Sandra Soares Frazao

Undular bores and secondary waves -Experiments and hybrid finite-volume modelling

Secondary free-surface undulations (Favre waves), appearing for example after the opening of a sluice gate or at the head of a bore, cannot be reproduced by numerical models based on the hydrostatic pressure assumption. The Boussinesq equations take into account the extra pressure gradients but are difficult to integrate due to the high-order derivative terms. The paper describes the physics of wave initiation and proposes a demonstration of the Boussinesq equation based on relatively wider assumptions than usually adopted. A linear stability analysis is developed in finite-difference frame to highlight some potential source of numerical instabilities. These conclusions are transposed in a new hybrid finite-volume / finite-difference scheme, which reveals a better accuracy in period and amplitude when evaluated against experiments.

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.