Extreme wave run-up on a vertical cliff

Francesco Carbone (1) , Denys Dutykh (1, 2, 3, 4) , John M. Dudley (5) , Frédéric Dias (1, 6)

1 School of Mathematical Sciences [Dublin]
2 LAMA - Laboratoire de Mathématiques
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
5 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
6 CMLA - Centre de Mathématiques et de Leurs Applications

Wave impact and run-up onto vertical obstacles constitutes one of the main phenomena which have to be taken into account in the design of coastal structures. From the linear wave theory we know that the wave height on a vertical wall is twice the incident wave amplitude. Weakly nonlinear theories bring some small corrections to this result. However, in the present study we show that certain simple wave groups may produce much higher run-ups ever predicted by previous theoretical investigations. Consequently, the results presented in this study can be considered as a note of caution for practitioners, on one side, and as a challenging novel material for theoreticians who work in the field of the wave/structure interaction.

Mots clés: coastal structures; Serre equations; wave/wall interaction; run-up

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Atmosphérique et Océanique [physics.ao-ph]; Systèmes Solubles et Intégrables [nlin.SI]; Formation de Structures et Solitons [nlin.PS]; Océan, Atmosphère; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Milieux et Changements globaux

Francesco Carbone, Denys Dutykh, John M. Dudley, Frédéric Dias. Extreme wave run-up on a vertical cliff. International Workshop on Water Waves and Floating Bodies, Apr 2013, Marseille, France. pp.17-20. ⟨hal-00927313⟩