More on the evolution of bed material waves in alluvial rivers

Sediment waves or pulses can form in rivers following variations in input from landslides, debris flows, and other sources. The question as to how rivers cope with such sediment inputs is of considerable practical interest. Experimental, numerical and field evidence assembled by the authors suggests that in mountain gravel-bed streams, such pulses show relatively little translation, instead mostly dispersing in place. This research has recently been the subject of discussion. In particular it has been suggested that (a) the equations of flow and sediment mass balance used in the analyses, and in most other morphodynamic analyses, require correction; (b) the dominance of dispersion appears only because the hyperbolic nature of the governing equations has not been adequately considered; and (c) the sediment transport equation used in the analyses does not lead to generalizable results. Here we suggest that (a) the relations for mass balance do not require the indicated correction; (b) the hyperbolic nature of the governing equations does not preclude the result of dispersion dominating translation in mountain streams; and (c) the general behaviour of an appropriate hyperbolic model of sediment waves (pulses) includes the relative roles of dispersion and translation, and is not affected by the precise choice of a sediment transport relation (as long as the choice is reasonable for the case in question).