[De l’art de concevoir des espaces-temps effectifs avec des écoulements à surface libre en Gravitation Analogue]
Les écoulements transcritiques accélérés/décélérés (chutes d’eau/cataractes) sont analogues aux espaces-temps des trous noirs/fontaines blanches depuis les travaux pionniers de Schützhold & Unruh en 2002. Un seul nombre est généralement utilisé pour classifier la transcriticité, à savoir le nombre de Froude de profondeur local qui est le rapport entre la vitesse locale du courant et la célérité locale des ondes longues de gravité analogue à la célérité de la lumière. Lorsque le premier atteint 1, les vagues ne peuvent plus se propager vers l’amont : le trou noir hydraulique est pour elles une rivière sans retour. À un niveau de compréhension supérieur, deux nombres globaux sans dimension, le nombre de Froude en amont Frup et le taux d’obstruction rup (la hauteur d’un obstacle de fond, la géométrie sous-jacente induisant l’espace-temps effectif, divisé par la profondeur de l’eau en amont) sont essentiels pour distinguer les zones sous-critiques, trans-critiques et supercritiques dans le diagramme - Frup versus rup - hydraulique et non dispersif. La relation entre les deux paramètres globaux pour les écoulements transcritiques s’avère être une limite particulière du comportement des bateaux naviguant dans des milieux confinés comme des canaux ou des écluses avec un facteur d’obstruction généralisé basé sur le rapport entre la section du bateau et la section du canal. Ici, nous revisitons la classification des écoulements au-dessus des obstacles dans les canaux à surface libre en prenant en compte à la fois les effets de dispersion et d’échelle du à la tension de surface, deux sujets négligés jusqu’à présent. Pour la première fois, nous donnons une classification complète des écoulements dans un canal à surface libre basée sur des mesures avec une méthode de détection sous-pixel de la surface libre appuyées par des simulations numériques. Nous avons généralisé le facteur d’obstruction par un facteur de remplissage prenant en compte la hauteur maximale du canal à surface libre, paramètre crucial et oublié jusqu’à présent. Notre objectif ultime est de comprendre comment reproduire en laboratoire des analogues d’espaces-temps courbes du point de vue dynamique.
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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.
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Mots-clés : gravitation analogue, classification des écoulements, canal à surface libre, dispersion gravitaire et capillaire
Alexis Bossard 1 ; Nicolas James 2 ; Valentin Jules 1 ; Johan Fourdrinoy 1 ; Scott Robertson 1 ; Germain Rousseaux 1
CC-BY 4.0
@article{CRPHYS_2024__25_G1_457_0,
author = {Alexis Bossard and Nicolas James and Valentin Jules and Johan Fourdrinoy and Scott Robertson and Germain Rousseaux},
title = {On the art of designing effective space-times with free surface flows in {Analogue} {Gravity}},
journal = {Comptes Rendus. Physique},
pages = {457--511},
publisher = {Acad\'emie des sciences, Paris},
volume = {25},
year = {2024},
doi = {10.5802/crphys.215},
language = {en},
}
TY - JOUR AU - Alexis Bossard AU - Nicolas James AU - Valentin Jules AU - Johan Fourdrinoy AU - Scott Robertson AU - Germain Rousseaux TI - On the art of designing effective space-times with free surface flows in Analogue Gravity JO - Comptes Rendus. Physique PY - 2024 SP - 457 EP - 511 VL - 25 PB - Académie des sciences, Paris DO - 10.5802/crphys.215 LA - en ID - CRPHYS_2024__25_G1_457_0 ER -
%0 Journal Article %A Alexis Bossard %A Nicolas James %A Valentin Jules %A Johan Fourdrinoy %A Scott Robertson %A Germain Rousseaux %T On the art of designing effective space-times with free surface flows in Analogue Gravity %J Comptes Rendus. Physique %D 2024 %P 457-511 %V 25 %I Académie des sciences, Paris %R 10.5802/crphys.215 %G en %F CRPHYS_2024__25_G1_457_0
Alexis Bossard; Nicolas James; Valentin Jules; Johan Fourdrinoy; Scott Robertson; Germain Rousseaux. On the art of designing effective space-times with free surface flows in Analogue Gravity. Comptes Rendus. Physique, Volume 25 (2024), pp. 457-511. doi : 10.5802/crphys.215. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.215/
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