Denys Dutykh
All publications
2019

Coupling conditions for water waves at forks

SSymmetry
J.-G. Caputo, D. Dutykh and B. Gleyse
Symmetry 11(3): 434 (2019)
Open Access
HAL VersionPublisher VersionDOI

Abstract

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.

Keywords

shallow water wavesStoker interface conditionswater wavesnonlinear waves2D simulationsconservation lawsfork2D effectsNetworkssymmetric fork1D effective modelnonlinear wave equationsnonlinear shallow water equationschannel flowcoupling conditionsnon-symmetric fork

Bibliographic record

Journal: Symmetry
Volume: 11
Issue: 3
Pages: 434
arXiv: 1509.09082

BibTeX Citation

@article{Caputo2019couplingconditions,
  author = {Caputo, J.-G. and Dutykh, D. and Gleyse, B.},
  title = {Coupling conditions for water waves at forks},
  journal = {Symmetry},
  year = {2019},
  volume = {11},
  number = {3},
  pages = {434},
  doi = {10.3390/sym11030434},
  abstract = {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.},
  keywords = {shallow water waves, Stoker interface conditions, water waves, nonlinear waves, 2D simulations, conservation laws, fork, 2D effects, Networks, symmetric fork, 1D effective model, nonlinear wave equations, nonlinear shallow water equations, channel flow, coupling conditions, non-symmetric fork}
}