Simulation of Depth-Limited Breaking Waves in a 3D Fully Nonlinear Potential Flow Model
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 150, Issue 4
Abstract
Extending an earlier two-dimensional (2D) implementation, a novel method is introduced for both detecting the onset of wave breaking and simulating the resulting energy dissipation in limited water depth, in a three-dimensional (3D) fully nonlinear potential flow (FNPF) model. Breaking onset is identified using a universal criterion, based on the ratio of the horizontal particle velocity at the crest to the crest phase velocity. The breaking-induced energy dissipation is based on the nondimensional breaking strength parameter and is implemented in the model as an absorbing surface pressure. The 3D-FNPF solves Laplace’s equation using a higher-order boundary element method based on Green’s second identity and marches the solution forward in time. The implementation of wave dissipation due to breaking is carried out in three steps: (i) a nondimensional breaking strength parameter is calculated based on a previous 2D unified depth-limited dissipation model; (ii) the instantaneous power to be dissipated is computed using this parameter and energy dissipation is modeled as a damping pressure specified in a region around the breaking crest; and (iii) the dissipation process of each breaking wave is terminated using a criterion calibrated through a comparison of the free surface elevation with experimental data from the literature. The new 3D model is experimentally validated for regular spilling and plunging breaking waves propagating over a 3D submerged bar and an elliptical shoal. Future work will extend this model to irregular 3D breaking waves.
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Data Availability Statement
All the numerical results that support the findings of this study are available from the corresponding author upon reasonable request. Some or all data, models, or code used during the study were provided by a third party. Direct requests for these materials may be made to the provider as indicated in the Acknowledgements.
Acknowledgments
The authors thank Arun Kamath and Betsy Seiffert for a copy of the 3D bar experimental data. This research was produced within the framework of Energy4Climate Interdisciplinary Center (E4C) of IP Paris and Ecole des Ponts ParisTech, and was supported by the 3rd Programme d’Investissements d’Avenir [ANR-18-EUR-0006-02]. This action benefited from the support of the Chair “Challenging Technology for Responsible Energy” led by l’X – Ecole Polytechnique and the Fondation de l’Ecole Polytechnique, sponsored by TotalEnergies. S.T.G. gratefully acknowledges support from the US National Science Foundation grant #OCE-19-47960. The authors also thank Luc Pastur (ENSTA Paris) and Christophe Peyrard (EDF R&D LNHE) for helpful discussions.
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Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 150 • Issue 4 • July 2024
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© 2024 American Society of Civil Engineers.
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Received: Sep 28, 2023
Accepted: Mar 22, 2024
Published online: May 8, 2024
Published in print: Jul 1, 2024
Discussion open until: Oct 8, 2024
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