A non-linear dynamical system: flow past a sluice gate

Abstract

We consider the steady flow of water past a sluice gate to find the upstream and downstream water heights for different parameters and gate geometries. This leads to a study of a two-dimensional non-linear dynamical system suitable for lecturers to use in second- and third-year courses on differential equations. A thorough analysis in the phase space of the problem enables us to establish under what conditions solutions for straight and curved sluice gates exist.