Bend theory of river meanders. Part 2. Nonlinear deformation of finite-amplitude bends

Meander bends typically show certain systematic deviations from simple Cartesian sinusoidal forms. Bends tend to be round and full, or ‘fat’, often to the point of possessing double-valued plan-forms, as Langbein & Leopold (1966) have noted. Bends also tend to be characteristically skewed in such a fashion that their direction of migration can be determined directly from an aerial photograph of the planform; the water margin of the downstream accreting half of a point bar describes a convex planform, whereas the upstream eroding side has a concave shape. In the present paper a generalized nonlinear equation of bend migration is treated based on the analysis of Part 1 (Ikeda, Parker & Sawai 1981). An expansion technique reminiscent of the Stokes expansion for water waves is developed to perform a nonlinear stability analysis. This analysis provides an explanation of skewing and fattening, and also indicates that lateral and downstream migration rates should increase as bend amplitude develops. These results agree qualitatively with field observations.