Generation of two-dimensional water waves by moving bottom disturbances

Hayk Nersisyan (1) , Denys Dutykh (2, 3) , Enrique Zuazua (1)

1 BCAM - Basque Center for Applied Mathematics
2 LAMA - Laboratoire de Mathématiques
3 School of Mathematical Sciences [Dublin]

In this study we investigate the potential and limitations of the wave generation by disturbances moving at the bottom. More precisely, we assume that the wavemaker is composed of an underwater object of a given shape which can be displaced according to a given trajectory. The practical question we address in this study is how to compute the wavemaker shape and its trajectory in order to generate a wave with prescribed characteristics? For the sake of simplicity we model the hydrodynamics by a generalized forced BBM equation. This practical problem is reformulated as a constrained nonlinear optimization problem. Some constraints are imposed in order to make practically feasible the computed solution. Finally, we show some numerical results to support our theoretical and algorithmic developments.

Mots clés: wave generation; moving bottom; BBM equation; optimization

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Milieux et Changements globaux; Optimisation et contrôle [math.OC]; Modélisation et simulation; Physique Classique [physics.class-ph]; Systèmes Solubles et Intégrables [nlin.SI]; Formation de Structures et Solitons [nlin.PS]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Océan, Atmosphère; Géophysique [physics.geo-ph]; Géophysique [physics.geo-ph]

Hayk Nersisyan, Denys Dutykh, Enrique Zuazua. Generation of two-dimensional water waves by moving bottom disturbances. 2012. ⟨hal-00752364v1⟩