The dynamics of breaker bars: Considered as a diffusion process

In the scope of NOURTEC, an EEC project, efforts are made to simulate the behaviour of executed foreshore supplies with the aid of mathematical computer models. One of the models used are line models. On behalf of the DUT two studies contribute to NOURTEC line modelling. One concentrates on the longshore transport, and the present study focuses on cross-shore sediment transport. Both studies try to improve the applicability of line models in evaluating and forecasting the behaviour of the coast, specially after a nourishment. The cross-shore profiles supplied and evaluated in the scope of NOURTEC, and many other cross-shore profiles as well, are characterised by one or more breaker bars. Foreshore supplies very often have the same length scales as these breaker bars. At the Terschelling coast, for instance, a nourishment was executed by filling the trough between the outer two bars. This illustrates that, studying cross-shore morphology after a supply, one should include the phenomenon of breaker bars in the study as well. This report contains a study about both breaker bars and supplies. Concentrating on the cross-shore profile, in this study breaker bars and supplies are interpreted as harmonic or instantaneous disturbances of an equilibrium profile respectively. An equilibrium profile is a profile shape for which there is no sediment transport. The essence of line modelling is that a cross-shore profile, for given wave and sediment parameters, tends towards an equilibrium shape. Using this concept, breaker bars can be schematised by a harmonic boundary condition and supplies by an initial surplus of sediment in the equilibrium profile. In this study, the equilibrium profile shape and the consequences of a disturbance are described by two expressions. One is the well known continuity equation, and the other is a sediment transport equation. The latter describes the magnitude and the direction of sediment transports as a function of the profile height and the profile slope. Transports due to wave asymmetry, undertow and the gravity force are included in this expression. In case the profile height and the profile slope meet the equilibrium profile shape for a certain location in the profile, the sediment transport equals zero. Thus it follows that, in case of a disturbance of the equilibrium profile slope, these two expressions describe a diffusion process. In this report, the diffusion process is analyzed both analytically and numerically. The analytical part merely concentrates on the derivation of scale rules, not on the accuracy of the outcome. A scale parameter was defined for the diffusion process due to the gravity force. A more extended analysis including wave asymmetry and undertow as well did not lead to significant different results. The analytical part is concluded with a proposal for further study. In the numerical part a computer program is developed based on the sediment transport equation and the continuity equation. As could be expected from the analytical results, no spontaneous increase of any disturbance was found. It appears that breaker bars can only be generated at the upper boundary of the profile. In that case propagation in seawards direction is found, together with a strong dissipation in the upper part of the profile.Hydraulic EngineeringCivil Engineering and Geoscience