A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics
The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parametrized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a diffusive parametrization, where the eddy-induced fluxes are r...
Published in: | Journal of Fluid Mechanics |
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Main Authors: | , , |
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Format: | Article in Journal/Newspaper |
Language: | English |
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HAL CCSD
2023
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Online Access: | https://hal.science/hal-04301204 https://hal.science/hal-04301204/document https://hal.science/hal-04301204/file/2304.09481.pdf https://doi.org/10.1017/jfm.2023.347 |
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ftinsalyonhal:oai:HAL:hal-04301204v1 |
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Open Polar |
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INSA Lyon HAL (Institut National des Sciences Appliquées) |
op_collection_id |
ftinsalyonhal |
language |
English |
topic |
Quasi-geostrophic flows Geostrophic turbulence Ocean processes Quasi-geostrophic flows Geostrophic turbulence Ocean processes [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] |
spellingShingle |
Quasi-geostrophic flows Geostrophic turbulence Ocean processes Quasi-geostrophic flows Geostrophic turbulence Ocean processes [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] Meunier, Julie Miquel, Benjamin Gallet, Basile A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics |
topic_facet |
Quasi-geostrophic flows Geostrophic turbulence Ocean processes Quasi-geostrophic flows Geostrophic turbulence Ocean processes [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] |
description |
The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parametrized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a diffusive parametrization, where the eddy-induced fluxes are related to the large-scale gradients by a diffusion tensor. The standard parametrization scheme in climate modelling consists in adopting the Gent–McWilliams/Redi (GM/R) form for the diffusion tensor, initially put forward based on physical intuition and educated guesses before being put on firm analytical footing using a thickness-weighted average (TWA). In the present contribution, we provide a direct derivation of this diffusion tensor from the quasi-geostrophic (QG) dynamics of a horizontally homogeneous three-dimensional patch of ocean hosting a large-scale vertically sheared zonal flow on the $\beta$ plane. The derivation hinges on the identification of a useful cross-invariant defined as the product of the buoyancy and QG potential vorticity fluctuations. While less general than the TWA approach, the present QG framework leads to rigorous constraints on the diffusion tensor. First, there is no diapycnal diffusivity arising in the QG GM/R tensor for low viscosity and small-scale diffusivities. The diffusion tensor then involves only two vertically dependent coefficients, namely the GM transport coefficient $K_{GM}(z)$ and the Redi diffusivity $K_R(z)$ . Second, as identified already by previous authors, the vertical structures of the two coefficients are related by the so-called Taylor–Bretherton relation. Finally, while the two coefficients differ generically in the interior of the water column, we show that they are equal to one another near the surface and near the bottom of the domain for low-enough dissipative coefficients. We illustrate these findings by simulating numerically the QG dynamics of a horizontally homogeneous patch of ocean hosting a vertically sheared zonal current resembling the Antarctic ... |
author2 |
Service de physique de l'état condensé (SPEC - UMR3680) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) European Project: 757239,FLAVE |
format |
Article in Journal/Newspaper |
author |
Meunier, Julie Miquel, Benjamin Gallet, Basile |
author_facet |
Meunier, Julie Miquel, Benjamin Gallet, Basile |
author_sort |
Meunier, Julie |
title |
A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics |
title_short |
A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics |
title_full |
A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics |
title_fullStr |
A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics |
title_full_unstemmed |
A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics |
title_sort |
direct derivation of the gent–mcwilliams/redi diffusion tensor from quasi-geostrophic dynamics |
publisher |
HAL CCSD |
publishDate |
2023 |
url |
