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We are interested in the modeling of wave-current interactions around surf zones at beaches. Any model that aims to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have therefore formulated the Hamilto-5 nian dynamics of a new water wave model, incorporating both the shallow(More)
We are interested in the numerical modeling of wave-current interactions around beaches' surf zones. Any model to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have formulated the Hamiltonian dynamics of a new water wave model. This model incorporates both the shallow water(More)
a r t i c l e i n f o a b s t r a c t A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a finite element discretization that(More)
Wave action, particularly during storms, drives the evolution of beaches. Beach evolution by non-linear breaking waves is poorly understood due to its three-dimensional character, the range of scales involved, and our limited understanding of particle-wave interactions. We show how a novel, three-phase extension to the classic " Hele-Shaw " laboratory(More)
a r t i c l e i n f o a b s t r a c t Keywords: Nonlinear water waves Finite element Galerkin method (Non-)autonomous variational formulation Symplectic time integration Various systems in nature have a Hamiltonian structure and therefore accurate time integrators for those systems are of great practical use. In this paper, a finite element method will be(More)
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