Numerical Simulation of Widening and Bed Deformation of Straight Sand-Bed Rivers. I: Model Development

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Abstract
Many existing morphological models are limited by their inability to account for changing channel width through time. In this and a companion paper, the development and testing of a numerical model of river widening are reported. The new model is applicable to straight, sand-bed streams with cohesive bank materials, and nonuniform bathymetry and width in the longitudinal direction. The flow field is obtained by solving versions of the flow resistance, flow momentum, and continuity equations, which account for the influence of gradually varied flow and lateral shear in the near bank zones. Secondary and overbank flows are excluded. Predicted flows are used to account for streamwise and transverse sediment transport fluxes. Numerical solution of the sediment continuity equation allows temporal variations in bed-material size, bed morphology, and bank geometry to be simulated. Channel widening is simulated by coupling bank stability with flow and sediment transport algorithms. A probabilistic approach is used to estimate the longitudinal extent of mass failures within modeled reaches, and mixed layer theory is used to model the transport of the resulting bed and bank material mixture. Assessment of the accuracy of the new model, discussed in the companion paper, indicates that the new model simulations of widths, depths, and deepening rates are within 15% of observed values, but widening rates are underpredicted by a factor of approximately 3.

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