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Numerical Discretization of Rotated Diffusion Operators in Ocean Models

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  • 1 University of Liège, Liege, Belgium
  • | 2 Joint Research Centre, Ispra, Italy
  • | 3 Unité ASTR, Université Catholique de Louvain, Louvain-La-Neuve, Belgium
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Abstract

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on the so-called z-coordinate system is presented. The authors then focus exclusively on the dynamically passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather complex, while simpler, linear schemes are shown to produce unphysical undershooting and overshooting. It is suggested that the choice of an appropriate discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically active or not.

* Research associate at the National Fund for Scientific Research, Brussels, Belgium.

+ Current affiliation: Institute for Oceanography, University of Hamburg, Hamburg, Germany.

# Current affiliation: Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture, now the Joint Research Centre, Ispra, Italy.

Corresponding author address: Dr. J.-M. Beckers GHER, University of Liege, Sart-Tilman B5, B-4000 Liège, Belgium.

Email: jm.beckers@ulg.ac.be

Abstract

A method to improve the behavior of the numerical discretization of a rotated diffusion operator such as, for example, the isopycnal diffusion parameterization used in large-scale ocean models based on the so-called z-coordinate system is presented. The authors then focus exclusively on the dynamically passive tracers and analyze some different approaches to the numerical discretization. Monotonic schemes are designed but are found to be rather complex, while simpler, linear schemes are shown to produce unphysical undershooting and overshooting. It is suggested that the choice of an appropriate discretization method depends on the importance of the rotated diffusion in a given simulation, whether the field to be diffused is dynamically active or not.

* Research associate at the National Fund for Scientific Research, Brussels, Belgium.

+ Current affiliation: Institute for Oceanography, University of Hamburg, Hamburg, Germany.

# Current affiliation: Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture, now the Joint Research Centre, Ispra, Italy.

Corresponding author address: Dr. J.-M. Beckers GHER, University of Liege, Sart-Tilman B5, B-4000 Liège, Belgium.

Email: jm.beckers@ulg.ac.be

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