Computer-simulated deformation of meandering river patterns

A new model for bed topography is developed herein which accounts for phase lag and the influence of the width to depth ratio. This model is used to analyze four sets of data: two from laboratory channels and two from natural channels. Good agreement is found between the actual and the predicted bed topography. An iterative, two-dimensional solution algorithm is developed for the nonlinear depth-averaged equations of motion. This is used to analyze the flow field for an idealized sine-generated channel pattern. The results are compared with the direct solution of the linearized equations of motion. There is good agreement between the phase lags from the two solutions. However, the direct solution results in a larger near bank velocity perturbation than the indirect solution. A new model for bank erosion is developed herein. This model is based on the sediment continuity equation, applied near the channel bank. A linear stability analysis is used to determine the conditions under which a small amplitude channel is most likely to evolve into a meander pattern with a typical wavelength. These conditions result in a reasonable value for the sediment transportation velocity exponent. This model is used to calculate the evolution of a meander pattern from an initially small amplitude sine generated shape to a neck cutoff condition. The final channel shape displays the characteristic asymmetry that is often observed in large amplitude meandering channels. The deformation model is used to analyze two rivers: the Minnesota River in Minnesota and the Genesee River in New York. There is reasonable agreement between the calculated pattern of migration and actual pattern of migration for bath rivers. There is also reasonable agreement between the optimized erosion coefficients for two different time periods with the Genesee River. Finally, the model is used to calculate future locations for both rivers. A critical evaluation of these predictions may be performed at same time in the future.