Revisiting the analysis of self-formed threshold alluvial channels

A self-formed threshold channel features a bank profile, where sediment particles on the wetted perimeter are at the threshold of entrainment. This article revisits the analysis of self-formed threshold alluvial channels using a refined mathematical framework. The framework includes the fluid flow momentum balance and the force balance at the particle scale of entrainment threshold. The spanwise momentum diffusion caused by the Reynolds shear stress is considered to follow a power law with the spanwise distance from the channel centerline. Unlike conventional models, our approach introduces a tetrahedral bed particle configuration, wherein a target sediment particle rests on three identical closely-packed bed particles. For sliding mode of entrainment threshold, the force balance relationship is derived by considering the instantaneous drag and lift forces acting on the target particle. In rough flow, the time-averaged streamwise flow velocity follows the logarithmic law. The channel-bank profile, flow discharge, and spanwise profile of bed shear stress are obtained. The bank profile steepens with an increase in relative particle size (ratio of bed particle size to target particle size). For a given relative particle size, the dimensionless flow discharge reduces with an increase in streamwise bed slope, whereas for a given streamwise bed slope, it reduces as the relative particle size increases. At a given spanwise distance, the dimensionless bed shear stress reduces with an increase in relative particle size. The model results show satisfactory agreement with the experimental data. This study offers valuable design curves for hydraulic engineers, providing insights into the threshold alluvial channels over broad ranges of parameters. Finally, it presents a new perspective on the analysis of threshold channels using the phenomenological theory of turbulence.