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Ces dernières décennies, une attention particulière a été portée sur la modélisation mathématique et la simulation numérique de la propagation de vagues en environnements côtiers. Une description physiquement correcte des phénomènes à grande échelle, qui apparaissent dans les régions d'eau peu profonde, doit prendre en compte de forts effets non-linéaires et dispersifs, ainsi que l'interaction avec des bathymétries complexes. Dans un premier temps, une étude du comportement en régime non linéaire de différents modèles de type Boussinesq est proposée, démontrant l'avantage d'utiliser des modèles fortement non-linéaires par rapport à des modèles faiblement non-linéaires et faiblement dispersifs (couramment utilisés). Ensuite, une nouvelle approche flexible pour résoudre les équations fortement non-linéaires et faiblement dispersives de Green-Naghdi est présentée. Cette stratégie permet d'améliorer un code "shallow water" existant par le simple ajout d'un terme algébrique dans l'équation du moment et est particulièrement adapté à l'utilisation de techniques hybrides pour le déferlement des vagues. De plus, la première discrétisation des équations de Green-Naghdi sur maillage non structuré est proposée via des schémas hybrides Volume Fini/Élément Fini. Finalement, les modèles et méthodes développés dans la thèse sont appliqués à l'étude du problème physique de la formation du mascaret dans des estuaires convergents et alluviaux. Cela a amené à la première caractérisation d'estuaire naturel en terme d'apparition de mascaret.; Over the last decades, there has been considerable attention in the accurate mathematical modeling and numerical simulations of free surface wave propagation in near-shore environments. A physical correct description of the large scale phenomena, which take place in the shallow water region, must account for strong nonlinear and dispersive effects, along with the interaction with complex topographies. First, a study on the behavior in nonlinear regime of different Boussinesq-type models is proposed, showing the advantage of using fully-nonlinear models with respect to weakly-nonlinear and weakly dispersive models (commonly employed). Secondly, a new flexible strategy for solving the fully-nonlinear and weakly-dispersive Green-Naghdi equations is presented, which allows to enhance an existing shallow water code by simply adding an algebraic term to the momentum balance and is particularly adapted for the use of hybrid techniques for wave breaking. Moreover, the first discretization of the Green-Naghdi equations on unstructured meshes is proposed via hybrid finite volume/ finite element schemes. Finally, the models and the methods developed in the thesis are deployed to study the physical problem of bore formation in convergent alluvial estuary, providing the first characterization of natural estuaries in terms of bore inception.

Tidal wave propagation can be described analytically by a set of four implicit equations, i.e., the phase lag equation, the scaling equation, the damping equation, and the celerity equation. It is demonstrated that this system of equations has an asymptotic solution for an infinite channel, reflecting the balance between friction and channel convergence. Subsequently, explicit expressions for the tidal amplitude and velocity amplitude are derived, which are different from the generally assumed exponential damping equation that follows from linearizing the friction term. Analysis of the asymptotic behavior demonstrates that exponential damping of the tidal amplitude is only correct for a frictionless wave or an ideal estuary (no damping). However, in estuaries with modest damping (near ideal) it provides a reasonable approximation. In natural estuaries, there is generally a need to take account of local variability of, e.g., depth and friction, by subdividing the estuary into multiple reaches. This is illustrated with an example of the Scheldt estuary, which has been gradually deepened for navigation purpose over the last half century. The analytical model is used to study the effect of this deepening on the tidal dynamics in the main navigation channel, demonstrating that the navigation channel will become “overamplified” when it reaches a depth larger than the critical depth. In the case of overamplification, a further increase of the depth reduces the amplification until critical convergence (condition for a frictionless standing wave) is reached asymptotically. Finally, based on the ratio between the tidal amplitude at the seaward boundary and the asymptotic tidal amplitude, estuaries can be classified into damped, amplified, or ideal estuaries, which is illustrated with 23 real estuaries.

