A unified bar–bend theory of river meanders

TLDR

The study develops a two‑dimensional model of flow and bed topography in sinuous channels with erodible boundaries to investigate meander initiation. The model is applied to analyze the mechanism of meander initiation. The analysis reveals a previously unknown resonance phenomenon that, when parameters are near critical values, drives bend growth and links bar instability to meander formation, a finding supported by experimental comparisons.

Abstract

A two-dimensional model of flow and bed topography in sinuous channels with erodible boundaries is developed and applied in order to investigate the mechanism of meander initiation. By reexamining the problem recently tackled by Ikeda, Parker & Sawai (1981), a previously undiscovered ‘resonance’ phenomenon is detected which occurs when the values of the relevant parameters fall within a neighbourhood of certain critical values. It is suggested that the above resonance controls the bend growth, and it is shown that it is connected in some sense with bar instability. In fact, by performing a linear stability analysis of flow in straight erodible channels, resonant flow in sinuous channels is shown to occur when curvature ‘forces’ a ‘natural’ solution represented by approximately steady perturbations of the alternate bar type. A comparison with experimental observations appears to support the idea that resonance is associated with meander formation.