Stability Criterion for Uniform Flow in Open Channel Cross Sections with Different Shapes

Abstract

This paper presents the derivation of an analytical method for identifying the stability of uniform flow in three open channel sections (rectangular, parabolic, and circular). Using a dimensionless relative slope factor, a general equation for the prediction of stability thresholds for the occurrence of roll waves for each cross-section shape was developed, enabling the flow stability zones to be classified. The derivation is predicated based on a combination of the Vedernikov number and the logarithmic law of resistance, which involves significant resistance parameters. The proposed method was verified using a numerical example and actual measurements. It is hoped that the presented method, which provides a direct solution for the stability criteria of uniform flow, will be useful in open channel design.