Bed‐Level Variation in Channel Expansions with Movable Beds

Abstract

This work presents analytical and numerical models for the analysis of steady‐state bed‐level variation in gradually expanded open channels with movable beds. The analytical model employs the one‐dimensional flow assumption, and equations for flow depth and bed‐level variation have been derived. The numerical model uses a false transient principle with the quasi‐steady uncoupled approach to solve the two‐dimensional governing equations in a transformed coordinate system, which allows an orthogonal grid and an easier inclusion of sidewall boundaries. A second‐order accurate, explicit finite‐difference scheme (Mac‐Cormack scheme) has been used for water flow computation. A comparison between the two shows that the analytical results are comparable to those obtained by the more complicated two‐dimensional numerical model for small expansion angles. Though not discussed in this technical note, the numerical model can be applied to any type of expansion and is capable of predicting the temporal variations of flow depth and bed level.