Theoretical regime equations for mobile gravel-bed rivers with stable banks

Abstract

A system of rational regime equations is developed for gravel-bed rivers with stable banks using the optimality theory (OT). The optimality theory is based on the premise that equilibrium river geometry is characterised by an optimum configuration, defined here as maximum sediment-transport efficiency. Theoretical dimensionless equations are derived for width, depth, slope, width/depth ratio, and meandering–braiding transition. Independent dimensionless variables comprise discharge, sediment concentration, and relative bank strength, μ′, which is defined as the ratio of the critical shear stresses for the bank and bed sediments. Discharge exponents and general form of the equations agree well with previously developed empirical relations. Relative bank strength, μ′, is used to parameterise the influence of riparian vegetation on bank strength and is evaluated by calibrating against observed width/depth ratio. Once calibrated, the hydraulic geometry of natural gravel rivers is well described by the theoretical equations, including discrimination between meandering and braiding channels. The results provide strong support for the assumption that equilibrium or regime river behavior is equivalent to an optimal state and underline the importance of bank strength and sediment load as controls on hydraulic geometry.