Waves arising from Hirano’s conservation model for mixed-size sediment morphodynamics

An experimental study

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Abstract

River bed degradation is sometimes counteracted with nourishment of sediment material. Numerical models — which include Hirano’s sediment continuity model for mixed-size sediment — can be used to predict the transport of different sediment fractions (the waves due to spatial variations in the grain size distribution of the bed material are here called Ribberink waves) in the dumped material to find an optimal grain size distribution of the nourishment. Little is known how well these numerical predictions represent physical reality. The uncertainty in predictions of the behaviour of the transport of mixed-size sediment can have severe impact: the grain size distribution influences degradation and aggradation processes and bed friction, both, directly or indirectly, influence water levels and flow velocities that are important for designing measures for hinterland protection. Moreover, numerical models predict Ribberink waves travelling faster than associated bed level perturbations (De Vries waves), which is never observed in reality. In order to gain insight into the behaviour of morphodynamic changes with mixed-size sediment — especially with regards to the Ribberink waves — two flume experiments were conducted in the Water Lab of Delft University of Technology. The first experiment is a case with uniform tracer sediment, installing a shoal of different colour than the sediment in the downstream part of the flume. The shoal was installed for the upstream end. Comparing the outcomes of the latter experiment with a numerical simulation gives insight into the question if the Ribberink wave travelling faster than the De Vries wave is an artefact of the Hirano model or that it has physical meaning and relevance. The second experiment was an experiment with a bimodal sediment mixture. A shoal consisting of the coarser fraction is installed at the upstream part of the flume. The coarse fraction has a different colour than the fine fraction so that we were able to track it through the domain. The tracer experiment shows a distinct propagation of the shoal through the domain. Downstream of the shoal no degradation occurred. The material initially present in the shoal did not travel faster than the shoal. The numerical simulation of the experiment shows tracer material being transported faster than the shoal. The tracer material spread over the bed downstream of the shoal, reaching the end of the computational domain before the end of the simulation. The mixed-size sediment experiment shows a distinct propagation of the shoal through the domain (De Vries wave), preceded by an degradational wave (Ribberink wave). This degradational wave is caused by the spatial increase of the sediment transport rate, which is the net effect of: (a) a streamwise increasing flow depth; (b) a streamwise decreasing average grain size diameter of the bed surface, and; (c) a turbulent recirculation zone increasing local sediment transport capacities. In the area of degradation, the bed gradually becomes finer than the initial situation. A numerical reproduction of this experiment reproduced the experiment well, showing the same propagation celerity of the shoal and the associated erosion wave (but less deep), but shows no significant change of the grain size distribution compared to the initial bed of the bed downstream of the shoal. The predicted Ribberink wave thus travels with the same celerity as the measured Ribberink wave and does not precedes the De Vries wave. The conclusions of this thesis show that the grain size distribution of a sediment nourishment is of great influence on the propagation of the nourished material and on bed level changes downstream of the nourishment. As concluded from the flume experiments, when the nourished material (a hump similar to the shoal of the conducted experiments in this thesis) is coarser than the river bed, an erosional wave downstream of the nourishment will arise, travelling with the same celerity as the nourished material. If the nourishment is done to protect or counteract river bed degradation, this erosional effect caused by the shoal should be considered seriously.