A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions

Belibassakis, KA; Athanassoulis, GA

dc.contributor.author	Belibassakis, KA	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T01:34:52Z
dc.date.available	2014-03-01T01:34:52Z
dc.date.issued	2011	en
dc.identifier.issn	0378-3839	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20908
dc.subject	Coupled modes	en
dc.subject	Finite depth	en
dc.subject	Nonlinear water waves	en
dc.subject	Variable bathymetry	en
dc.subject.classification	Engineering, Civil	en
dc.subject.classification	Engineering, Ocean	en
dc.subject.other	Bottom topography	en
dc.subject.other	Boundary integral formulations	en
dc.subject.other	Cnoidal wave	en
dc.subject.other	Coupled mode	en
dc.subject.other	Evanescent mode	en
dc.subject.other	Experimental data	en
dc.subject.other	Fast convergence	en
dc.subject.other	Finite depth	en
dc.subject.other	Finite water depth	en
dc.subject.other	Fourier methods	en
dc.subject.other	Free surfaces	en
dc.subject.other	Intermediate depths	en
dc.subject.other	Non-linear	en
dc.subject.other	Non-linear methods	en
dc.subject.other	Non-Linearity	en
dc.subject.other	Nonlinear water waves	en
dc.subject.other	Numerical investigations	en
dc.subject.other	Numerical results	en
dc.subject.other	Numerical solution	en
dc.subject.other	Series expansion	en
dc.subject.other	Shallow-water waves	en
dc.subject.other	Travelling wave solution	en
dc.subject.other	Variable bathymetry	en
dc.subject.other	Vertical structures	en
dc.subject.other	Water depth	en
dc.subject.other	Wave potentials	en
dc.subject.other	Wavefields	en
dc.subject.other	Bathymetry	en
dc.subject.other	Hydrodynamics	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Numerical methods	en
dc.subject.other	Waves	en
dc.subject.other	Water waves	en
dc.subject.other	bathymetry	en
dc.subject.other	boundary integral method	en
dc.subject.other	coupling	en
dc.subject.other	Fourier transform	en
dc.subject.other	nonlinearity	en
dc.subject.other	water depth	en
dc.subject.other	wave dispersion	en
dc.subject.other	wave field	en
dc.subject.other	wave propagation	en
dc.title	A coupled-mode system with application to nonlinear water waves propagating in finite water depth and in variable bathymetry regions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.coastaleng.2010.11.007	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.coastaleng.2010.11.007	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	A non-linear coupled-mode system of horizontal equations is presented, modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. The vertical structure of the wave field is 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 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 the local-mode series exhibits fast convergence. Thus, a small number of modes (up to 5-6) are usually enough for precise numerical solution. In the present work, the coupled-mode system is applied to the numerical investigation of families of steady travelling wave solutions in constant depth, corresponding to a wide range of water depths, ranging from intermediate depth to shallow-water wave conditions, and its results are compared vs. Stokes and cnoidal wave theories, as well as with fully nonlinear Fourier methods. Furthermore, numerical results are presented for waves propagating over variable bathymetry regions and compared with nonlinear methods based on boundary integral formulation and experimental data, showing good agreement. (C) 2010 Elsevier B.V. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Coastal Engineering	en
dc.identifier.doi	10.1016/j.coastaleng.2010.11.007	en
dc.identifier.isi	ISI:000288358000006	en
dc.identifier.volume	58	en
dc.identifier.issue	4	en
dc.identifier.spage	337	en
dc.identifier.epage	350	en