Coupling Conditions for Water Waves at Forks

TL;DR

This paper investigates how nonlinear shallow water waves propagate through forks in channels, deriving effective 1D coupling conditions from 2D simulations and conservation laws, with results applicable to small and large amplitude waves.

Contribution

It provides a rigorous derivation of coupling conditions for water waves at forks, validating the Stoker interface conditions for small amplitudes and analyzing effects of symmetry and asymmetry.

Findings

Stoker conditions hold for small amplitude waves regardless of fork angle

Symmetric large amplitude waves tend to follow Stoker's relations

2D effects are significant in non-symmetric forks, requiring detailed flow analysis

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.