Coupling dispersive water waves to shallow-water bores on a beach

Abstract: Potential-flow water waves are coupled to a shallow-water model, including hydraulic bores, at a beach to deal with unidirectional wave propagation in a finite domain. Such a set-up also matches wavetank conditions used for testing and validation of model structures such as ships in maritime engineering. Note that shorter, non-breaking and dispersive waves in deeper water are thus damped by wave breaking at the beach. A suitable coupling point is chosen in sufficiently shallow water, where the two models are coupled by using variational techniques. Numerically, a space-time variational approach is followed for the potential-flow water waves coupled to a classical finite-volume method for the shallow-water model. The entire approach has been validated numerically against bespoke wavetank experiments undertaken at the TU Delft. The main work was performed by Floriane Gidel [1], in collaboration with Tim Bunnik and Geert Kapsenberg (MARIN, Maritime Research Institute Netherlands), Mark Kelmanson and the speaker (Leeds).

[1] F. Gidel 2018: Variational water-wave models and pyramidal freak waves. PhD thesis. University of Leeds: etheses.whiterose.ac.uk/21730/

[2] O. Bokhove 2021: Variational water-wave modeling: from deep water to beaches. Book chapter. Mathematics of Marine Modeling. Springer. Eds. Deleersnijder, Heemink and Schuttelaars.

mathematical physicsanalysis of PDEsdynamical systems

Audience: researchers in the topic

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