A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry
A non-linear coupled-mode system of horizontal equations has been derived with the aid of Luke's (1967) variational principle, modelling the evolution of nonlinear water waves in intermediate depth and over a general bathymetry Athanassoulis & Belibassakis (2002, 2008). Following previous w...
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ftntunivathens:oai:dspace.lib.ntua.gr:123456789/35742 2023-05-15T14:20:54+02:00 A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry Belibassakis, KA Athanassoulis, GA 2009 http://dspace.lib.ntua.gr/handle/123456789/35742 unknown info:eu-repo/semantics/openAccess free Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE Additional mode Cnoidal wave Elastic body Evanescent mode Flexural rigidities Floating bodies Floating structures Free surfaces General bathymetry Hydro-elastic analysis Hydrodynamic and hydroelastic analysis Ice sheet Intermediate depths Mass distribution Non-linear Non-Linearity Nonlinear travelling waves Nonlinear water waves Numerical example Numerical investigations Numerical solution Series expansion Thin plate Variable bathymetry Variable thickness Variational principles Vertical structures Wave potentials Wavefields Arctic engineering Bathymetry Hydrodynamics Nonlinear equations Numerical analysis Oceanography Offshore structures Rigid structures Thickness control Variational techniques Water waves Waves Hydroelasticity info:eu-repo/semantics/conferenceObject 2009 ftntunivathens 2019-07-13T16:34:09Z A non-linear coupled-mode system of horizontal equations has been derived with the aid of Luke's (1967) variational principle, modelling the evolution of nonlinear water waves in intermediate depth and over a general bathymetry Athanassoulis & Belibassakis (2002, 2008). Following previous work by the authors in the case of linearised water waves (Athanassoulis & Belibassakis 1999), the vertical structure of the wave field is exactly represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional modes, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The coupled-mode system fully accounts for the effects of non-linearity and dispersion. The main feature of this approach that a small number of modes (of the order of 5-6) are enough for the precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included in the local-mode series. The consistent coupled-mode system has been applied to numerical investigation of families of steady nonlinear travelling wave solutions in constant depth (Athanassoulis & Belibassakis 2007) showing good agreement with known solutions both in the Stokes and the cnoidal wave regimes. In the present work we focus on the hydroelastic analysis of floating bodies lying over variable bathymetry regions, with application to the non-linear scattering of water waves by large floating structures (of VLFS type or ice sheets) characterised by variable thickness (draft), flexural rigidity and mass distributions, modelled as thin plates of variable thickness, extending previous approaches (see, e.g., Porter & Porter 2004, Belibassakis & Athanassoulis 2005, 2006, Bennets et al 2007). Numerical examples are presented, showing that useful results can be obtained for the analysis of large floating elastic bodies or structures very efficiently by keeping only a few terms in the expansion. Ideas for extending our approach to 3D are also discussed. Copyright © 2009 by ASME. Conference Object Arctic Arctic Ice Sheet National Technical University of Athens (NTUA): DSpace Arctic |
institution |
Open Polar |
collection |
National Technical University of Athens (NTUA): DSpace |
op_collection_id |
ftntunivathens |
language |
unknown |
topic |
Additional mode Cnoidal wave Elastic body Evanescent mode Flexural rigidities Floating bodies Floating structures Free surfaces General bathymetry Hydro-elastic analysis Hydrodynamic and hydroelastic analysis Ice sheet Intermediate depths Mass distribution Non-linear Non-Linearity Nonlinear travelling waves Nonlinear water waves Numerical example Numerical investigations Numerical solution Series expansion Thin plate Variable bathymetry Variable thickness Variational principles Vertical structures Wave potentials Wavefields Arctic engineering Bathymetry Hydrodynamics Nonlinear equations Numerical analysis Oceanography Offshore structures Rigid structures Thickness control Variational techniques Water waves Waves Hydroelasticity |
spellingShingle |
