Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization
Abstract The representation of turbulent fluxes during oceanic convective events is important to capture the evolution of the oceanic mixed layer. To improve the accuracy of turbulent fluxes, we examine the possibility of adding a non‐local component in their expression in addition to the usual down...
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| Language: | English |
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American Geophysical Union (AGU)
2025-01-01
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| Series: | Journal of Advances in Modeling Earth Systems |
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| Online Access: | https://doi.org/10.1029/2024MS004243 |
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| _version_ | 1832583459384590336 |
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| author | Alexandre Legay Bruno Deremble Hans Burchard |
| author_facet | Alexandre Legay Bruno Deremble Hans Burchard |
| author_sort | Alexandre Legay |
| collection | DOAJ |
| description | Abstract The representation of turbulent fluxes during oceanic convective events is important to capture the evolution of the oceanic mixed layer. To improve the accuracy of turbulent fluxes, we examine the possibility of adding a non‐local component in their expression in addition to the usual downgradient part. To do so, we extend the k–ε algebraic second‐moment closure by relaxing the assumption on the equilibrium of the temperature variance θ′2‾. With this additional evolution equation for the temperature variance, we obtain a k–ε–θ′2‾ model (the “kεt” model) which includes a non‐local term for the temperature flux. We validate this new model against Large Eddy Simulations (LES) in three test cases: free convection (FC), wind‐driven mixing, and diurnal cycle (DC). For wind‐driven mixing, kεt is equivalent to k–ε. However, in the presence of a buoyancy flux (FC and DC), we find that the vertical profile of temperature of the LES is better captured by kεt than k–ε. Particularly, the non‐local term increases the fraction of the mixed layer that is stably stratified. For FC, this fraction is near 50% for both kεt and the LES, whereas the k–ε value is 20%. We show that this improvement is due to a better representation of the temperature variance in the inner part of the mixed layer. This better representation is mainly caused by the diffusion of temperature variance, which is described by kεt and not by k–ε. |
| format | Article |
| id | doaj-art-2d7bcd60b0f4478cb9da482424cd4dcd |
| institution | Kabale University |
| issn | 1942-2466 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Geophysical Union (AGU) |
| record_format | Article |
| series | Journal of Advances in Modeling Earth Systems |
| spelling | doaj-art-2d7bcd60b0f4478cb9da482424cd4dcd2025-01-28T13:21:10ZengAmerican Geophysical Union (AGU)Journal of Advances in Modeling Earth Systems1942-24662025-01-01171n/an/a10.1029/2024MS004243Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ ParameterizationAlexandre Legay0Bruno Deremble1Hans Burchard2CNRS INRAE IRD Grenoble INP IGE Université Grenoble Alpes Grenoble FranceCNRS INRAE IRD Grenoble INP IGE Université Grenoble Alpes Grenoble FranceLeibniz Institute for Baltic Sea Research Warnemünde Rostock GermanyAbstract The representation of turbulent fluxes during oceanic convective events is important to capture the evolution of the oceanic mixed layer. To improve the accuracy of turbulent fluxes, we examine the possibility of adding a non‐local component in their expression in addition to the usual downgradient part. To do so, we extend the k–ε algebraic second‐moment closure by relaxing the assumption on the equilibrium of the temperature variance θ′2‾. With this additional evolution equation for the temperature variance, we obtain a k–ε–θ′2‾ model (the “kεt” model) which includes a non‐local term for the temperature flux. We validate this new model against Large Eddy Simulations (LES) in three test cases: free convection (FC), wind‐driven mixing, and diurnal cycle (DC). For wind‐driven mixing, kεt is equivalent to k–ε. However, in the presence of a buoyancy flux (FC and DC), we find that the vertical profile of temperature of the LES is better captured by kεt than k–ε. Particularly, the non‐local term increases the fraction of the mixed layer that is stably stratified. For FC, this fraction is near 50% for both kεt and the LES, whereas the k–ε value is 20%. We show that this improvement is due to a better representation of the temperature variance in the inner part of the mixed layer. This better representation is mainly caused by the diffusion of temperature variance, which is described by kεt and not by k–ε.https://doi.org/10.1029/2024MS004243k–ɛ modelnon‐local termcoherent structuresvertical mixing schemesecond‐moment closure |
| spellingShingle | Alexandre Legay Bruno Deremble Hans Burchard Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization Journal of Advances in Modeling Earth Systems k–ɛ model non‐local term coherent structures vertical mixing scheme second‐moment closure |
| title | Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization |
| title_full | Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization |
| title_fullStr | Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization |
| title_full_unstemmed | Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization |
| title_short | Derivation and Implementation of a Non‐Local Term to Improve the Oceanic Convection Representation Within the k–ɛ Parameterization |
| title_sort | derivation and implementation of a non local term to improve the oceanic convection representation within the k e parameterization |
| topic | k–ɛ model non‐local term coherent structures vertical mixing scheme second‐moment closure |
| url | https://doi.org/10.1029/2024MS004243 |
| work_keys_str_mv | AT alexandrelegay derivationandimplementationofanonlocaltermtoimprovetheoceanicconvectionrepresentationwithinthekɛparameterization AT brunoderemble derivationandimplementationofanonlocaltermtoimprovetheoceanicconvectionrepresentationwithinthekɛparameterization AT hansburchard derivationandimplementationofanonlocaltermtoimprovetheoceanicconvectionrepresentationwithinthekɛparameterization |