Tidal wave propagation can be described analytically by a set of four implicit equations, i.e., the phase lag equation, the scaling equation, the damping equation, and the celerity equation. It is demonstrated that this system of equations has an asymptotic solution for an infinite channel, reflecting the balance between friction and channel convergence. Subsequently, explicit expressions for the tidal amplitude and velocity amplitude are derived, which are different from the generally assumed exponential damping equation that follows from linearizing the friction term. Analysis of the asymptotic behavior demonstrates that exponential damping of the tidal amplitude is only correct for a frictionless wave or an ideal estuary (no damping). However, in estuaries with modest damping (near ideal) it provides a reasonable approximation. In natural estuaries, there is generally a need to take account of local variability of, e.g., depth and friction, by subdividing the estuary into multiple reaches. This is illustrated with an example of the Scheldt estuary, which has been gradually deepened for navigation purpose over the last half century. The analytical model is used to study the effect of this deepening on the tidal dynamics in the main navigation channel, demonstrating that the navigation channel will become “overamplified” when it reaches a depth larger than the critical depth. In the case of overamplification, a further increase of the depth reduces the amplification until critical convergence (condition for a frictionless standing wave) is reached asymptotically. Finally, based on the ratio between the tidal amplitude at the seaward boundary and the asymptotic tidal amplitude, estuaries can be classified into damped, amplified, or ideal estuaries, which is illustrated with 23 real estuaries.

The main objective of this research is to investigate the governing processes and characteristics that drive morphodynamic evolution in alluvial estuaries by application of a process-based numerical model (Delft3D). It is of utmost importance to understand estuarine processes so that impact of human interference (like dredging and land reclamation) and long-term changes (like sea level rise) can be evaluated.The research addresses a number of cases ranging from an rectangular basins to real estuaries like the Western Scheldt in the Netherlands and San Pablo Bay in California. The more schematized approach allows to study morphodynamic evolution over several millennia under constant forcing and answers more fundamental questions related to conditions of equilibrium and related time scales. The more realistic cases give insight into the skill of the approach in predicting decadal morphodynamic developments. More processes are included to mimic realistic conditions and model results are compared to bathymetric measurements over the last century. The research shows that the modeling approach is good capable of describing stable morphodynamic calculations over a timescale of millennia with patterns similar to patterns observed in reality. Additionally, the approach shows that it is possible to predict decadal morphodynamic developments in real estuaries with significant skill.

The main objective of this research is to investigate the governing processes and characteristics that drive morphodynamic evolution in alluvial estuaries by application of a process-based numerical model (Delft3D). It is of utmost importance to understand estuarine processes so that impact of human interference (like dredging and land reclamation) and long-term changes (like sea level rise) can be evaluated.The research addresses a number of cases ranging from an rectangular basins to real estuaries like the Western Scheldt in the Netherlands and San Pablo Bay in California. The more schematized approach allows to study morphodynamic evolution over several millennia under constant forcing and answers more fundamental questions related to conditions of equilibrium and related time scales. The more realistic cases give insight into the skill of the approach in predicting decadal morphodynamic developments. More processes are included to mimic realistic conditions and model results are compared to bathymetric measurements over the last century. The research shows that the modeling approach is good capable of describing stable morphodynamic calculations over a timescale of millennia with patterns similar to patterns observed in reality. Additionally, the approach shows that it is possible to predict decadal morphodynamic developments in real estuaries with significant skill.

Observations in estuaries indicate that an amplified tidal wave moves considerably faster than is indicated by the classical equation for wave propagation. Similarly, the celerity of propagation is lower if the tidal wave is damped. This phenomenon is clearly observed in the Schelde estuary (located in the Netherlands and Belgium) and in the Incomati estuary in Mozambique. In the Incomati, the tidal wave is damped throughout, whereas in the Schelde the tidal range increases from the mouth until the city of Antwerp, after which it decreases until Gent. This paper derives a new analytical expression for the celerity of the tidal wave that takes into account the effect of tidal damping, as an expansion of the classical equation for tidal wave propagation. In the new equation the phase lag between high water and high water slack plays a crucial role. It is one of the main parameters determining tidal wave propagation in alluvial estuaries. The equation is successfully applied to observations in the Schelde and the Incomati.