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We investigate the potential and limitations of the wave generation bydisturbances moving at the bottom. More precisely, we assume that the wavemakeris composed of an underwater object of a given shape which can be displacedaccording to a prescribed trajectory. We address the practical question ofcomputing the wavemaker shape and trajectory generating a wave with prescribedcharacteristics. For the sake of simplicity we model the hydrodynamics by ageneralized forced Benjamin-Bona-Mahony (BBM) equation. This practical problemis reformulated as a constrained nonlinear optimization problem. Additionalconstraints are imposed in order to fulfill various practical designrequirements. Finally, we present some numerical results in order todemonstrate the feasibility and performance of the proposed methodology.

Generation of two-dimensional water waves by moving bottom disturbances