• Alford, M. H., and R. Pinkel, 2000: Observations of overturning in the thermocline: The context of ocean mixing, Part I. J. Phys. Oceanogr., 30, 805832, https://doi.org/10.1175/1520-0485(2000)030<0805:OOOITT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Allen, K. R., and R. I. Joseph, 1989: A canonical statistical theory of oceanic internal waves. J. Fluid Mech., 204, 185228, https://doi.org/10.1017/S0022112089001722.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chunchuzov, I. P., 1996: The spectrum of high-frequency internal waves in the atmospheric wave-guide. J. Atmos. Sci., 53, 17981814, https://doi.org/10.1175/1520-0469(1996)053<1798:TSOHFI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chunchuzov, I. P., 2002: On the high-wavenumber form of the Eulerian internal wave spectrum in the atmosphere. J. Atmos. Sci., 59, 17531774, https://doi.org/10.1175/1520-0469(2002)059<1753:OTHWFO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov length scales. J. Geophys. Res., 87, 96019613, https://doi.org/10.1029/JC087iC12p09601.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Galbraith, P. S., and D. E. Kelly, 1996: Identifying overturns in CTD profiles. J. Atmos. Oceanic Technol., 13, 688702, https://doi.org/10.1175/1520-0426(1996)013<0688:IOICP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garrett, C. J. R., and W. H. Munk, 1972: Space-time scales of internal waves. Geophys. Fluid Dyn., 3, 225264, https://doi.org/10.1080/03091927208236082.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garrett, C. J. R., and W. H. Munk, 1975: Space-time scales of internal waves: A progress report. J. Geophys. Res., 80, 291297, https://doi.org/10.1029/JC080i003p00291.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gregg, M., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94, 96869698, https://doi.org/10.1029/JC094iC07p09686.

  • Gregg, M. C., and E. Kunze, 1991: Shear and strain in Santa Monica basin. J. Geophys. Res., 96, 16 70916 719, https://doi.org/10.1029/91JC01385.

  • Henyey, F. S., and J. Wright, and S. M. Flatté, 1986: Energy and action flow through the internal wave field: An Eikonal approach. J. Geophys. Res., 91, 8487, https://doi.org/10.1029/JC091iC07p08487.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hibiya, T., N. Furuichi, and R. Robertson, 2012: Assessment of fine-scale parameterizations of turbulent dissipation rates near mixing hotspots in the deep ocean. Geophys. Res. Lett., 39, L24601, https://doi.org/10.1029/2012GL054068.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holloway, G., 1980: Oceanic internal waves are not weak waves. J. Phys. Oceanogr., 10, 906914, https://doi.org/10.1175/1520-0485(1980)010<0906:OIWANW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunze, E., 2017: Internal-wave-driven mixing: Global geography and budgets. J. Phys. Oceanogr., 47, 13251345, https://doi.org/10.1175/JPO-D-16-0141.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kunze, E., 2019: A unified model for anisotropic stratified and isotropic turbulence in the ocean and atmosphere. J. Phys. Oceanogr., 49, 385407, https://doi.org/10.1175/JPO-D-18-0092.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lvov, Y. V., K. L. Polzin, and E. G. Tabak, 2004: Energy spectra of the ocean’s internal wave field: Theory and observations. Phys. Rev. Lett., 92, 128501, http://doi.org/10.1103/physrevlett.92.128501.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McComas, C., and P. Muller, 1981a: The dynamic balance of internal waves. J. Phys. Oceanogr., 11, 970986, https://doi.org/10.1175/1520-0485(1981)011<0970:TDBOIW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McComas, C., and P. Muller, 1981b: Time scales of resonant interactions among oceanic internal waves. J. Phys. Oceanogr., 11, 139147, https://doi.org/10.1175/1520-0485(1981)011<0139:TSORIA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Müller, P., and D. Olbers, 1975: On the dynamics of internal waves in the deep ocean. J. Geophys. Res., 80, 38483860, https://doi.org/10.1029/JC080i027p03848.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Müller, P., E. A. D’Asaro, and G. Holloway, 1992: Internal gravity waves and mixing. Eos, Trans. Amer. Geophys. Union, 73, 25 and 31–32, http://doi.org/10.1029/91eo00018.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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.

  • Orlanski, I., and K. Bryan, 1969: The formation of thermocline step structure by large-amplitude internal gravity waves. J. Geophys. Res., 74, 69756983, https://doi.org/10.1029/JC074i028p06975.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pinkel, R., 2014: Vortical and internal wave shear and strain. J. Phys. Oceanogr., 44, 20702092, https://doi.org/10.1175/JPO-D-13-090.1.

  • Pinkel, R., 2020: The Poisson link between internal wave and dissipation scales in the thermocline. Part I: Probability density functions and the Poisson modeling of vertical strain. J. Phys. Oceanogr., 50, 34033424, https://doi.org/10.1175/JPO-D-19-0286.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pinkel, R., and S. Anderson, 1992: Toward a statistical description of finescale strain in the thermocline. J. Phys. Oceanogr., 22, 773795, https://doi.org/10.1175/1520-0485(1992)022<0773:TASDOF>2.0.CO;2.

