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Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability

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  • 1 Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, Michigan
  • | 2 School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia
  • | 3 Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi
  • | 4 Department of Physics, University of Michigan, Ann Arbor, Michigan
  • | 5 ** Institute for Geophysics, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas, and Departement de Physique et LPO, Université de Bretagne Occidentale, CNRS, Brest, France
  • | 6 Laboratoire de Glaciologie et Géophysique de l'Environnement, CNRS, and Université Grenoble Alpes, Grenoble, and Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique, Toulouse, France
  • | 7 Laboratoire de Glaciologie et Géophysique de l'Environnement, CNRS, and Université Grenoble Alpes, Grenoble, France
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Abstract

Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Naval Research Laboratory Contribution Number NRL/JA/7320-12-1515 and University of Texas Institute for Geophysics Contribution Number 2638.

These authors contributed equally to this manuscript.

Current affiliation: Research and Development Department, Norwegian Meteorological Institute, Oslo, Norway.

Corresponding author address: Dr. Brian K. Arbic, Department of Earth and Environmental Sciences, University of Michigan, 1100 North University Avenue, Ann Arbor, MI 48109-1005. E-mail: arbic@umich.edu

Abstract

Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Naval Research Laboratory Contribution Number NRL/JA/7320-12-1515 and University of Texas Institute for Geophysics Contribution Number 2638.

These authors contributed equally to this manuscript.

Current affiliation: Research and Development Department, Norwegian Meteorological Institute, Oslo, Norway.

Corresponding author address: Dr. Brian K. Arbic, Department of Earth and Environmental Sciences, University of Michigan, 1100 North University Avenue, Ann Arbor, MI 48109-1005. E-mail: arbic@umich.edu
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