Generation of 2D water waves by moving bottom disturbances

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 equation. This practical problem is reformulated as a constrained non-linear optimization problem. Additional constraints are imposed in order to fulfil various practical design requirements. Finally, we present some numerical results in order to demonstrate the feasibility and performance of the proposed methodology.