Analysis of the water surface profiles of spatially varied flow with increasing discharge using the method of singular points

Abstract

Spatially varied flows with increasing discharge can be encountered in several hydraulic systems. The analysis of water surface profiles in such flow conditions is useful for the verification and design of these systems. In this paper, a comprehensive analysis of the possible flow profiles in non-prismatic trapezoidal channels is performed using the method of singular points, by taking into account bed slope and friction. Different cases are identified depending on whether singular points occur or not along the collecting channel. It is verified that a singular point can be of the saddle, nodal, or spiral type, and that two singular points may occur in special circumstances. Furthermore, water depth profiles may be non-monotonic, showing a minimum or a maximum. The method is applied to both a theoretical example and three experimental tests taken from the literature, and to a real-field case concerning the side spillway channel of a dam.