Coupling Conditions for Water Waves at Forks
We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-kn...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/3/434 |
| _version_ | 1811297930730012672 |
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| author | Jean–Guy Caputo Denys Dutykh Bernard Gleyse |
| author_facet | Jean–Guy Caputo Denys Dutykh Bernard Gleyse |
| author_sort | Jean–Guy Caputo |
| collection | DOAJ |
| description | We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker’s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics. |
| first_indexed | 2024-04-13T06:11:30Z |
| format | Article |
| id | doaj.art-32b1c1a146094f49af0783b23fd10036 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T06:11:30Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-32b1c1a146094f49af0783b23fd100362022-12-22T02:59:00ZengMDPI AGSymmetry2073-89942019-03-0111343410.3390/sym11030434sym11030434Coupling Conditions for Water Waves at ForksJean–Guy Caputo0Denys Dutykh1Bernard Gleyse2Laboratoire de Mathématiques, INSA Rouen Normandie, 76801 Saint–Etienne du Rouvray, FranceUniversity Grenoble Alpes, University Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, FranceLaboratoire de Mathématiques, INSA Rouen Normandie, 76801 Saint–Etienne du Rouvray, FranceWe considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker’s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics.https://www.mdpi.com/2073-8994/11/3/434networksnonlinear shallow water equationsnonlinear wave equations |
| spellingShingle | Jean–Guy Caputo Denys Dutykh Bernard Gleyse Coupling Conditions for Water Waves at Forks Symmetry networks nonlinear shallow water equations nonlinear wave equations |
| title | Coupling Conditions for Water Waves at Forks |
| title_full | Coupling Conditions for Water Waves at Forks |
| title_fullStr | Coupling Conditions for Water Waves at Forks |
| title_full_unstemmed | Coupling Conditions for Water Waves at Forks |
| title_short | Coupling Conditions for Water Waves at Forks |
| title_sort | coupling conditions for water waves at forks |
| topic | networks nonlinear shallow water equations nonlinear wave equations |
| url | https://www.mdpi.com/2073-8994/11/3/434 |
| work_keys_str_mv | AT jeanguycaputo couplingconditionsforwaterwavesatforks AT denysdutykh couplingconditionsforwaterwavesatforks AT bernardgleyse couplingconditionsforwaterwavesatforks |