A unified coupled-mode approach to nonlinear waves in finite depth potential flow
A non-linear coupled-mode system of horizontal equations is presented, as derived from Luke's (1967) variational principle, which models the evolution of nonlinear water waves in intermediate depth over a general bottom topography. The vertical structure of the wave field is represented by mean...
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ftntunivathens:oai:dspace.lib.ntua.gr:123456789/35545 2023-05-15T14:20:54+02:00 A unified coupled-mode approach to nonlinear waves in finite depth potential flow Athanassoulis, GA Belibassakis, KA 2008 http://dspace.lib.ntua.gr/handle/123456789/35545 unknown info:eu-repo/semantics/openAccess free Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE Bottom topography Cnoidal wave Evanescent mode Experimental data Finite depth Free surfaces Intermediate depths Mode approach Non-linear Non-Linearity Nonlinear water waves Nonlinear waves Numerical investigations Numerical results Numerical solution Second-order stokes Series expansion Shallow-water waves Standard model Traveling wave solution Variable bathymetry Variational principles Vertical structures Water depth Wave potentials Wavefields Arctic engineering Hydrodynamics Mechanics Nonlinear equations Renewable energy resources Technical presentations Variational techniques Wave propagation Water waves info:eu-repo/semantics/conferenceObject 2008 ftntunivathens 2019-07-13T16:33:39Z A non-linear coupled-mode system of horizontal equations is presented, as derived from Luke's (1967) variational principle, which models the evolution of nonlinear water waves in intermediate depth over a general bottom topography. The vertical structure of the wave field is represented by means of a complete local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, 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 present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and has the following main features: (i) various standard models of water-wave propagation are recovered by appropriate simplifications, and (ii) it exhibits fast convergenge, and thus, a small number of modes (up to 5) are usually 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. In the present work, the couplcd-mode system is applied to the numerical investigation of families of steady traveling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate to shallow-water wave conditions and its results are compared vs. Stokes and cnoidal wave theories, respectively. Also, numerical results are presented for waves propagating over variable bathymetry regions and compared with second-order Stokes theory and experimental data. Copyright © 2008 by ASME. Conference Object Arctic Arctic 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 |
Bottom topography Cnoidal wave Evanescent mode Experimental data Finite depth Free surfaces Intermediate depths Mode approach Non-linear Non-Linearity Nonlinear water waves Nonlinear waves Numerical investigations Numerical results Numerical solution Second-order stokes Series expansion Shallow-water waves Standard model Traveling wave solution Variable bathymetry Variational principles Vertical structures Water depth Wave potentials Wavefields Arctic engineering Hydrodynamics Mechanics Nonlinear equations Renewable energy resources Technical presentations Variational techniques Wave propagation Water waves |
spellingShingle |
Bottom topography Cnoidal wave Evanescent mode Experimental data Finite depth Free surfaces Intermediate depths Mode approach Non-linear Non-Linearity Nonlinear water waves Nonlinear waves Numerical investigations Numerical results Numerical solution Second-order stokes Series expansion Shallow-water waves Standard model Traveling wave solution Variable bathymetry Variational principles Vertical structures Water depth Wave potentials Wavefields Arctic engineering Hydrodynamics Mechanics Nonlinear equations Renewable energy resources Technical presentations Variational techniques Wave propagation Water waves Athanassoulis, GA Belibassakis, KA A unified coupled-mode approach to nonlinear waves in finite depth potential flow |
topic_facet |
Bottom topography Cnoidal wave Evanescent mode Experimental data Finite depth Free surfaces Intermediate depths Mode approach Non-linear Non-Linearity Nonlinear water waves Nonlinear waves Numerical investigations Numerical results Numerical solution Second-order stokes Series expansion Shallow-water waves Standard model Traveling wave solution Variable bathymetry Variational principles Vertical structures Water depth Wave potentials Wavefields Arctic engineering Hydrodynamics Mechanics Nonlinear equations Renewable energy resources Technical presentations Variational techniques Wave propagation Water waves |
description |
A non-linear coupled-mode system of horizontal equations is presented, as derived from Luke's (1967) variational principle, which models the evolution of nonlinear water waves in intermediate depth over a general bottom topography. The vertical structure of the wave field is represented by means of a complete local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent modes, plus two additional terms, 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 present coupled-mode system fully accounts for the effects of non-linearity and dispersion, and has the following main features: (i) various standard models of water-wave propagation are recovered by appropriate simplifications, and (ii) it exhibits fast convergenge, and thus, a small number of modes (up to 5) are usually 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. In the present work, the couplcd-mode system is applied to the numerical investigation of families of steady traveling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate to shallow-water wave conditions and its results are compared vs. Stokes and cnoidal wave theories, respectively. Also, numerical results are presented for waves propagating over variable bathymetry regions and compared with second-order Stokes theory and experimental data. Copyright © 2008 by ASME. |
format |
Conference Object |
author |
Athanassoulis, GA Belibassakis, KA |
author_facet |
Athanassoulis, GA Belibassakis, KA |
author_sort |
Athanassoulis, GA |
title |
A unified coupled-mode approach to nonlinear waves in finite depth potential flow |
title_short |
A unified coupled-mode approach to nonlinear waves in finite depth potential flow |
title_full |
A unified coupled-mode approach to nonlinear waves in finite depth potential flow |
title_fullStr |
A unified coupled-mode approach to nonlinear waves in finite depth potential flow |
title_full_unstemmed |
A unified coupled-mode approach to nonlinear waves in finite depth potential flow |
title_sort |
unified coupled-mode approach to nonlinear waves in finite depth potential flow |
publishDate |
2008 |
url |
http://dspace.lib.ntua.gr/handle/123456789/35545 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic Arctic |
genre_facet |
Arctic Arctic |
op_source |
Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE |
op_rights |
info:eu-repo/semantics/openAccess free |
_version_ |
1766293375424659456 |