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Article: Unified intrinsic functional expansion theory for solitary waves

TitleUnified intrinsic functional expansion theory for solitary waves
Authors
KeywordsExact Solution
High-Accuracy Computation Of Wave Of Arbitrary Height
Mass And Energy Transfer
Solitary Waves On Water
Unified Intrinsic Functional Expansion Theory
Issue Date2005
PublisherSpringer Verlag. The Journal's web site is located at http://www.springeronline.com/sgw/cda/frontpage/0,11855,1-102-70-28739617-0,00.html?changeHeader=true
Citation
Acta Mechanica Sinica/Lixue Xuebao, 2005, v. 21 n. 1, p. 1-15 How to Cite?
AbstractA new theory is developed for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120° down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokes's formula, F 2 μπ=tan μπ, relating the wave speed (the Froude number F) and the logarithmic decrement μ of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokes's basic term (singular in μ), such that 2M μ is just somewhat beyond unity, i.e. 2M μ ≃ 1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio α=a/h, especially about α ≃ 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with α ≤ 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined to give the maximum height α hst=0.8331990, and speed F hst=1.290890, accurate to the last significant figure, which seems to be a new record.
Persistent Identifierhttp://hdl.handle.net/10722/177725
ISSN
2015 Impact Factor: 0.832
2015 SCImago Journal Rankings: 0.426
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWu, TYen_US
dc.contributor.authorKao, Jen_US
dc.contributor.authorZhang, JEen_US
dc.date.accessioned2012-12-19T09:39:43Z-
dc.date.available2012-12-19T09:39:43Z-
dc.date.issued2005en_US
dc.identifier.citationActa Mechanica Sinica/Lixue Xuebao, 2005, v. 21 n. 1, p. 1-15en_US
dc.identifier.issn0567-7718en_US
dc.identifier.urihttp://hdl.handle.net/10722/177725-
dc.description.abstractA new theory is developed for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120° down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokes's formula, F 2 μπ=tan μπ, relating the wave speed (the Froude number F) and the logarithmic decrement μ of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokes's basic term (singular in μ), such that 2M μ is just somewhat beyond unity, i.e. 2M μ ≃ 1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio α=a/h, especially about α ≃ 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with α ≤ 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined to give the maximum height α hst=0.8331990, and speed F hst=1.290890, accurate to the last significant figure, which seems to be a new record.en_US
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://www.springeronline.com/sgw/cda/frontpage/0,11855,1-102-70-28739617-0,00.html?changeHeader=trueen_US
dc.relation.ispartofActa Mechanica Sinica/Lixue Xuebaoen_US
dc.subjectExact Solutionen_US
dc.subjectHigh-Accuracy Computation Of Wave Of Arbitrary Heighten_US
dc.subjectMass And Energy Transferen_US
dc.subjectSolitary Waves On Wateren_US
dc.subjectUnified Intrinsic Functional Expansion Theoryen_US
dc.titleUnified intrinsic functional expansion theory for solitary wavesen_US
dc.typeArticleen_US
dc.identifier.emailZhang, JE: jinzhang@hku.hken_US
dc.identifier.authorityZhang, JE=rp01125en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s10409-004-0001-yen_US
dc.identifier.scopuseid_2-s2.0-19644393349en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-19644393349&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume21en_US
dc.identifier.issue1en_US
dc.identifier.spage1en_US
dc.identifier.epage15en_US
dc.identifier.isiWOS:000228656600001-
dc.publisher.placeGermanyen_US
dc.identifier.scopusauthoridWu, TY=7404815163en_US
dc.identifier.scopusauthoridKao, J=32668160400en_US
dc.identifier.scopusauthoridZhang, JE=7601346659en_US

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