Generation of two-dimensional water waves by moving bottom disturbances

Abstract

In this study we investigate the potential and limitations of the wave genera- tion 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. 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 char- acteristics? 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.