River Channel Forms in Relation to Bank Steepness: A Theoretical Investigation Using a Variational Analytical Method

Riverbanks vary considerably in anti-scourability and consequently take various profiles. By using an isosceles trapezoid as the generalized form of river channel cross-sections and then incorporating the effects of bank angle into the variational analytical approach developed by Huang and Nanson (2000), this study presents a detailed theoretical investigation of the self-adjustment of alluvial channel forms. It is demonstrated that when alluvial channel flow achieves stable equilibrium, a significant decrease in riverbank steepness leads to a slight decrease in maximum sediment (bedload) discharge, and yet results in a significant increase in optimal channel width and a considerable decrease in optimal channel depth. The hydraulic geometry relations, theoretically derived for bank steepness to vary across a wide range, show that among the multivariant controls, the roles of bed sediment size, channel roughness, flow discharge and sediment (bedload) discharge are independent of bank steepness. While the effects of bank steepness illustrated in the theoretically derived hydraulic geometry relations are highly consistent with the results of threshold theory and previous empirical studies, limitations on using bank angle to reflect the anti-scourability of natural riverbanks are also highlighted.