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Article

Dissipation Trends in a Shallow Water Model

C. Nicolis1
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  • 1 Institut Royal Météorologique de Belgique, Brussels, Belgium
Print Publication:
01 Nov 2000
DOI:
https://doi.org/10.1175/1520-0469(2000)057<3559:DTIASW>2.0.CO;2
Page(s):
3559–3570
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Abstract

The formalism of irreversible thermodynamics is applied to the shallow water model. Entropy production and entropy flow terms are identified, describing the ways dissipation and exchange processes unfold in space and time. Explicit evaluations are carried out in the case of Lorenz’s nine-mode truncation and in the quasigeostrophic limit of the model. A number of systematic trends are identified by studying the way dissipation and kinetic energy vary as the forcing is increased and the system undergoes qualitative changes of behavior between different regimes, from simple symmetric flow to intermittent chaos. The constraints imposed by thermodynamics on the structure of the model equations and, especially, on the parameterization schemes are brought out.

Corresponding author address: Catherine Nicolis, Institut Royal Météorologique de Belgique, Avenue Circulaire 3, B-1180 Brussels, Belgium.

Email: cnicolis@oma.be

Abstract

The formalism of irreversible thermodynamics is applied to the shallow water model. Entropy production and entropy flow terms are identified, describing the ways dissipation and exchange processes unfold in space and time. Explicit evaluations are carried out in the case of Lorenz’s nine-mode truncation and in the quasigeostrophic limit of the model. A number of systematic trends are identified by studying the way dissipation and kinetic energy vary as the forcing is increased and the system undergoes qualitative changes of behavior between different regimes, from simple symmetric flow to intermittent chaos. The constraints imposed by thermodynamics on the structure of the model equations and, especially, on the parameterization schemes are brought out.

Corresponding author address: Catherine Nicolis, Institut Royal Météorologique de Belgique, Avenue Circulaire 3, B-1180 Brussels, Belgium.

Email: cnicolis@oma.be

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