Simulating sine-generated meandering channel evolution with an analytical model

An analytical model to simulate the evolution of a meandering channel was developed based on the analytical solution of flow field in a sine-generated meandering channel and application of the bank erosion model by Duan et al. The flow-field solution was derived from two-dimensional, depth-averaged, steady-flow equations in channel-fitted, curvilinear orthogonal coordinates where the transverse bed slope was treated as a variable increasing with channel sinuosity. The flow-field solution indicated that the location where the shift of maximum velocity zone from the convex to concave banks in sine-generated channels varies with the transverse bed slope and the strength of secondary current. The rate of bank erosion was calculated as a gradient function of the longitudinal sediment transport rate and strength of the secondary flow rather than being proportional to the magnitude of excessive near-bank velocity or shear stress. This model replicated the evolution of meandering channels from mildly to highly sinuous ones. Simulation results showed the migration of meandering channel is a combination of downstream translation, lateral extension, expansion, and downstream and upstream rotation. Low-sinuous free meanders migrate rapidly toward downstream. As the sinuosity increases, downstream translation diminishes, and meandering loops expand laterally with its head rotating toward downstream and then upstream. The simulated results indicated the gradient of the longitudinal sediment transport rate is essential in modeling meandering evolution.