A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection
Abstract This paper introduces a unified model for layered rotating shallow‐water (RSW) and quasi‐geostrophic (QG) equations, based on the intrinsic relationship between these two sets of equations. We propose a novel formulation of the QG equations as a projection of the RSW equations. This formula...
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| Format: | Article |
| Language: | English |
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American Geophysical Union (AGU)
2024-10-01
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| Series: | Journal of Advances in Modeling Earth Systems |
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| Online Access: | https://doi.org/10.1029/2024MS004510 |
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| author | Louis Thiry Long Li Etienne Mémin Guillaume Roullet |
| author_facet | Louis Thiry Long Li Etienne Mémin Guillaume Roullet |
| author_sort | Louis Thiry |
| collection | DOAJ |
| description | Abstract This paper introduces a unified model for layered rotating shallow‐water (RSW) and quasi‐geostrophic (QG) equations, based on the intrinsic relationship between these two sets of equations. We propose a novel formulation of the QG equations as a projection of the RSW equations. This formulation uses the same prognostic variables as RSW, namely velocity and layer thickness, thereby restoring the proximity of these two sets of equations. It provides direct access to the ageostrophic velocities embedded within the geostrophic velocities resolved by the QG equations. This approach facilitates the study of differences between QG and RSW using a consistent numerical discretization. We demonstrate the effectiveness of this formulation through examples including vortex shear instability, double‐gyre circulation, and a simplified North Atlantic configuration. |
| format | Article |
| id | doaj-art-679882e0f1874bb9afa67bdb96075eca |
| institution | OA Journals |
| issn | 1942-2466 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | American Geophysical Union (AGU) |
| record_format | Article |
| series | Journal of Advances in Modeling Earth Systems |
| spelling | doaj-art-679882e0f1874bb9afa67bdb96075eca2025-08-20T02:12:10ZengAmerican Geophysical Union (AGU)Journal of Advances in Modeling Earth Systems1942-24662024-10-011610n/an/a10.1029/2024MS004510A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via ProjectionLouis Thiry0Long Li1Etienne Mémin2Guillaume Roullet3ANGE Team INRIA Paris Laboratoire Jacques‐Louis Lions Sorbonne University Paris FranceODYSSEY Team, INRIA Rennes, IRMAR, University of Rennes I Rennes FranceODYSSEY Team, INRIA Rennes, IRMAR, University of Rennes I Rennes FranceLaboratoire d’Océanographie Physique et Spatiale Université de Bretagne Occidentale Brest FranceAbstract This paper introduces a unified model for layered rotating shallow‐water (RSW) and quasi‐geostrophic (QG) equations, based on the intrinsic relationship between these two sets of equations. We propose a novel formulation of the QG equations as a projection of the RSW equations. This formulation uses the same prognostic variables as RSW, namely velocity and layer thickness, thereby restoring the proximity of these two sets of equations. It provides direct access to the ageostrophic velocities embedded within the geostrophic velocities resolved by the QG equations. This approach facilitates the study of differences between QG and RSW using a consistent numerical discretization. We demonstrate the effectiveness of this formulation through examples including vortex shear instability, double‐gyre circulation, and a simplified North Atlantic configuration.https://doi.org/10.1029/2024MS004510ocean modelsshallow waterquasigeostrophicprojection |
| spellingShingle | Louis Thiry Long Li Etienne Mémin Guillaume Roullet A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection Journal of Advances in Modeling Earth Systems ocean models shallow water quasigeostrophic projection |
| title | A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection |
| title_full | A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection |
| title_fullStr | A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection |
| title_full_unstemmed | A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection |
| title_short | A Unified Formulation of Quasi‐Geostrophic and Shallow Water Equations via Projection |
| title_sort | unified formulation of quasi geostrophic and shallow water equations via projection |
| topic | ocean models shallow water quasigeostrophic projection |
| url | https://doi.org/10.1029/2024MS004510 |
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