Local Runup Amplification By Resonant Wave Interactions

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

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

Until now the analysis of long wave runup on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the Nonlinear Shallow Water Equations (NSWE) are used to investigate the Boundary Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the BVP. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced runup of non-leading waves. The evolution of energy reveals the existence of a quasi-periodic state for the case of sinusoidal waves, the energy level of which, as well as the time required to reach that state, depend on the incident wavelength for a given beach slope. Dispersion is found to slightly reduce the value of maximum runup, but not to change the overall picture. Runup amplification occurs for both leading elevation and depression waves.

Mots clés: long wave runup; resonance; NSWE; BVP

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]; Océan, Atmosphère; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]; Milieux et Changements globaux; Formation de Structures et Solitons [nlin.PS]; Milieux fluides et réactifs

Themistoklis Stefanakis, Frédéric Dias, Denys Dutykh. Local Runup Amplification By Resonant Wave Interactions. Physical Review Letters, 2011, 107, pp.124502. ⟨10.1103/PhysRevLett.107.124502⟩. ⟨hal-00605461v2⟩