The De Saint-Venant equations in curved channels

Abstract

After introducing the subject of curvilinear flow, particularly in the context of meandering natural channels, this thesis then describes the three conventional models for unsteady flow in open channels, namely kinematic, diffusion and dynamic. These descriptions are in terms of the straight channel de Saint-Venant equations. The discussion also considers some aspects of the diffusion model which raise questions as to the appropriateness of the usual engineering approach to this model. As to date, these models treat curvature cursorily, if at all, the models are then expanded to incorporate curvature in a more systematic manner. This is done by deriving the de Saint-Venant equations in terms of curvilinear coordinates. The models are then presented in terms of the curvilinear mass-conservation and various forms of the curvilinear momentum equation. The new models are found to be expressed by equations of the form 'linear model + curvilinear correction' thus allowing the engineer to estimate the size of any curvature effect. The derived dynamic model is compared with a laboratory study, and the results indicate that the new curvilinear model is a reasonable description of dam-break flow. Subsequent calculations, based on field data, of the celerity of the dynamic wave illustrate how big the corrections can be.