A weakly nonlinear coupled-mode model for wave-current-seabed interaction over general bottom topography

Belibassakis, KA; Gerostathis, ThP; Athanassoulis, GA

dc.contributor.author	Belibassakis, KA	en
dc.contributor.author	Gerostathis, ThP	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T02:51:33Z
dc.date.available	2014-03-01T02:51:33Z
dc.date.issued	2008	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35546
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-77957981381&partnerID=40&md5=a4f9dca015a2561526032f3d91a9c3ce	en
dc.subject.other	Analytical structure	en
dc.subject.other	Bottom boundary conditions	en
dc.subject.other	Bottom topography	en
dc.subject.other	Coupled systems	en
dc.subject.other	Evanescent mode	en
dc.subject.other	Finite difference scheme	en
dc.subject.other	Horizontal planes	en
dc.subject.other	Nonlinear waves	en
dc.subject.other	Numerical results	en
dc.subject.other	One-equation model	en
dc.subject.other	Propagating mode	en
dc.subject.other	Scattered waves	en
dc.subject.other	Seabed interaction	en
dc.subject.other	Second orders	en
dc.subject.other	Steady current	en
dc.subject.other	Test case	en
dc.subject.other	Variational principles	en
dc.subject.other	Vertical distributions	en
dc.subject.other	Vertical modes	en
dc.subject.other	Wave current interaction	en
dc.subject.other	Wave potentials	en
dc.subject.other	Wave scattering	en
dc.subject.other	Arctic engineering	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Mechanics	en
dc.subject.other	Ocean engineering	en
dc.subject.other	Topography	en
dc.subject.other	Variational techniques	en
dc.subject.other	Wave propagation	en
dc.subject.other	Wave equations	en
dc.title	A weakly nonlinear coupled-mode model for wave-current-seabed interaction over general bottom topography	en
heal.type	conferenceItem	en
heal.publicationDate	2008	en
heal.abstract	A weakly nonlinear, coupled-mode model is developed for the wave-current-seabed interaction problem, with application to wave scattering by steady currents over general bottom topography. Based on previous work by the authors (Athanassoulis & Belibassakis [1], Belibassakis et al [2]), 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 an additional term accounting for the bottom boundary condition when the bottom slope is not negligible. Using the above representation, in conjunction with Luke's [3] variational principle, the wave-current-seabed interaction problem is reduced to a coupled system of differential equations on the horizontal plane. If only the propagating mode is retained in the vertical expansion of the wave potential, and after simplifications, the present system is reduced to an one-equation model compatible with Kirby's [4] mild-slope model with application to the problem of wave-current interaction over slowly varying topography. The present coupled-mode system is discretized on the horizontal plane by using a second-order finite difference scheme and numerically solved by iterations. Numerical results are presented for two representative test cases, demonstrating the importance of the first evanescent modes and the sloping-bottom mode. The analytical structure of the present model facilitates its extension to treat fully non-linear waves, and it can be further elaborated to study wave propagation over random bottom topography and general currents. Copyright © 2008 by ASME.	en
heal.journalName	Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE	en
dc.identifier.volume	4	en
dc.identifier.spage	465	en
dc.identifier.epage	473	en