Generation of 2D water waves by moving bottom disturbances

Abstract

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 prescribed trajectory. We address the practical question of computing the wavemaker shape and trajectory generating a wave with prescribed characteristics. For the sake of simplicity we model the hydrodynamics by a generalized forced Benjamin-Bona-Mahony (BBM) equation. This practical problem is reformulated as a constrained nonlinear optimization problem. Additional constraints are imposed in order to fulfill various practical design requirements. Finally, we present some numerical results in order to demonstrate the feasibility and performance of the proposed methodology.

Keywords

Bibliographic record

BibTeX Citation

@article{Nersisyan2015generationwater,
  author = {Nersisyan, H. and Dutykh, D. and Zuazua, E.},
  title = {Generation of 2D water waves by moving bottom disturbances},
  journal = {IMA J. Appl. Math.},
  year = {2015},
  volume = {80},
  number = {4},
  pages = {1235--1253},
  doi = {10.1093/imamat/hxu051},
  abstract = {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 prescribed trajectory. We address the practical question of computing the wavemaker shape and trajectory generating a wave with prescribed characteristics. For the sake of simplicity we model the hydrodynamics by a generalized forced Benjamin-Bona-Mahony (BBM) equation. This practical problem is reformulated as a constrained nonlinear optimization problem. Additional constraints are imposed in order to fulfill various practical design requirements. Finally, we present some numerical results in order to demonstrate the feasibility and performance of the proposed methodology.},
  keywords = {wave generation, moving bottom, BBM equation, optimization}
}