Modelling of nonlinear wave-buoy dynamics using constrained variational methods

Kalogirou, Anna; Bokhove, Onno; Ham, David

Abstract

We consider a comprehensive mathematical and numerical strategy to couple water-wave motion with rigid ship dynamics using variational principles. We present a methodology that applies to three-dimensional potential flow water waves and ship dynamics. For simplicity, in this paper we demonstrate the method for shallow-water waves coupled to buoy motion in two dimensions, the latter being the symmetric motion of a cross-section of a ship. The novelty in the presented model is that it employs a Lagrange multiplier to impose a physical restriction on the water height under the buoy in the form of an inequality constraint. A system of evolution equations can be obtained from the model and consists of the classical shallow-water equations for shallow, incompressible and irrotational waves, and relevant equations for the dynamics of the wave-energy buoy. One of the advantages of the variational approach followed is that, when combined with symplectic integrators, it eliminates any numerical damping and preserves the discrete energy; this is confirmed in our numerical results.

Citation

Kalogirou, A., Bokhove, O., & Ham, D. (2017). Modelling of nonlinear wave-buoy dynamics using constrained variational methods. In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering (1-10). https://doi.org/10.1115/OMAE2017-61966

• Conference Name: ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering
• Conference Location: Trondheim, Norway
• Start Date: Jun 25, 2017
• End Date: Jun 30, 2017
• Acceptance Date: Feb 27, 2017
• Publication Date: Jun 25, 2017
• Deposit Date: Jun 4, 2019
• Publicly Available Date: Aug 15, 2019
• Publisher: American Society of Mechanical Engineers
• Volume: 7A-2017
• Pages: 1-10
• Book Title: ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering
• ISBN: 9780791857731
• DOI: https://doi.org/10.1115/OMAE2017-61966
• Public URL: https://nottingham-repository.worktribe.com/output/2138060
• Publisher URL: http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=2655744