res., 26, 227–232.

  • Kunze, E., E. Firing, J. M. Hummon, T. K. Chereskin, and A. M. Thurnherr, 2006: Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J. Phys. Oceanogr., 36, 1553–1576.

    • Search Google Scholar
    • Export Citation

  • Large, W. G., and G. Crawford, 1995: Observations and simulations of upper-ocean response to wind events during the ocean storms experiment. J. Phys. Oceanogr., 25, 2831–2852.

    • Search Google Scholar
    • Export Citation

  • Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with nonlocal boundary layer parameterization. Rev. Geophys., 32, 363–403.

    • Search Google Scholar
    • Export Citation

  • Levitus, S., and Coauthors, 1998: Introduction. Vol. 1, World Ocean Database 1998, NOAA Atlas NESDIS 18, 346 pp.

  • Llewellyn Smith, S., and W. Young, 2002: Conversion of the barotropic tide. J. Phys. Oceanogr., 32, 1554–1566.

  • Lvov, Y., and E. Tabak, 2001: Hamiltonian formalism and the Garrett–Munk spectrum of internal waves in the ocean. Phys. Rev. Lett., 87, 168501, doi:10.1103/PhysRevLett.87.168501.

    • Search Google Scholar
    • Export Citation

  • Maas, L., 2011: Topographies lacking tidal conversion. J. Fluid Mech., 1, 1–20.

  • MacKinnon, J. A., and K. B. Winters, 2005: Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9 degree latitude. Geophys. Res. Lett., 32, L15605, doi:10.1029/2005GL023376.

    • Search Google Scholar
    • Export Citation

  • McComas, C. H., 1977: Equilibrium mechanisms within the oceanic internal wave field. J. Phys. Oceanogr., 7, 836–845.

  • McComas, C. H., and F. P. Bretherton, 1977: Resonant interaction of oceanic internal waves. J. Geophys. Res., 82, 1397–1412.

  • McComas, C. H., and P. Müller, 1981: Time scales of resonant interactions among oceanic internal waves. J. Phys. Oceanogr., 11, 139–147.

    • Search Google Scholar
    • Export Citation

  • Molemaker, M., J. McWilliams, and I. Yavneh, 2005: Baroclinic instability and loss of balance. J. Phys. Oceanogr., 35, 1505–1517.

  • Müller, P., and M. Briscoe, 1999: Diapycnal mixing and internal waves. Dynamics of Oceanic Internal Gravity Waves: Proc. 11th Aha Huliko'a Hawaiian Workshop, Honolulu, HI, University of Hawai‘i at Mānoa, 289–294.

  • Müller, P., and A. Natarov, 2003: The internal wave action model (IWAM). Near Boundary Processes and Their Parameterization: Proc. 13th Aha Huliko'a Hawaiian Winter Workshop, Honolulu, HI, University of Hawai‘i at Mānoa, 95–105.

  • Müller, P., D. J. Olbers, and J. Willebrand, 1978: The IWEX spectrum. J. Geophys. Res., 83, 479–500.

  • Müller, P., G. Holloway, F. Henyey, and N. Pomphrey, 1986: Nonlinear interactions among internal gravity waves. Rev. Geophys., 24, 493–536.

    • Search Google Scholar
    • Export Citation

  • Munk, W. H., 1966: Abyssal recipes. Deep-Sea Res., 13, 707–730.

  • Munk, W. H., 1981: Internal waves and small-scale processes. Evolution of Physical Oceanography, B. A. Warren and C. Wunsch, Eds., MIT Press, 264–291.

  • Nikurashin, M., and R. Ferrari, 2011: Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett., 38, L08610, doi:10.1029/2011GL046576

    • Search Google Scholar
    • Export Citation

  • Nikurashin, M., G. Vallis, and A. Adcroft, 2013: Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nat. Geosci., 6, 48–51.

    • Search Google Scholar
    • Export Citation

  • Nycander, J., 2005: Generation of internal waves in the deep ocean by tides. J. Geophys. Res., 110, C10028 , doi:10.1029/2004JC002487.

  • Olbers, D. J., 1974: On the energy balance of small-scale internal waves in the deep sea. Hamb. Geophys. Einzelschriften,24, 91.

  • Olbers, D. J., 1976: Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean. J. Fluid Mech., 74, 375–399.