https://hal.science/hal-04301204 https://hal.science/hal-04301204/document https://hal.science/hal-04301204/file/2304.09481.pdf https://doi.org/10.1017/jfm.2023.347 |
genre |
Antarc* Antarctic |
genre_facet |
Antarc* Antarctic |
op_source |
ISSN: 0022-1120 EISSN: 1469-7645 Journal of Fluid Mechanics https://hal.science/hal-04301204 Journal of Fluid Mechanics, 2023, 963, pp.A22. ⟨10.1017/jfm.2023.347⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/2304.09481 info:eu-repo/semantics/altIdentifier/doi/10.1017/jfm.2023.347 info:eu-repo/grantAgreement//757239/EU/Energetics of natural turbulent flows: the impact of waves and radiation./FLAVE hal-04301204 https://hal.science/hal-04301204 https://hal.science/hal-04301204/document https://hal.science/hal-04301204/file/2304.09481.pdf ARXIV: 2304.09481 doi:10.1017/jfm.2023.347 |
op_rights |
http://creativecommons.org/licenses/by-nc-sa/ info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1017/jfm.2023.347 |
container_title |
Journal of Fluid Mechanics |
container_volume |
963 |
_version_ |
1786789635367632896 |
spelling |
ftinsalyonhal:oai:HAL:hal-04301204v1 2023-12-31T10:00:40+01:00 A direct derivation of the Gent–McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics Meunier, Julie Miquel, Benjamin Gallet, Basile Service de physique de l'état condensé (SPEC - UMR3680) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) Laboratoire de Mecanique des Fluides et d'Acoustique (LMFA) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) European Project: 757239,FLAVE 2023-05-19 https://hal.science/hal-04301204 https://hal.science/hal-04301204/document https://hal.science/hal-04301204/file/2304.09481.pdf https://doi.org/10.1017/jfm.2023.347 en eng HAL CCSD Cambridge University Press (CUP) info:eu-repo/semantics/altIdentifier/arxiv/2304.09481 info:eu-repo/semantics/altIdentifier/doi/10.1017/jfm.2023.347 info:eu-repo/grantAgreement//757239/EU/Energetics of natural turbulent flows: the impact of waves and radiation./FLAVE hal-04301204 https://hal.science/hal-04301204 https://hal.science/hal-04301204/document https://hal.science/hal-04301204/file/2304.09481.pdf ARXIV: 2304.09481 doi:10.1017/jfm.2023.347 http://creativecommons.org/licenses/by-nc-sa/ info:eu-repo/semantics/OpenAccess ISSN: 0022-1120 EISSN: 1469-7645 Journal of Fluid Mechanics https://hal.science/hal-04301204 Journal of Fluid Mechanics, 2023, 963, pp.A22. ⟨10.1017/jfm.2023.347⟩ Quasi-geostrophic flows Geostrophic turbulence Ocean processes Quasi-geostrophic flows Geostrophic turbulence Ocean processes [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] info:eu-repo/semantics/article Journal articles 2023 ftinsalyonhal https://doi.org/10.1017/jfm.2023.347 2023-12-06T17:28:40Z The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parametrized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a diffusive parametrization, where the eddy-induced fluxes are related to the large-scale gradients by a diffusion tensor. The standard parametrization scheme in climate modelling consists in adopting the Gent–McWilliams/Redi (GM/R) form for the diffusion tensor, initially put forward based on physical intuition and educated guesses before being put on firm analytical footing using a thickness-weighted average (TWA). In the present contribution, we provide a direct derivation of this diffusion tensor from the quasi-geostrophic (QG) dynamics of a horizontally homogeneous three-dimensional patch of ocean hosting a large-scale vertically sheared zonal flow on the $\beta$ plane. The derivation hinges on the identification of a useful cross-invariant defined as the product of the buoyancy and QG potential vorticity fluctuations. While less general than the TWA approach, the present QG framework leads to rigorous constraints on the diffusion tensor. First, there is no diapycnal diffusivity arising in the QG GM/R tensor for low viscosity and small-scale diffusivities. The diffusion tensor then involves only two vertically dependent coefficients, namely the GM transport coefficient $K_{GM}(z)$ and the Redi diffusivity $K_R(z)$ . Second, as identified already by previous authors, the vertical structures of the two coefficients are related by the so-called Taylor–Bretherton relation. Finally, while the two coefficients differ generically in the interior of the water column, we show that they are equal to one another near the surface and near the bottom of the domain for low-enough dissipative coefficients. We illustrate these findings by simulating numerically the QG dynamics of a horizontally homogeneous patch of ocean hosting a vertically sheared zonal current resembling the Antarctic ... Article in Journal/Newspaper Antarc* Antarctic INSA Lyon HAL (Institut National des Sciences Appliquées) Journal of Fluid Mechanics 963 |