Meander bends of high amplitude

Meander bends of high amplitude in alluvial rivers often display a high degree of coherency. The only analytical equation heretofore available to describe such bends is the sine-generated curve, which has no rigorous derivation in the context of rivers. Herein a nonlinear “bend equation,” based on a dynamical description of flow in bends and a kinematical description of bank erosion, is used to describe channel migration. This equation admits solutions of constant amplitude that migrate downstream with constant speed. The solution at high amplitude displays a prominent skewing that reveals the direction of flow. At low amplitude, the solution reduces to the sine-generated curve.