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On Eddy Viscosity, Energy Cascades, and the Horizontal Resolution of Gridded Satellite Altimeter Products

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

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Kurt L. PolzinPhysical Oceanography Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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

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

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

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Abstract

Motivated by the recent interest in ocean energetics, the widespread use of horizontal eddy viscosity in models, and the promise of high horizontal resolution data from the planned wide-swath satellite altimeter, this paper explores the impacts of horizontal eddy viscosity and horizontal grid resolution on geostrophic turbulence, with a particular focus on spectral kinetic energy fluxes Π(K) computed in the isotropic wavenumber (K) domain. The paper utilizes idealized two-layer quasigeostrophic (QG) models, realistic high-resolution ocean general circulation models, and present-generation gridded satellite altimeter data. Adding horizontal eddy viscosity to the QG model results in a forward cascade at smaller scales, in apparent agreement with results from present-generation altimetry. Eddy viscosity is taken to roughly represent coupling of mesoscale eddies to internal waves or to submesoscale eddies. Filtering the output of either the QG or realistic models before computing Π(K) also greatly increases the forward cascade. Such filtering mimics the smoothing inherent in the construction of present-generation gridded altimeter data. It is therefore difficult to say whether the forward cascades seen in present-generation altimeter data are due to real physics (represented here by eddy viscosity) or to insufficient horizontal resolution. The inverse cascade at larger scales remains in the models even after filtering, suggesting that its existence in the models and in altimeter data is robust. However, the magnitude of the inverse cascade is affected by filtering, suggesting that the wide-swath altimeter will allow a more accurate determination of the inverse cascade at larger scales as well as providing important constraints on smaller-scale dynamics.

Naval Research Laboratory Contribution Number NRL/JA/7320-2011-802, and The University of Texas at Austin Institute for Geophysics Contribution Number 2482.

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 recent interest in ocean energetics, the widespread use of horizontal eddy viscosity in models, and the promise of high horizontal resolution data from the planned wide-swath satellite altimeter, this paper explores the impacts of horizontal eddy viscosity and horizontal grid resolution on geostrophic turbulence, with a particular focus on spectral kinetic energy fluxes Π(K) computed in the isotropic wavenumber (K) domain. The paper utilizes idealized two-layer quasigeostrophic (QG) models, realistic high-resolution ocean general circulation models, and present-generation gridded satellite altimeter data. Adding horizontal eddy viscosity to the QG model results in a forward cascade at smaller scales, in apparent agreement with results from present-generation altimetry. Eddy viscosity is taken to roughly represent coupling of mesoscale eddies to internal waves or to submesoscale eddies. Filtering the output of either the QG or realistic models before computing Π(K) also greatly increases the forward cascade. Such filtering mimics the smoothing inherent in the construction of present-generation gridded altimeter data. It is therefore difficult to say whether the forward cascades seen in present-generation altimeter data are due to real physics (represented here by eddy viscosity) or to insufficient horizontal resolution. The inverse cascade at larger scales remains in the models even after filtering, suggesting that its existence in the models and in altimeter data is robust. However, the magnitude of the inverse cascade is affected by filtering, suggesting that the wide-swath altimeter will allow a more accurate determination of the inverse cascade at larger scales as well as providing important constraints on smaller-scale dynamics.

Naval Research Laboratory Contribution Number NRL/JA/7320-2011-802, and The University of Texas at Austin Institute for Geophysics Contribution Number 2482.

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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