A unified formulation of quasi-geostrophic and shallow water equations via projection
International audience 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...
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ftinstagro:oai:HAL:hal-04673756v1 2024-10-13T14:09:24+00:00 A unified formulation of quasi-geostrophic and shallow water equations via projection Thiry, Louis Li, Long Mémin, Etienne Roullet, Guillaume Numerical Analysis, Geophysics and Ecology (ANGE) Inria de Paris Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) Institut de Recherche Mathématique de Rennes (IRMAR) Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes) Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro) Océan Dynamique Observations Analyse (ODYSSEY) Université de Rennes (UR)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Université de Brest (UBO)-Inria Rennes – Bretagne Atlantique Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IMT Atlantique (IMT Atlantique) Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT) Université de Brest (UBO) Laboratoire d'Océanographie Physique et Spatiale (LOPS) Institut de Recherche pour le Développement (IRD)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS) European Project: 856408,STUOD(2020) 2024 https://hal.science/hal-04673756 https://hal.science/hal-04673756/document https://hal.science/hal-04673756/file/QGSW_JAMES.pdf en eng HAL CCSD info:eu-repo/grantAgreement//856408/EU/Stochastic Transport in Upper Ocean Dynamics/STUOD hal-04673756 https://hal.science/hal-04673756 https://hal.science/hal-04673756/document https://hal.science/hal-04673756/file/QGSW_JAMES.pdf http://creativecommons.org/licenses/by/ info:eu-repo/semantics/OpenAccess https://hal.science/hal-04673756 2024 Quasi-geostrophic equation Shallow water equation Projection [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph] [SDU.OCEAN]Sciences of the Universe [physics]/Ocean Atmosphere info:eu-repo/semantics/preprint Preprints, Working Papers, . 2024 ftinstagro 2024-09-18T23:37:56Z International audience 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. Report North Atlantic Portail HAL Institut Agro |
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Open Polar |
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Portail HAL Institut Agro |
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language |
English |
topic |
Quasi-geostrophic equation Shallow water equation Projection [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph] [SDU.OCEAN]Sciences of the Universe [physics]/Ocean Atmosphere |
spellingShingle |
Quasi-geostrophic equation Shallow water equation Projection [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph] [SDU.OCEAN]Sciences of the Universe [physics]/Ocean Atmosphere Thiry, Louis Li, Long Mémin, Etienne Roullet, Guillaume A unified formulation of quasi-geostrophic and shallow water equations via projection |
topic_facet |
Quasi-geostrophic equation Shallow water equation Projection [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph] [SDU.OCEAN]Sciences of the Universe [physics]/Ocean Atmosphere |
description |
International audience 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. |
author2 |
Numerical Analysis, Geophysics and Ecology (ANGE) Inria de Paris Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité) Institut de Recherche Mathématique de Rennes (IRMAR) Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes) Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-Institut Agro Rennes Angers Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro) Océan Dynamique Observations Analyse (ODYSSEY) Université de Rennes (UR)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Université de Brest (UBO)-Inria Rennes – Bretagne Atlantique Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-IMT Atlantique (IMT Atlantique) Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT) Université de Brest (UBO) Laboratoire d'Océanographie Physique et Spatiale (LOPS) Institut de Recherche pour le Développement (IRD)-Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS) European Project: 856408,STUOD(2020) |
format |
Report |
author |
Thiry, Louis Li, Long Mémin, Etienne Roullet, Guillaume |
author_facet |
Thiry, Louis Li, Long Mémin, Etienne Roullet, Guillaume |
author_sort |
Thiry, Louis |
title |
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_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_sort |
unified formulation of quasi-geostrophic and shallow water equations via projection |
publisher |
HAL CCSD |
publishDate |
2024 |
url |
https://hal.science/hal-04673756 https://hal.science/hal-04673756/document https://hal.science/hal-04673756/file/QGSW_JAMES.pdf |
genre |
North Atlantic |
genre_facet |
North Atlantic |
op_source |
https://hal.science/hal-04673756 2024 |
op_relation |
info:eu-repo/grantAgreement//856408/EU/Stochastic Transport in Upper Ocean Dynamics/STUOD hal-04673756 https://hal.science/hal-04673756 https://hal.science/hal-04673756/document https://hal.science/hal-04673756/file/QGSW_JAMES.pdf |
op_rights |
http://creativecommons.org/licenses/by/ info:eu-repo/semantics/OpenAccess |
_version_ |
1812816337962008576 |