Additional mode Cnoidal wave Elastic body Evanescent mode Flexural rigidities Floating bodies Floating structures Free surfaces General bathymetry Hydro-elastic analysis Hydrodynamic and hydroelastic analysis Ice sheet Intermediate depths Mass distribution Non-linear Non-Linearity Nonlinear travelling waves Nonlinear water waves Numerical example Numerical investigations Numerical solution Series expansion Thin plate Variable bathymetry Variable thickness Variational principles Vertical structures Wave potentials Wavefields Arctic engineering Bathymetry Hydrodynamics Nonlinear equations Numerical analysis Oceanography Offshore structures Rigid structures Thickness control Variational techniques Water waves Waves Hydroelasticity Belibassakis, KA Athanassoulis, GA A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
topic_facet |
Additional mode Cnoidal wave Elastic body Evanescent mode Flexural rigidities Floating bodies Floating structures Free surfaces General bathymetry Hydro-elastic analysis Hydrodynamic and hydroelastic analysis Ice sheet Intermediate depths Mass distribution Non-linear Non-Linearity Nonlinear travelling waves Nonlinear water waves Numerical example Numerical investigations Numerical solution Series expansion Thin plate Variable bathymetry Variable thickness Variational principles Vertical structures Wave potentials Wavefields Arctic engineering Bathymetry Hydrodynamics Nonlinear equations Numerical analysis Oceanography Offshore structures Rigid structures Thickness control Variational techniques Water waves Waves Hydroelasticity |
description |
A non-linear coupled-mode system of horizontal equations has been derived with the aid of Luke's (1967) variational principle, modelling the evolution of nonlinear water waves in intermediate depth and over a general bathymetry Athanassoulis & Belibassakis (2002, 2008). Following previous work by the authors in the case of linearised water waves (Athanassoulis & Belibassakis 1999), the vertical structure of the wave field is exactly represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional modes, the free-surface mode and the sloping-bottom mode, enabling to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. The coupled-mode system fully accounts for the effects of non-linearity and dispersion. The main feature of this approach that a small number of modes (of the order of 5-6) are enough for the precise numerical solution, provided that the two new modes (the free-surface and the sloping-bottom ones) are included in the local-mode series. The consistent coupled-mode system has been applied to numerical investigation of families of steady nonlinear travelling wave solutions in constant depth (Athanassoulis & Belibassakis 2007) showing good agreement with known solutions both in the Stokes and the cnoidal wave regimes. In the present work we focus on the hydroelastic analysis of floating bodies lying over variable bathymetry regions, with application to the non-linear scattering of water waves by large floating structures (of VLFS type or ice sheets) characterised by variable thickness (draft), flexural rigidity and mass distributions, modelled as thin plates of variable thickness, extending previous approaches (see, e.g., Porter & Porter 2004, Belibassakis & Athanassoulis 2005, 2006, Bennets et al 2007). Numerical examples are presented, showing that useful results can be obtained for the analysis of large floating elastic bodies or structures very efficiently by keeping only a few terms in the expansion. Ideas for extending our approach to 3D are also discussed. Copyright © 2009 by ASME. |
format |
Conference Object |
author |
Belibassakis, KA Athanassoulis, GA |
author_facet |
Belibassakis, KA Athanassoulis, GA |
author_sort |
Belibassakis, KA |
title |
A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
title_short |
A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
title_full |
A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
title_fullStr |
A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
title_full_unstemmed |
A fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
title_sort |
fast convergent modal-expansion of the wave potential with application to the hydrodynamic and hydroelastic analysis of floating bodies in general bathymetry |
publishDate |
2009 |
url |
http://dspace.lib.ntua.gr/handle/123456789/35742 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic Arctic Ice Sheet |
genre_facet |
Arctic Arctic Ice Sheet |
op_source |
Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE |
op_rights |
info:eu-repo/semantics/openAccess free |
_version_ |
1766293376098893824 |