Stream Curvature and Bank Erosion: A Model Based on the Momentum Equation

Based on the momentum equation of flow, the force per unit area which the flow exerts radially on the outer bank of a stream bend is expressed by an equation in which the force is explicitly related to the curvature ratio R/w (curve radius/channel width). A dimensionless curvature coefficient Cα is defined, which is dependent on R/w and the coefficient of dynamic bedload friction, tan α. Exploring the changes of Cα with R/w reveals a functional relationship which, for the known values of tan α, shows maximal values of Cα for R/w values between 2 and 4. The theoretical results agree with field measurements of the relationship between R/w and the rate of channel migration.