Hydraulic geometry and maximum flow efficiency as products of the principle of least action

Abstract

Basic flow relationships have previously been seen to be insufficient to explain the self-adjusting mechanism of alluvial channels and as a consequence extremal hypotheses have been incorporated into the analyses. In contrast, this study finds that by introducing a channel form factor (width/depth ratio), the self-adjusting mechanism of alluvial channels can be illustrated directly with the basic flow relations of continuity, resistance and sediment transport. Natural channel flow is able to reach an optimum state (Maximum Flow Efficiency (MFE), defined as the maximum sediment transporting capacity per unit available stream power) with regard to the adjustment of channel form such that rivers exhibit regular hydraulic geometry relations at dominant or bankfull stage. Within the context of MFE, this study offers support for the use of the concepts of maximum sediment transporting capacity (MSTC) and minimum stream power (MSP). Furthermore, this study indicates that the principle of least action is able to provide a physical explanation for the existence of MFE, MSTC and MSP. Potential energy is minimized and consequently sediment transport is maximized in alluvial channels. Copyright © 2000 John Wiley & Sons, Ltd.