A stability criterion inherent in laws governing alluvial channel flow

The stability criterion of maximum flow efficiency (MFE) has previously been found inherent in typical alluvial channel flow relationships, and this study investigates the general nature of this criterion using a wider range of flow resistance and bedload transport formulae. For straight alluvial channels, in which the effect of sediment sorting is insignificant, our detailed mathematical analysis demonstrates that a flow efficiency factor ε occurs generally as the ratio of sediment (bedload) discharge Qs to stream power Ω (γQS) in the form of $\def\endash{\hbox{--}}\def\lambdabar{{\mathchar'26\mkern-9mu\lambda}} {\varepsilon = {Q_{\rm s}}/ \Omega^{\lambdabar} (\lambdabar = 0{\cdot}86\endash 0{\cdot}88)}$. When ε is maximized (i.e. Qs is maximized or Ω is minimized), maximally efficient straight channel geometries derived from most flow resistance and bedload transport formulae are found compatible with observed bankfull hydraulic geometry relations. This study provides support for the use of the criteria of MFE, maximum sediment transporting capacity and minimum stream power for understanding the operation of alluvial rivers, and also addresses limitations to the direct application of its findings. Copyright © 2002 John Wiley & Sons, Ltd.