A coupled-mode model for water wave scattering by horizontal, non-homogeneous current in general bottom topography

Belibassakis, KA; Gerostathis, TP; Athanassoulis, GA

dc.contributor.author	Belibassakis, KA	en
dc.contributor.author	Gerostathis, TP	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	0141-1187	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20907
dc.subject	Coupled modes	en
dc.subject	Wave-current-seabed interaction	en
dc.subject.classification	Engineering, Ocean	en
dc.subject.classification	Oceanography	en
dc.subject.other	Analytical structure	en
dc.subject.other	Bottom boundary conditions	en
dc.subject.other	Bottom topography	en
dc.subject.other	Coupled mode	en
dc.subject.other	Coupled systems	en
dc.subject.other	Evanescent mode	en
dc.subject.other	Finite difference	en
dc.subject.other	Free surfaces	en
dc.subject.other	Horizontal planes	en
dc.subject.other	Interaction problems	en
dc.subject.other	Modified mild-slope equations	en
dc.subject.other	Non-homogeneous	en
dc.subject.other	Nonlinear waves	en
dc.subject.other	One-equation model	en
dc.subject.other	Propagating mode	en
dc.subject.other	Scattered waves	en
dc.subject.other	Second orders	en
dc.subject.other	Steady current	en
dc.subject.other	Test case	en
dc.subject.other	Variable bathymetry	en
dc.subject.other	Variational principles	en
dc.subject.other	Vertical distributions	en
dc.subject.other	Vertical modes	en
dc.subject.other	Water wave scattering	en
dc.subject.other	Wave current interaction	en
dc.subject.other	Wave potentials	en
dc.subject.other	Wave scattering	en
dc.subject.other	Wave-current-seabed interaction	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Topography	en
dc.subject.other	Variational techniques	en
dc.subject.other	Water waves	en
dc.subject.other	Electromagnetic wave scattering	en
dc.subject.other	bottom topography	en
dc.subject.other	boundary condition	en
dc.subject.other	seafloor	en
dc.subject.other	water wave	en
dc.subject.other	wave modeling	en
dc.subject.other	wave scattering	en
dc.subject.other	wave-current interaction	en
dc.title	A coupled-mode model for water wave scattering by horizontal, non-homogeneous current in general bottom topography	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.apor.2011.05.004	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.apor.2011.05.004	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	A coupled-mode model is developed for treating the wave-current-seabed interaction problem, with application to wave scattering by non-homogeneous, steady current over general bottom topography. The vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanescent modes, plus additional terms accounting for the satisfaction of the free-surface and bottom boundary conditions. Using the above representation, in conjunction with unconstrained variational principle, an improved coupled system of differential equations on the horizontal plane, with respect to the modal amplitudes, is derived. In the case of small-amplitude waves, a linearised version of the above coupled-mode system is obtained, generalizing previous results by Athanassoulis and Belibassakis [J Fluid Mech 1999;389:275-301] for the propagation of small-amplitude water waves over variable bathymetry regions. Keeping only the propagating mode in the vertical expansion of the wave potential, the present system reduces to an one-equation model, that is shown to be compatible with mild-slope model concerning wave-current interaction over slowly varying topography, and in the case of no current it exactly reduces to the modified mild-slope equation. The present coupled-mode system is discretized on the horizontal plane by using second-order finite differences and numerically solved by iterations. Results are presented for various representative test cases demonstrating the usefulness of the model, as well as the importance of the first evanescent modes and the additional sloping-bottom mode when the bottom slope is not negligible. The analytical structure of the present model facilitates its extension to fully non-linear waves, and to wave scattering by currents with more general structure. (C) 2011 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	Applied Ocean Research	en
dc.identifier.doi	10.1016/j.apor.2011.05.004	en
dc.identifier.isi	ISI:000295994300013	en
dc.identifier.volume	33	en
dc.identifier.issue	4	en
dc.identifier.spage	384	en
dc.identifier.epage	397	en