    • Crossref
    • 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, 306328, https://doi.org/10.1175/1520-0485(1995)025<0306:FPOTD>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polzin, K. L., A. C. N. Garabato, T. N. Huussen, B. M. Sloyan, and S. Waterman, 2014: Finescale parameterizations of turbulent dissipation. J. Geophys. Res. Oceans, 119, 13831419, https://doi.org/10.1002/2013JC008979.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stommel, H., and K. N. Fedorov, 1967: Small scale structure in temperature and salinity near Timor and Mindanao. Tellus, 19, 306325, https://doi.org/10.3402/tellusa.v19i2.9792.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, H., and E. Kunze, 1999: Internal wave–wave interactions: Part I. The role of internal wave vertical divergence. J. Phys. Oceanogr., 29, 28862904, https://doi.org/10.1175/1520-0485(1999)029<2886:IWWIPI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1977: Turbulence and mixing in a Scottish loch. Philos. Trans. Roy. Soc. London, A286, 125181, https://doi.org/10.1098/rsta.1977.0112.

    • Search Google Scholar
    • Export Citation
  • Whalen, C. B., L. D. Talley, and J. A. MacKinnon, 2012: Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys. Res. Lett., 39, L18612, https://doi.org/10.1029/2012GL053196.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Winters, K. B., and E. A. D’Asaro, 1994: Three-dimensional wave instability near a critical level. J. Fluid Mech., 272, 255284, https://doi.org/10.1017/S0022112094004465.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 70 70 21
Full Text Views 15 15 3
PDF Downloads 23 23 5

The Poisson Link between Internal Wave and Dissipation Scales in the Thermocline. Part II: Internal Waves, Overturns, and the Energy Cascade

View More View Less
  • 1 Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California
© Get Permissions
Restricted access

Abstract

The irregular nature of vertical profiles of density in the thermocline appears well described by a Poisson process over vertical scales 2–200 m. To what extent does this view of the thermocline conflict with established models of the internal wavefield? Can a one-parameter Poisson subrange be inserted between the larger-scale wavefield and the microscale field of intermittent turbulent dissipation, both of which require many parameters for their specification? It is seen that a small modification to the Poisson vertical correlation function converts it to the corresponding correlation function of the Garrett–Munk (GM) internal wave spectral model. The linear scaling relations and vertical wavenumber dependencies of the GM model are maintained provided the Poisson constant κ0 is equated with the ratio of twice the displacement variance to the vertical correlation scale of the wavefield. Awareness of this Poisson wavefield relation enables higher-order strain statistics to be determined directly from the strain spectrum. Using observations from across the Pacific Ocean, the average Thorpe scale of individual overturning events is found to be nearly equal to the inverse of κ0, the metric of background thermocline distortion. If the fractional occurrence of overturning ϕ is introduced as an additional parameter, a Poisson version of the Gregg–Henyey relationship can be derived. The Poisson constant, buoyancy frequency, and ϕ combine to create a complete parameterization of energy transfer from internal wave scales through the Poisson subrange to dissipation. An awareness of the underlying Poisson structure of the thermocline will hopefully facilitate further improvement in both internal wave spectral models and ocean mixing parameterizations.

Denotes content that is immediately available upon publication as open access.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Robert Pinkel, rpinkel@ucsd.edu

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-19-0286.1.

Abstract

The irregular nature of vertical profiles of density in the thermocline appears well described by a Poisson process over vertical scales 2–200 m. To what extent does this view of the thermocline conflict with established models of the internal wavefield? Can a one-parameter Poisson subrange be inserted between the larger-scale wavefield and the microscale field of intermittent turbulent dissipation, both of which require many parameters for their specification? It is seen that a small modification to the Poisson vertical correlation function converts it to the corresponding correlation function of the Garrett–Munk (GM) internal wave spectral model. The linear scaling relations and vertical wavenumber dependencies of the GM model are maintained provided the Poisson constant κ0 is equated with the ratio of twice the displacement variance to the vertical correlation scale of the wavefield. Awareness of this Poisson wavefield relation enables higher-order strain statistics to be determined directly from the strain spectrum. Using observations from across the Pacific Ocean, the average Thorpe scale of individual overturning events is found to be nearly equal to the inverse of κ0, the metric of background thermocline distortion. If the fractional occurrence of overturning ϕ is introduced as an additional parameter, a Poisson version of the Gregg–Henyey relationship can be derived. The Poisson constant, buoyancy frequency, and ϕ combine to create a complete parameterization of energy transfer from internal wave scales through the Poisson subrange to dissipation. An awareness of the underlying Poisson structure of the thermocline will hopefully facilitate further improvement in both internal wave spectral models and ocean mixing parameterizations.

Denotes content that is immediately available upon publication as open access.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Robert Pinkel, rpinkel@ucsd.edu

This article has a companion article which can be found at http://journals.ametsoc.org/doi/abs/10.1175/JPO-D-19-0286.1.

Save