Bend theory of river meanders with spatial width variations

Abstract

The present work revisits the classical, uniform-width bend theory with the aim to understand whether and how spatial width oscillations can affect the process of linear bend stability that initiates meander planform evolution. Although longitudinal oscillations of channel width are common along many meandering streams, little investigation of their properties and dynamic effects has been pursued so far. The theory therefore accounts for width variations as a geometrical forcing in a depth-averaged model of meander morphodynamics by assuming the potential interaction with the classical curvature forcing effect. A first quantification of width variations is made by referring to a freely evolving meandering river, which shows that the dimensionless amplitude of width variations is a ‘small’ parameter with comparable magnitude to that of curvature variations, thus suggesting the use of a two-parameter perturbation expansion. Moreover, it is reasonable to assume that channel width oscillates in space with a double frequency relative to curvature, which implies that one nonlinear interaction between the two forcing effects is enough to reproduce the effect of spatial width variations on the process of bend stability. Overall, width variations consistently promote the instability of shorter bends with respect to meanders with uniform width: on average, this predicted tendency is supported by analysis of field data referring to hundreds of natural meander bends. The effect on meander wavelength selection depends on the location of the widest section relative to the bend apex. Under typical formative conditions of gravel-bed rivers, with large-enough channel aspect ratios, two distinct most unstable longitudinal modes develop. Such behaviour is absent when the width is uniform, and suggests a mechanistic interpretation for the reach-scale occurrence of chute cutoffs that can be observed more frequently in wider-at-bends than in equiwidth meandering channels.