Coupling Conditions for Water Waves at Forks

Jean-Guy Caputo (1) , Denys Dutykh (2, 3, 4) , Bernard Gleyse (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie
2 LAMA - Laboratoire de Mathématiques
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

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.

Mots clés: Networks; nonlinear shallow water equations; nonlinear wave equations

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Mathématiques générales [math.GM]; Analyse classique [math.CA]; Analyse numérique [math.NA]; Physique Numérique [physics.comp-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Classique [physics.class-ph]; Formation de Structures et Solitons [nlin.PS]; Systèmes Solubles et Intégrables [nlin.SI]

Jean-Guy Caputo, Denys Dutykh, Bernard Gleyse. Coupling Conditions for Water Waves at Forks. Symmetry, 2019, 11 (3), pp.434. ⟨10.3390/sym11030434⟩. ⟨hal-01206504v3⟩