On evolution of bed material waves in alluvial rivers

Description/Abstract

Field and laboratory measurements have shown distinct characteristics of bed sediment waves under differing conditions, whilst their theoretical interpretation has emerged to be equivocal. This note aims to clarify the interpretation of evolution of bed material waves. The complete set of governing equations for the flow-sediment-morphology system is deduced to demonstrate its universally hyperbolic nature, irrespective of the sediment transport functions implemented to close the equations. The hyperbolic nature can admit not only attenuating bed material waves, but also shock-like waves that are not unusual in the real world. It is suggested that the theory of dispersion/diffusion is not universally appropriate for evolution of bed material waves.