Extension of second-order Stokes theory to variable bathymetry

Belibassakis, KA; Athanassoulis, GA

dc.contributor.author	Belibassakis, KA	en
dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T01:17:54Z
dc.date.available	2014-03-01T01:17:54Z
dc.date.issued	2002	en
dc.identifier.issn	0022-1120	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14697
dc.subject	Second Order	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Fluids & Plasmas	en
dc.subject.other	Computational fluid dynamics	en
dc.subject.other	Computer simulation	en
dc.subject.other	Energy transfer	en
dc.subject.other	Second harmonic generation	en
dc.subject.other	Nonlinear waves	en
dc.subject.other	Bathymetry	en
dc.subject.other	bathymetry	en
dc.subject.other	Stokes flow	en
dc.subject.other	wave diffraction	en
dc.subject.other	wave propagation	en
dc.subject.other	wave reflection	en
dc.subject.other	wave-seafloor interaction	en
dc.subject.other	bathymetry	en
dc.subject.other	Stokes formula	en
dc.subject.other	wave diffraction	en
dc.subject.other	wave propagation	en
dc.subject.other	wave reflection	en
dc.subject.other	wave-seafloor interaction	en
dc.title	Extension of second-order Stokes theory to variable bathymetry	en
heal.type	journalArticle	en
heal.identifier.primary	10.1017/S0022112002008753	en
heal.identifier.secondary	http://dx.doi.org/10.1017/S0022112002008753	en
heal.language	English	en
heal.publicationDate	2002	en
heal.abstract	In the present work second-order Stokes theory has been extended to the case of a generally shaped bottom profile connecting two half-strips of constant (but possibly different) depths, initiating a method for generalizing the Stokes hierarchy of second- and higher-order wave theory, without the assumption of spatial periodicity. In modelling the wave-bottom interaction three partial problems arise: the first order, the unsteady second order and the steady second order. The three problems are solved by using appropriate extensions of the consistent coupled-mode theory developed by the present authors for the linearized problem. Apart from the Stokes small-amplitude expansibility assumption, no additional asymptotic assumptions have been introduced. Thus, bottom slope and curvature may be arbitrary, provided that the resulting wave dynamics is Stokes-compatible. Accordingly, the present theory can be used for the study of various wave phenomena (propagation, reflection, diffraction) arising from the interaction of weakly nonlinear waves with a general bottom topography, in intermediate water depth. An interesting phenomenon, that is also very naturally resolved, is the net mass flux induced by the depth variation, which is consistently calculated by means of the steady second-order potential. The present method has been validated against experimental results and fully nonlinear numerical solutions. It has been found that it correctly predicts the second-order harmonic generation, the amplitude nonlinearity, and the amplitude variation due to non-resonant first- and-second harmonic interaction, up to the point where the energy transfer to the third and higher harmonics can no longer be neglected. Under the restriction of weak nonlinearity, the present model can be extended to treat obliquely incident waves and the resulting second-order refraction patterns, and to study bichromatic and/or bidirectional wave-wave interactions, with application to the transformation of second-order random seas in variable bathymetry regions.	en
heal.publisher	CAMBRIDGE UNIV PRESS	en
heal.journalName	Journal of Fluid Mechanics	en
dc.identifier.doi	10.1017/S0022112002008753	en
dc.identifier.isi	ISI:000177475500002	en
dc.identifier.volume	464	en
dc.identifier.spage	35	en
dc.identifier.epage	80	en