Inertia effects in bed-load transport models

Inertia effects are seldom considered in morphological modeling, and most of the transport models were developed from laboratory experiments in steady uniform flow conditions. This paper considers first the hysteresis effects in transient flows between discharge, velocity, and bottom shear stress. These effects can be taken into account as far as the complete shallow-water equations are used. Secondly, inertia effects linked to the sediment response to acting forces are considered. Three types of models are investigated: (i) sediment movement instantaneously adapting to hydrodynamic changes, (ii) spatial or temporal lag laws to give space or time to the sediments to progressively reach the transport capacity, and (iii) a two-layer model, able to account for the inertia of the sediment layer. Finally, three examples are presented: a scour hole downstream of an apron, a jump over a mobile bed, and a dam-break wave. Inertia effects appear significant in the modeling, especially the latter case.