Resonant Long-Wave Run-Up On A Plane Beach

Themistoklis Stefanakis (1, 2) , Frédéric Dias (1, 2) , Denys Dutykh (1, 3, 4, 5)

1 School of Mathematical Sciences [Dublin]
2 CMLA - Centre de Mathématiques et de Leurs Applications
3 LAMA - Laboratoire de Mathématiques
4 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
5 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

Even though wave run-up is not a new subject, until recently analytical and numerical studies of long wave run-up on a plane beach have failed to identify the existence of resonant regimes. Furthermore, it was a common belief that the leading wave will result in the maximum run-up. Stefanakis et al. (2011) underlined the importance of resonant long wave interactions during run-up and run-down. In the current paper we provide additional results with the use of one-dimensional numerical simulations in the framework of the nonlinear shallow water equations with boundary forcing for plane and nontrivial beaches. Several wave profiles are used as forcing conditions to the boundary value problem. Resonant interactions between incident and receding waves are found to occur, depending on the beach slope and the wavelength, and result in enhanced run-up of non-leading waves.

Mots clés: Long wave; run-up; resonance

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]; Milieux fluides et réactifs; Océan, Atmosphère; Océanographie; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Milieux et Changements globaux

Themistoklis Stefanakis, Frédéric Dias, Denys Dutykh. Resonant Long-Wave Run-Up On A Plane Beach. The Twenty-second International Offshore and Polar Engineering Conference, Dec 2019, Rodes, Greece. ⟨hal-00728747⟩