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Accueil du site > Évènements > Séminaires > Séminaires IRPHE > Archives IRPHE > 2019

Vendredi 25 octobre 2019 / IRPHE

publié le

Séminaire régulier IRPHE

Hamiltonian approach for the modeling of the dynamics of fully nonlinear water waves over variable bathymetry, including the effects of breaking

Orateur : Christos Papoutsellis
Aix Marseille Univ, CNRS, IRD, INRA, Coll France, CEREGE

Abstract : The accurate prediction of the complex dynamics of water waves is of fundamental importance for the better understanding of the marine environment. The co-existence of strongly nonlinear and dispersive interactions and bathymetric effects renders the accurate simulation of water waves a challenging issue. In this work, a modelling approach is presented that takes into account full nonlinearity, dispersion and bottom variability. The critical feature of this approach, called Hamiltonian Coupled-Mode Theory (HCMT), is the use of an enhanced vertical mode expansion that serves as an exact representation of the velocity potential in terms of horizontal amplitudes. Using this representation, the classical water wave problem is reformulated as a Hamiltonian system in terms of the free-surface elevation and free-surface potential. Most importantly, the computationally expensive Laplace problem for the velocity potential is replaced by a Coupled-Mode System (CMS) of horizontal differential equations for the modal amplitudes.

For the numerical solution of the model equations, a fourth-order accurate finite-difference scheme is developed and applied to several demanding wave problems. It is shown that the present method accurately describes strongly nonlinear and dispersive propagation up to the breaking limit.

In order to extend HCMT to the breaking case in shallow water, two strategies are developed and applied. Both methods introduce dissipative terms in the dynamic free-surface condition and are constructed by analogy with the hydraulic jump paradigm. Dissipation is activated and deactivated on the basis of an appropriate criterion. In the first method, a pressure-type absorption is introduced while the second considers an eddy viscosity term. Comparisons with experimental measurements indicate that both methods provide a good description of the post-breaking evolution. Further, they can be applied to other wave models that are based on the Hamiltonian structure of free-surface potential flow.

Date et lieu : vendredi 25 octobre 2019 à 11h dans la salle de séminaire IRPHE