Coupling conditions for waterwaves at forks

Jean Guy Caputo, Denys Dutykh, Bernard Gleyse

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageBritish English
Article number434
Issue number3
StatePublished - 1 Mar 2019


  • Networks
  • Nonlinear shallow water equations
  • Nonlinear wave equations


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