On the art of designing effective space-times with free surface flows in Analogue Gravity
Accelerating/decelerating trans-critical flows (waterfalls/cataracts) are analogous to space-times of black holes/white fountains since the pioneering work of Schützhold & Unruh in 2002. A single number is usually employed to classify trans-criticality namely the local depth Froude number which...
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Académie des sciences
2025-01-01
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| Series: | Comptes Rendus. Physique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.215/ |
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| author | Bossard, Alexis James, Nicolas Jules, Valentin Fourdrinoy, Johan Robertson, Scott Rousseaux, Germain |
| author_facet | Bossard, Alexis James, Nicolas Jules, Valentin Fourdrinoy, Johan Robertson, Scott Rousseaux, Germain |
| author_sort | Bossard, Alexis |
| collection | DOAJ |
| description | Accelerating/decelerating trans-critical flows (waterfalls/cataracts) are analogous to space-times of black holes/white fountains since the pioneering work of Schützhold & Unruh in 2002. A single number is usually employed to classify trans-criticality namely the local depth Froude number which is the ratio between the local current speed and the local celerity of long gravity waves analogous to the light celerity. When the former reaches one, water waves are no more able to propagate upstream: the hydraulic black hole is a river of no return for them. At a higher level of understanding, two global dimensionless numbers, the upstream Froude number Frup and the obstruction ratio rup (the height of a bottom obstacle, the underlying geometry inducing the effective space-time, divided by the upstream water depth) are essential to distinguish subcritical, trans-critical and supercritical zones in the - Frup versus rup - hydraulic and non-dispersive diagram. The relationship between both global parameters for transcritical flows turns out to be a peculiar limit of the behaviour of boats navigating in confined media like canals or locks with a generalized obstruction factor based on the ratio between the boat section and the canal section. Here, we revisit the classification of flows over obstacles in open water channel taking into account both effects of dispersion and scale due to surface tension, two neglected topics so far. For the first time, we give a complete classification of flows in an open water channel based on sub-pixel detection method measurements of the free surface supported by numerical simulations. We generalized the obstruction factor by a filling factor taking into account the maximum height of the water channel, a crucial parameter that was overlooked so far. Our ultimate purpose is to understand how to reproduce in the laboratory analogues of curved space-times from the dynamical point of view. |
| format | Article |
| id | doaj-art-7d9589f72deb428f8b6f230b3a9b9ed0 |
| institution | Kabale University |
| issn | 1878-1535 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Physique |
| spelling | doaj-art-7d9589f72deb428f8b6f230b3a9b9ed02025-02-07T13:53:47ZengAcadémie des sciencesComptes Rendus. Physique1878-15352025-01-0125G145751110.5802/crphys.21510.5802/crphys.215On the art of designing effective space-times with free surface flows in Analogue GravityBossard, Alexis0James, Nicolas1Jules, Valentin2Fourdrinoy, Johan3Robertson, Scott4Rousseaux, Germain5https://orcid.org/0000-0001-6576-4878Institut Pprime, CNRS-Université de Poitiers-ISAE ENSMA, Poitiers, FranceLMA, CNRS-Université de Poitiers, Poitiers, FranceInstitut Pprime, CNRS-Université de Poitiers-ISAE ENSMA, Poitiers, FranceInstitut Pprime, CNRS-Université de Poitiers-ISAE ENSMA, Poitiers, FranceInstitut Pprime, CNRS-Université de Poitiers-ISAE ENSMA, Poitiers, FranceInstitut Pprime, CNRS-Université de Poitiers-ISAE ENSMA, Poitiers, FranceAccelerating/decelerating trans-critical flows (waterfalls/cataracts) are analogous to space-times of black holes/white fountains since the pioneering work of Schützhold & Unruh in 2002. A single number is usually employed to classify trans-criticality namely the local depth Froude number which is the ratio between the local current speed and the local celerity of long gravity waves analogous to the light celerity. When the former reaches one, water waves are no more able to propagate upstream: the hydraulic black hole is a river of no return for them. At a higher level of understanding, two global dimensionless numbers, the upstream Froude number Frup and the obstruction ratio rup (the height of a bottom obstacle, the underlying geometry inducing the effective space-time, divided by the upstream water depth) are essential to distinguish subcritical, trans-critical and supercritical zones in the - Frup versus rup - hydraulic and non-dispersive diagram. The relationship between both global parameters for transcritical flows turns out to be a peculiar limit of the behaviour of boats navigating in confined media like canals or locks with a generalized obstruction factor based on the ratio between the boat section and the canal section. Here, we revisit the classification of flows over obstacles in open water channel taking into account both effects of dispersion and scale due to surface tension, two neglected topics so far. For the first time, we give a complete classification of flows in an open water channel based on sub-pixel detection method measurements of the free surface supported by numerical simulations. We generalized the obstruction factor by a filling factor taking into account the maximum height of the water channel, a crucial parameter that was overlooked so far. Our ultimate purpose is to understand how to reproduce in the laboratory analogues of curved space-times from the dynamical point of view.https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.215/analogue gravityflows classificationopen channelgravity and capillary dispersion |
| spellingShingle | Bossard, Alexis James, Nicolas Jules, Valentin Fourdrinoy, Johan Robertson, Scott Rousseaux, Germain On the art of designing effective space-times with free surface flows in Analogue Gravity Comptes Rendus. Physique analogue gravity flows classification open channel gravity and capillary dispersion |
| title | On the art of designing effective space-times with free surface flows in Analogue Gravity |
| title_full | On the art of designing effective space-times with free surface flows in Analogue Gravity |
| title_fullStr | On the art of designing effective space-times with free surface flows in Analogue Gravity |
| title_full_unstemmed | On the art of designing effective space-times with free surface flows in Analogue Gravity |
| title_short | On the art of designing effective space-times with free surface flows in Analogue Gravity |
| title_sort | on the art of designing effective space times with free surface flows in analogue gravity |
| topic | analogue gravity flows classification open channel gravity and capillary dispersion |
| url | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.215/ |
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