Equilibrium Cross Section of River Channels With Cohesive Erodible Banks

Predicting the equilibrium cross section of natural rivers has been widely investigated in fluvial morphology. Several approaches have been developed to meet this aim, starting from regime equations to the empirical formulations of Parker et al. (2007) and Wilkerson and Parker (2011), who proposed quasi-universal relations for describing bankfull conditions in sand and gravel bed rivers. Nevertheless, a general physics-based framework is still missing, and it remains an open issue to better clarify the basic mechanisms whereby a river selects its width. In this contribution we focus our attention on lowland rivers with cohesive banks, whose resistance to erosion is crucial to control the river width. In particular, we formulate a theoretical model that evaluates the equilibrium width of river cross sections modeling the interaction between the core flow in the central part of the section and the boundary layer that forms in the vicinity of the cohesive banks. The model computes the cross-section equilibrium configuration by which the shear stresses on the banks equal a critical threshold value. These stresses are computed by partitioning the total shear stress into an effective grain roughness component and a form component (Kean and Smith, 2006a). The model is applied to a large data set, concerning both sand and gravel bed rivers, and it is used to determine the relations expressing the channel width and the bankfull flow depth to the bankfull discharge, which appear to provide a unitary description of bankfull hydraulic geometry.