Author(s): John D. Fenton; Yebegaeshet T. Zerihun
Linked Author(s): John D. Fenton
Keywords: Boussinesq; Flume; Gradually-varied; Long waves; Non-hydrostatic; Open channel; Trans-critical; Weir
Abstract: The one-dimensional long wave equations are used throughout open channel hydraulics as a simple model of complicated reality. Nevertheless they suffer from an important limitation, that if the flow ever becomes critical, they break down. Boussinesq in 1877 developed a nonhydrostatic approximation that leads to a relatively simple correction with the ability to describe both sub- and super-critical flow and transitions between them. That equation, which might have formed the basis of open-channel hydraulics, has instead been substantially ignored. This paper develops a similar approach to Boussinesq, but for channels of greater generality. When compared with experiment it is found to provide a good model for flows that pass through critical, in flumes, over weirs and embankments, and in undular bores.