Generation of two-dimensional water waves by moving bottom disturbances

TL;DR

This paper explores how to generate specific water waves using moving bottom disturbances, modeling the problem with a generalized BBM equation and solving it through constrained optimization, supported by numerical demonstrations.

Contribution

It introduces a novel optimization-based method to design bottom disturbances for desired wave characteristics, incorporating practical constraints.

Findings

Feasibility of the proposed wave generation method demonstrated.

Numerical results show effective wave control with the approach.

Method can be adapted for various practical wave generation scenarios.

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.