An expansion theorem for water-wave potentials

Athanassoulis, GA

dc.contributor.author	Athanassoulis, GA	en
dc.date.accessioned	2014-03-01T01:06:14Z
dc.date.available	2014-03-01T01:06:14Z
dc.date.issued	1984	en
dc.identifier.issn	0022-0833	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9254
dc.subject	Boundary Condition	en
dc.subject	Cross Section	en
dc.subject	Free Surface	en
dc.subject	Incompressible Fluid	en
dc.subject	Laplace Equation	en
dc.subject	Numerical Solution	en
dc.subject	Satisfiability	en
dc.subject	Water Waves	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	MATHEMATICAL TECHNIQUES - Boundary Value Problems	en
dc.subject.other	WATER WAVES	en
dc.subject.other	FLOW OF WATER	en
dc.title	An expansion theorem for water-wave potentials	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF00039187	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF00039187	en
heal.language	English	en
heal.publicationDate	1984	en
heal.abstract	Consider an infinitely long, horizontal cylinder of arbitrary cross section, floating on the free surface of an inviscid, incompressible fluid of infinite depth. The fluid motion is assumed two-dimensional, irrotational and of small amplitude, and it is described by a wave potential satisfying the Laplace equation, the usual linearized free-surface and body-boundary conditions, as well as proper conditions at infinity. A general multipole expansion for the wave potential is derived, converging throughout the fluid domain. Conditions are also stated under which the corresponding expansion for the fluid velocity converges up to and on the body boundary. In this case the multipole expansion may be used in the numerical solution or in the theoretical study of various water-wave problems. To obtain the expansion, a decomposition of the wave potential in a regular wave, a wave source, a wave dipole and a regular wave-free part is first invoked. Subsequently, using Texeira's series and the conformal mapping between the semicircular region \|ζ\|≥1, Im ζ≤0, and the fluid domain, it is shown that the regular part of the wave potential can be represented by a convergent series of wave-free multipoles, which are given explicitly in terms of the mapping function. © 1984 Martinus Nijhoff Publishers.	en
heal.publisher	Martinus Nijhoff, The Hague/Kluwer Academic Publishers	en
heal.journalName	Journal of Engineering Mathematics	en
dc.identifier.doi	10.1007/BF00039187	en
dc.identifier.isi	ISI:A1984TG67800002	en
dc.identifier.volume	18	en
dc.identifier.issue	3	en
dc.identifier.spage	181	en
dc.identifier.epage	194	en