Hydraulic geometry of straight alluvial channels and the principle of least action

Abstract

Natural rivers exhibit regular hydraulic geometry relationships for which no widely accepted explanation has been given. This paper applies the physical principle of least action to the determination of stable alluvial-channel form. For steady, uniform alluvial-channel flow, both theoretical inferences and a case study show that least action occurs when the criteria of minimum potential energy and MFE (Maximum Flow Efficiency, defined here as the maximum sediment transporting capacity per unit available stream power) are satisfied. The consistency between bankfull hydraulic geometry relationships of natural channels and those of maximally efficient or 'least action' channels identified in this study demonstrates that alluvial channels commonly adjust to a maximally efficient section. Support for the use of the extremal hypotheses of maximum sediment transporting capacity and minimum stream power is provided by illustrating that they are essentially expressions of, and hence subsumed by, the more general principle of MFE.