Coupling Conditions for Water Waves at Forks

Symmetry. 2019;11(3):434 DOI 10.3390/sym11030434

 

Journal Homepage

Journal Title: Symmetry

ISSN: 2073-8994 (Print)

Publisher: MDPI AG

LCC Subject Category: Science: Mathematics

Country of publisher: Switzerland

Language of fulltext: English

Full-text formats available: PDF, HTML

 

AUTHORS


Jean–Guy Caputo (Laboratoire de Mathématiques, INSA Rouen Normandie, 76801 Saint–Etienne du Rouvray, France)

Denys Dutykh (University Grenoble Alpes, University Savoie Mont Blanc, CNRS, LAMA, 73000 Chambéry, France)

Bernard Gleyse (Laboratoire de Mathématiques, INSA Rouen Normandie, 76801 Saint–Etienne du Rouvray, France)

EDITORIAL INFORMATION

Blind peer review

Editorial Board

Instructions for authors

Time From Submission to Publication: 11 weeks

 

Abstract | Full Text

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.