A conceptual model for meander initiation in bedload‐dominated streams

Abstract

AbstractA simple analytic model is presented relating local sediment transport capacity to variance in the transverse shear stress distribution in a stream channel. The model is used to develop a physically based conceptual model for the initiation of meandering in straight, bedload‐dominated streams as a result of a feedback mechanism. The feedback maximizes the cross‐sectional shear stress variance and – in order to achieve stability – ultimately minimizes the energy slope at repeated locations along the channel, subject to steady‐state mass flux and the stability of the channel boundary. These locations develop into pools in a fully developed meandering channel; they represent attractor states wherein sediment continuity is satisfied using the least possible energy expenditure per unit length of channel. However, since the cross‐sectional geometry of a pool (and the adjacent bar) is asymmetric, these attractor states are only conditionally stable, requiring strong, curvature‐induced secondary circulation to maintain their asymmetry. Between two successive pools, a stream occupies a metastable, higher energy state (corresponding to a riffle) that requires greater energy expenditure per unit length of channel to transport the same volume of sediment. The model we present links processes at the scale of a channel width to adjustments of the channel sinuosity and slope at the scale of a channel reach. We argue that the reach‐scale extremal hypotheses employed by rational regime models are mathematical formalisms that permit a one‐dimensional theory to describe the three‐dimensional dynamics producing stream morphology. Our model is consistent with the results from stream table experiments, with respect to both the rate of development of meandering and the characteristics of the equilibrium channel morphology. Copyright © 2006 John Wiley & Sons, Ltd.