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Les effets non-lineaires et dispersifs etant particulierement importants pour les vagues en zone cotiere, nous etudions et developpons un modele potentiel completement non-lineaire et dispersif resolvant les equations d’Euler-Zakharov qui regissent l’evolution temporelle de la position et du potentiel des vitesses a la surface libre. La formulation mathematique ainsi que sa mise en œuvre numerique sont exposees, avec la presentation de la methode d’extension du domaine d’une a deux dimensions d’espace horizontales. Les capacites non-lineaires et dispersives de la version 1DH du modele sont demontrees a travers l’application a deux cas tests : d’abord, la generation et la propagation des harmoniques libres et liees associees aux vagues regulieres creees par un generateur de vagues de type piston sur un fond plat d’apres les experiences de CHAPALAIN et al. (1992), puis la propagation de vagues irregulieres au-dessus d’une barre sous-marine d’apres les experiences de BECQ-GIRARD et al. (1999). La bonne representation des transferts d’energie entre les differentes composantes harmoniques montre la capacite et la precision du modele a representer les effets dispersifs et non-lineaires d’ordres eleves. Le developpement d’une version 2DH du modele a ete teste pour simuler la propagation de vagues regulieres sur une marche immergee semi-circulaire agissant comme une lentille convergente, afin de reproduire deux des experiences de WHALIN (1971). Les premiers resultats obtenus utilisant des fonctions de base radiales pour calculer les derivees dans le plan horizontal montrent la capacite du modele de simuler des cas de bathymetries variables en 2DH. Cette methode semble prometteuse en vue de l’application a des cas realistes. Development of a nonlinear and dispersive numerical model of wave propagation in the coastal zone Abstract: Nonlinear and dispersive effects are significant for nearshore waves, leading to the study and development of a fully nonlinear and dispersive potential-flow model solving the Euler-Zakharov equations, which determine the temporal evolution of the free surface elevation and velocity potential. The mathematical model and its numerical implementation are presented, as well as the approach chosen to extend the model to two horizontal dimensions. The nonlinear and dispersive capabilities of the 1DH version of the model are demonstrated by applying the model to two test cases: (1) the generation of regular waves created by a piston-like wave maker and the propagation of the associated free and bound harmonics over a flat bottom, following the experiments of CHAPALAIN et al. (1992), and (2) the propagation of irregular waves over a barred beach profile, following the experiments of BECQ-GIRARD et al. (1999). The accuracy of the model in representing high-order nonlinear and dispersive effects is demonstrated by the reproduction of the energy transfers between different harmonic components. Then, the development of the 2DH version of the model is tested simulating the propagation of regular waves over a semi-circular step acting as a converging lens, reproducing two experiments of WHALIN (1971). The initial results obtained using Radial Basis Functions to estimate the horizontal derivatives demonstrate the ability of the model to simulate wave propagation over variable 2DH bathymetries. These results indicate the potential of applying the model to simulate realistic cases. Keywords: Nonlinear waves; Coastal hydrodynamics; Water wave simulation; Numerical modeling; Wave models; Radial Basis Functions.

Développement d’un modèle numérique non-linéaire et dispersif pour la propagation des vagues en zone côtière