    • Search Google Scholar
    • Export Citation

  • Olbers, D. J., 1983: Models of the oceanic internal wave field. Rev. Geophys. Space Phys., 21, 1567–1606.

  • Olbers, D. J., and K. Herterich, 1979: The spectral energy transfer from surface waves to internal waves. J. Fluid Mech., 92, 349–379.

    • Search Google Scholar
    • Export Citation

  • Olbers, D., J. Willebrand, and C. Eden, 2012: Ocean Dynamics. Springer Verlag, 704 pp.

  • Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10, 83–89.

  • Osborn, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Astrophys. Fluid Dyn., 3, 321–345.

  • Plueddemann, A., and J. Farrar, 2006: Observations and models of the energy flux from the wind to mixed-layer inertial currents. Deep-Sea Res., 53 (1–2), 5–30.

    • Search Google Scholar
    • Export Citation

  • Polzin, K. L., 2004a: A heuristic description of internal wave dynamics. J. Phys. Oceanogr., 34, 214–230.

  • Polzin, K. L., 2004b: Idealized solutions for the energy balance of the finescale internal wave field. J. Phys. Oceanogr., 34, 231–246.

    • Search Google Scholar
    • Export Citation

  • Polzin, K. L., 2009: An abyssal recipe. Ocean Modell., 30, 298–309.

  • Polzin, K. L., and Y. V. Lvov, 2011: Toward regional characterizations of the oceanic internal wavefield. Rev. Geophys., 49, RG4003, doi:10.1029/2010RG000329.

    • Search Google Scholar
    • Export Citation

  • Polzin, K. L., J. M. Toole, and R. W. Schmitt, 1995: Finescale parameterizations of turbulent dissipation. J. Phys. Oceanogr., 25, 306–328.

    • Search Google Scholar
    • Export Citation

  • Pomphrey, N., J. D. Meiss, and K. M. Watson, 1980: Description of nonlinear internal wave interactions using langevin methods. J. Geophys. Res., 85 (C2), 1085–1094.

    • Search Google Scholar
    • Export Citation

  • Simmons, H., S. Jayne, L. St. Laurent, and A. Weaver, 2004: Tidally driven mixing in a numerical model of the ocean general circulation. Ocean Modell., 6, 245–263.

    • Search Google Scholar
    • Export Citation

  • Staquet, C., 2004: Gravity and inertia-gravity internal waves: Breaking processes and induced mixing. Surv. Geophys., 25, 281–314.

  • Staquet, C., and J. Sommeria, 2002: Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech., 34, 559–593.

  • St. Laurent, L., H. Simmons, and S. Jayne, 2002: Estimating tidally driven mixing in the deep ocean. Geophys. Res. Lett., 29, 2106, doi:10.1029/2002GL015633.

    • Search Google Scholar
    • Export Citation

  • Sun, H., and E. Kunze, 1999: Internal wave–wave interactions. Part II: Spectral energy transfer and turbulence production. J. Phys. Oceanogr., 29, 2905–2919.

    • Search Google Scholar
    • Export Citation

  • Tandon, A., and C. Garrett, 1996: On a recent parameterization of mesoscale eddies. J. Phys. Oceanogr., 26, 406–416.

  • Walter, M., C. Mertens, and M. Rhein, 2005: Mixing estimates from a large-scale hydrographic survey in the North Atlantic. Geophys. Res. Lett., 32, L13605, 10.1029/2005GL022471.

    • Search Google Scholar
    • Export Citation

  • Watanabe, M., and T. Hibiya, 2002: Global estimates of the wind-induced energy flux to inertial motions in the surface mixed layer. Geophys. Res. Lett., 29, 1239, doi:10.1029/2001GL014422.

    • Search Google Scholar
    • Export Citation

  • Watson, K., B. West, and B. Cohen, 1976: Coupling of surface and internal gravity waves: A mode coupling model. J. Fluid Mech., 77, 185–208.

    • Search Google Scholar
    • Export Citation

  • Whalen, C., L. Talley, and J. MacKinnon, 2012: Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys. Res. Lett., 39, L18612, doi:10.1029/2012GL053196.

    • Search Google Scholar
    • Export Citation

  • Wu, L., Z. Jing, S. Riser, and M. Visbeck, 2011: Seasonal and spatial variations of Southern Ocean diapycnal mixing from Argo profiling floats. Nat. Geosci., 4, 363–366.

    • Search Google Scholar
    • Export Citation
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