A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions

Athanassoulis, GA; Belibassakis, KA

dc.contributor.author	Athanassoulis, GA	en
dc.contributor.author	Belibassakis, KA	en
dc.date.accessioned	2014-03-01T01:14:17Z
dc.date.available	2014-03-01T01:14:17Z
dc.date.issued	1999	en
dc.identifier.issn	0022-1120	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12979
dc.subject	Coupled Mode Theory	en
dc.subject	Water Waves	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Fluids & Plasmas	en
dc.subject.other	MILD-SLOPE EQUATION	en
dc.subject.other	FREE-SURFACE FLOWS	en
dc.subject.other	GRAVITY-WAVES	en
dc.subject.other	HAMILTONS PRINCIPLE	en
dc.subject.other	VARYING TOPOGRAPHY	en
dc.subject.other	NUMERICAL-METHODS	en
dc.subject.other	ELEMENT METHOD	en
dc.subject.other	REFLECTION	en
dc.subject.other	APPROXIMATIONS	en
dc.subject.other	DIFFRACTION	en
dc.title	A consistent coupled-mode theory for the propagation of small-amplitude water waves over variable bathymetry regions	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S0022112099004978	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S0022112099004978	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	Extended mild-slope equations for the propagation of small-amplitude water waves over variable bathymetry regions, recently proposed by Massel (1993) and Porter & Staziker (1995), are shown to exhibit an inconsistency concerning the sloping-bottom boundary condition, which renders them non-conservative with respect to wave energy. In the present work, a consistent coupled-mode theory is derived from a variational formulation of the complete linear problem, by representing the vertical distribution of the wave potential as a uniformly convergent series of local vertical modes at each horizontal position. This series consists of the vertical eigenfunctions associated with the propagating and all evanescent modes and, when the slope of the bottom is different from zero, an additional mode, carrying information about the bottom slope. The coupled-mode system obtained in this way contains an additional equation, as well as additional interaction terms in all other equations, and reduces to the previous extended mild-slope equations when the additional mode is neglected. Extensive numerical results demonstrate that the present model leads to the exact satisfaction of the bottom boundary condition and, thus, it is energy conservative. Moreover, it is numerically shown that the rate of decay of the modal-amplitude functions is improved from O(n-2), where n is the mode number, to O(n-4), when the additional sloping-bottom mode is included in the representation. This fact substantially accelerates the convergence of the modal series and ensures the uniform convergence of the velocity field up to and including the boundaries.	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	Journal of Fluid Mechanics	en
dc.identifier.doi	10.1017/S0022112099004978	en
dc.identifier.isi	ISI:000081596900012	en
dc.identifier.volume	389	en
dc.identifier.spage	275	en
dc.identifier.epage	301	en