Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems
We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar velocity profiles. Our theory accommodates with continuous stratif...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.665/ |
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| author | Adim, Mahieddine Bianchini, Roberta Duchêne, Vincent |
| author_facet | Adim, Mahieddine Bianchini, Roberta Duchêne, Vincent |
| author_sort | Adim, Mahieddine |
| collection | DOAJ |
| description | We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar velocity profiles. Our theory accommodates with continuous stratification, so that admissible deviations from bilayer profiles are not pointwise small. This leads us to define refined approximate solutions that are able to describe at first order the flow in the pycnocline. Because the hydrostatic Euler equations are not known to enjoy suitable stability estimates, we rely on thickness-diffusivity contributions proposed by Gent and McWilliams. Our strategy also applies to one-layer and multilayer frameworks. |
| format | Article |
| id | doaj-art-0a78c5bdcac04cfc82305958ad0a95db |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-0a78c5bdcac04cfc82305958ad0a95db2025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121597162610.5802/crmath.66510.5802/crmath.665Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systemsAdim, Mahieddine0Bianchini, Roberta1Duchêne, Vincent2IRMAR, Univ. Rennes, F-35000 Rennes, FranceIAC, Consiglio Nazionale delle Ricerche, 00185 Rome, ItalyCNRS; IRMAR, Univ. Rennes, F-35000 Rennes, FranceWe rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar velocity profiles. Our theory accommodates with continuous stratification, so that admissible deviations from bilayer profiles are not pointwise small. This leads us to define refined approximate solutions that are able to describe at first order the flow in the pycnocline. Because the hydrostatic Euler equations are not known to enjoy suitable stability estimates, we rely on thickness-diffusivity contributions proposed by Gent and McWilliams. Our strategy also applies to one-layer and multilayer frameworks.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.665/Internal wavesHydrostatic modelsSharp stratification limitColumnar motion |
| spellingShingle | Adim, Mahieddine Bianchini, Roberta Duchêne, Vincent Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems Comptes Rendus. Mathématique Internal waves Hydrostatic models Sharp stratification limit Columnar motion |
| title | Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems |
| title_full | Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems |
| title_fullStr | Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems |
| title_full_unstemmed | Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems |
| title_short | Relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems |
| title_sort | relaxing the sharp density stratification and columnar motion assumptions in layered shallow water systems |
| topic | Internal waves Hydrostatic models Sharp stratification limit Columnar motion |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.665/ |
| work_keys_str_mv | AT adimmahieddine relaxingthesharpdensitystratificationandcolumnarmotionassumptionsinlayeredshallowwatersystems AT bianchiniroberta relaxingthesharpdensitystratificationandcolumnarmotionassumptionsinlayeredshallowwatersystems AT duchenevincent relaxingthesharpdensitystratificationandcolumnarmotionassumptionsinlayeredshallowwatersystems |