Semi-nonlinear analysis of the effect of deepening on tidal asymmetry

In the last century, various tidal rivers in Europe have seen a large tidal amplication, which is believed to be caused by the deepening and channelization of these rivers. Additionally, large increases in suspended sediment concentrations induced by flood dominance are thought to have decreased the effective hydraulic drag, enhancing further tidal amplication. The tidal amplication causes problems with respect to flood defenses and navigational safety. Furthermore, the increased concentration of suspended sediment causes ecological problems. In the meanwhile, ports along these rivers consider further deepening to accompany ever-larger ships. This research aims at a better understanding of the consequences of deepening and/or a reduced hydraulic drag for tidal asymmetry. Special attention is given to the non-linear behavior of tidal propagation into rivers. Much research has already been done on the implications of deepening tidal rivers. These studies have been done by using either linearized models or fully non-linear ones to solve the Saint Venant equations. This research uses a perturbation model to relate those linear analyses to non-linear behavior. The model uses linear solutions for the water levels and flow velocities (referred to as the leading order solutions) to generate estimates of the effect of the non-linearities, allowing to calculate them separately. By comparing the solutions to those of the fully non-linear SOBEK model we show that this perturbation model provides good estimates of the magnitude and the behavior of the residual and the M4 tide for values of epsilon up to at least 0.5. This research also shows that a linearized friction parameter r can be just as sensitive to boundary conditions or geometrical parameters, as it is to quadratic friction parameters such as the Chezy coefficient. This is done by consistently fitting the leading order solutions of the perturbation model to the M2 frequency solutions of SOBEK with a constant Chezy coefficient. Especially for variations of the imposed tidal wave amplitude, we found a strong sensitivity of the linear friction parameter r. This notion makes the interpretation of changes in r complex and reduces the utility of linearized models. Concerning the role of non-linearities with respect to tidal asymmetry we show that for all realistic depths in the Upper Sea Scheldt, the internally generated M4 tide and residual flow is of the same order of magnitude or larger than the external M4 tide and river flow. Moreover, in case of deepening, the relation between the importance of the non-linearities or overtides and the non-linearity parameter epsilon is not trivial. We depicted a range of epsilon which no clear relation to the overtides exists, denoted as the arbitrary range. The main reason for the existence of this range is the complex response of the leading order water level and flow velocity to deepening. The largest non-linearities depend on both these leading order solutions. Additionally, all non-linearities have a different direct dependency on the average water depth h. It is encouraged to continue work with the perturbation model as it shows great analysis potential. The use of a more accurate description of the friction term is recommended.