![]() ![]() The integration of upstream curvatures results in a phase lag between curvature and migration rate, and this phase lag has not been considered in most previous studies. In parallel with these field measurements, theoretical work has clearly shown that the velocity excess at the outer bank depends not only on the local curvature, but it is also a function of the weighted sum of upstream curvatures ( Ikeda et al., 1981 Howard and Knutson, 1984 Furbish, 1988). ![]() High-curvature bends with an R/ W value < 2 appeared to migrate more slowly, potentially due to a higher energy expenditure and the development of a separation zone on the upstream side of the bend ( Hickin, 1978). However, early studies of the relationship between curvature and migration rate suggested that migration rate reaches its highest value when the radius of curvature is about two to three times the width of the river ( W Hickin and Nanson, 1975 Nanson and Hickin, 1983, 1986). Therefore, bends with high curvature should also have the highest migration rates. In theory, the larger the curvature (1/ R, where R is the radius of curvature), the larger is the centrifugal force and the shear stress exerted on the outer bank. Inertial forces drive the high-velocity core of the river toward the outer bank the strength of this effect is dependent on the bend curvature (e.g., Leopold and Wolman, 1960). The meandering process consists of erosion on the outer bank and deposition on the inner bank, which are the result of an asymmetric distribution of flow velocity and shear stress in curved channel segments (e.g., Dietrich et al., 1979). Understanding and predicting how meanders change through time have major implications for a myriad of engineering and geological problems, including management of agricultural land, loss of infrastructure, bridge design, and distribution of heterogeneities in porous sediments and sedimentary rocks. Meander bends of large rivers, especially ones with high sediment discharge, can migrate several meters per year ( Constantine et al., 2014). ![]() Meandering rivers are among the most dynamic sedimentary systems on Earth. The implication is that one of the most important ways river migration is rejuvenated and meandering patterns are reshuffled is the generation of high-curvature bends through cutoffs. Overall, bends with the highest curvatures show the highest migration rates exceptions with limited migration seem to be related to the low erodibility of the outer bank, not the hydrodynamics of the flow. A quasi-linear relationship exists between the two if this lag is taken into account. However, locations of maximum migration rate are shifted downstream relative to peak curvature, with a phase lag that shows limited variability for the same river segment. High-resolution measurements of migration rates of more than 1600 bends in time-lapse Landsat satellite images, covering more than 4000 km of seven rapidly migrating meandering rivers in the Amazon Basin, suggest that the variation of migration rate closely follows that of the local channel curvature. One of the long- and widely held ideas about the dynamics of meandering rivers is that migration slows down in bends with higher curvatures. ![]()
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