Steady-State Parallel Retreat Migration in River Bends with Noncohesive
1 (Composite) Banks
Abstract
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 can result without the characteristic cyclic process
observed in cohesive banks (fluvial erosion, oversteepening, and mass
failure). This suggests that the linear excess shear stress formulation
that applies to cohesive soils misrepresents noncohesive bank erosion
processes. 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.