Nonlinear Cascades of Surface Oceanic Geostrophic Kinetic Energy in the Frequency Domain

Brian K. Arbic Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, Michigan

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Robert B. Scott Institute for Geophysics, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas, and Department de Physique et LPO, Université de Bretagne Occidental, CNRS, Brest, France

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Glenn R. Flierl Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts

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Andrew J. Morten Department of Physics, University of Michigan, Ann Arbor, Michigan

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James G. Richman Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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Jay F. Shriver Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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Abstract

Motivated by the ubiquity of time series in oceanic data, the relative lack of studies of geostrophic turbulence in the frequency domain, and the interest in quantifying the contributions of intrinsic nonlinearities to oceanic frequency spectra, this paper examines the spectra and spectral fluxes of surface oceanic geostrophic flows in the frequency domain. Spectra and spectral fluxes are computed from idealized two-layer quasigeostrophic (QG) turbulence models and realistic ocean general circulation models, as well as from gridded satellite altimeter data. The frequency spectra of the variance of streamfunction (akin to sea surface height) and of geostrophic velocity are qualitatively similar in all of these, with substantial variance extending out to low frequencies. The spectral flux Π(ω) of kinetic energy in the frequency ω domain for the QG model documents a tendency for nonlinearity to drive energy toward longer periods, in like manner to the inverse cascade toward larger length scales documented in calculations of the spectral flux Π(k) in the wavenumber k domain. Computations of Π(ω) in the realistic model also display an “inverse temporal cascade.” In satellite altimeter data, some regions are dominated by an inverse temporal cascade, whereas others exhibit a forward temporal cascade. However, calculations performed with temporally and/or spatially filtered output from the models demonstrate that Π(ω) values are highly susceptible to the smoothing inherent in the construction of gridded altimeter products. Therefore, at present it is difficult to say whether the forward temporal cascades seen in some regions in altimeter data represent physics that is missing in the models studied here or merely sampling artifacts.

Naval Research Laboratory Contribution Number NRL/JA/7320-2011-803, and The University of Texas at Austin Institute for Geophysics Contribution Number 2471.

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

Abstract

Motivated by the ubiquity of time series in oceanic data, the relative lack of studies of geostrophic turbulence in the frequency domain, and the interest in quantifying the contributions of intrinsic nonlinearities to oceanic frequency spectra, this paper examines the spectra and spectral fluxes of surface oceanic geostrophic flows in the frequency domain. Spectra and spectral fluxes are computed from idealized two-layer quasigeostrophic (QG) turbulence models and realistic ocean general circulation models, as well as from gridded satellite altimeter data. The frequency spectra of the variance of streamfunction (akin to sea surface height) and of geostrophic velocity are qualitatively similar in all of these, with substantial variance extending out to low frequencies. The spectral flux Π(ω) of kinetic energy in the frequency ω domain for the QG model documents a tendency for nonlinearity to drive energy toward longer periods, in like manner to the inverse cascade toward larger length scales documented in calculations of the spectral flux Π(k) in the wavenumber k domain. Computations of Π(ω) in the realistic model also display an “inverse temporal cascade.” In satellite altimeter data, some regions are dominated by an inverse temporal cascade, whereas others exhibit a forward temporal cascade. However, calculations performed with temporally and/or spatially filtered output from the models demonstrate that Π(ω) values are highly susceptible to the smoothing inherent in the construction of gridded altimeter products. Therefore, at present it is difficult to say whether the forward temporal cascades seen in some regions in altimeter data represent physics that is missing in the models studied here or merely sampling artifacts.

Naval Research Laboratory Contribution Number NRL/JA/7320-2011-803, and The University of Texas at Austin Institute for Geophysics Contribution Number 2471.

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