Generation of two-dimensional 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.

21 pages, 7 figures, 1 table, 69 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (7)

• Finite volume schemes for dispersive wave propagation and runup
• Finite volume methods for unidirectional dispersive wave models
• On the use of finite fault solution for tsunami generation problems
• On the contribution of the horizontal sea-bed displacements into the tsunami generation process
• Dispersive wave runup on non-uniform shores
• Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain
• Unique continuation property and control for the Benjamin-Bona-Mahony equation on the torus

Cited by in corpus (3)

• Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space
• A numerical procedure and unified formulation for the adjoint approach in hyperbolic PDE-constrained optimal control problems
• Optimization of Bathymetry for Long Waves with Small Amplitude