Curvature Ratio and Rate of River Bend Migration—Update

Using the momentum equation it is shown that the radial force per unit area exerted by the flow on the external bank of a circular river bend is directly proportional to a certain curvature coefficient, C. This coefficient is dependent on the ratio of bend radius (R) to flow width (w), as well as on the dynamic friction coefficient of the bedload. The variation of C with R/w shows a maximum at $(R/w)\sim 3\text{.}$ The rate of lateral bend migration in 16 bends of the Beatton River, Canada, was found to be well correlated with C over a range of $1.2⩽(R/w)⩽13.0\text{.}$ This correlation suggests that the hydraulic analysis based on the momentum equation may offer a partial explanation to the variation in the rate of channel migration with R/w, and to its maximum at $(R/w)\sim 3\text{.}$