Analysis of dynamic wave model for unsteady flow and sediment transport in alluvial rivers

The coupling interactions between flood propagation, sediment transport, and river morphology in alluvial rivers are mathematically described by the high-order dynamic wave model. The coupling capability of currently used dynamic wave models is systematically conducted. The results indicate that the propagation of a dynamic flood wave only depends on the Froude number, but is independent of the coupling of sediment transport and river mobility. Furthermore, based on the continuum hypothesis, the dynamic equations describing the motion of the active bed layer are obtained. A renewed dynamic wave model is established. Four families of asymptotic solutions to the eigenvalues of the renewed four-order hyperbolic system are obtained by means of the singular-perturbation technology. The results demonstrate that the interactions between flood propagation, sediment transport, and riverbed mobility are coupled. Propagation of the main dynamic flood wave and the dynamic sediment wave will be slower with the increasing deposition rate, but will be faster when the erosion intensity is enhanced. These mainly occur in the lower flow regime. In the process of deposition, the second dynamic flood wave and the dynamic bed wave will propagate both upward and downstream. Besides, the dynamic bed wave will propagate downstream and the second dynamic flood wave will only propagate upstream, regardless of the flow regime.