Steady-State Parallel Retreat Migration in River Bends With Noncohesive (Composite) Banks

A substantial body of research has addressed the equilibrium cross-sectional geometry of straight noncohesive channels, along with bends having fixed outer banks. However, development of a characteristic cross-section during active migration has been confounded by inaccurate treatment of noncohesive bank erosion processes. This analysis characterizes a steady-state migrating cross-section and the associated migration rate for the highly conceptualized case of an infinite bend of constant centerline radius with noncohesive lower banks consisting of uniform-sized grains mobilized as bedload. Analytical, numerical, and field analyses are presented to rationally constrain the geometry and obtain a physically based migration rate equation dependent on the following dimensionless groupings: excess Shields stress, flow depth to radius of curvature ratio, and noncohesive bank thickness to grain size ratio. Migration rate is shown to be dictated by transverse sediment flux at the thalweg due to secondary flow, not bank slope as in previous formulations developed from similar principles. Simple outward translation of the noncohesive portion of the cross section is achieved with concurrent mass failure in the upper cohesive layer. Such translation cannot be achieved using a linear excess shear formulation applied to noncohesive fluvial erosion. A numerical model of cross-sectional evolution to steady-state migration is developed; when applied to the lower Mackinaw River in Illinois, it reveals that the river behaves as if the critical shear stress is considerably larger than that indicated by the grain size distribution. This conceptualized treatment is intended to provide a canonical basis of comparison for actual meander bend geometries.