  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.
