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Open AccessArticle

Coupling Conditions for Water Waves at Forks

1
Laboratoire de Mathématiques, INSA Rouen Normandie, 76801 Saint–Etienne du Rouvray, France
2
University Grenoble Alpes, University Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(3), 434; https://doi.org/10.3390/sym11030434
Received: 15 January 2019 / Revised: 15 March 2019 / Accepted: 19 March 2019 / Published: 24 March 2019
(This article belongs to the Special Issue Symmetries of Nonlinear PDEs on Metric Graphs and Branched Networks)
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. View Full-Text
Keywords: networks; nonlinear shallow water equations; nonlinear wave equations networks; nonlinear shallow water equations; nonlinear wave equations
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Caputo, J.; Dutykh, D.; Gleyse, B. Coupling Conditions for Water Waves at Forks. Symmetry 2019, 11, 434.

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