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Kinematic wave theory for transient bed sediment waves in alluvial rivers
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Transient bed sediment waves in alluvial rivers have been described using a multitude of hydraulic formulations. These formulations are based on some form of the St. Venant equations and conservation of mass of sediment in suspension and in bed. Depending on the assumptions employed, a hierarchy of formulations is expressed. These formulations in the literature employ uncoupled, semicoupled, or fully coupled transport models treating the sediment waves as either hyperbolic (dynamic wave) or parabolic (diffusion wave). It is, however, hypothesized that the movement of bed sediment waves in alluvial rivers can be described as a kinematic wave. Kinematic wave theory employs a functional relation between sediment transport rate and concentration and a relation between flow velocity and depth. This study summarizes the hierarchy of the formulations while emphasizing the kinematic wave theory for describing transient bed sediment waves. The applicability of the theory is shown for laboratory flume data and hypothetical cases.