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Article: Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids

TitleInterfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids
Authors
KeywordsAsymptotic solution
Fundamental singularity
Interfacial wave
Surface tension
Viscosity
Issue Date2008
PublisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0022-0833
Citation
Journal Of Engineering Mathematics, 2008, v. 62 n. 3, p. 233-245 How to Cite?
AbstractThe interfacial capillary-gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three- dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier-Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity. © Springer Science+Business Media B.V. 2007.
Persistent Identifierhttp://hdl.handle.net/10722/59069
ISSN
2015 Impact Factor: 0.665
2015 SCImago Journal Rankings: 0.347
ISI Accession Number ID
Funding AgencyGrant Number
National Natural Science Foundation of China10602032
Shanghai Rising-Star Program07QA14022
Shanghai Leading Academic DisciplineY0103
Council of the Hong Kong Special Administrative Region, ChinaHKU 7199/03E
Funding Information:

This research was sponsored by the National Natural Science Foundation of China under Grant No. 10602032, Shanghai Rising-Star Program under Grant No. 07QA14022, and the Shanghai Leading Academic Discipline Project under Project No. Y0103. Support by the Research Grants Council of the Hong Kong Special Administrative Region, China, through Project No. HKU 7199/03E is also gratefully acknowledged.

References
Grants

 

DC FieldValueLanguage
dc.contributor.authorLu, DQen_HK
dc.contributor.authorNg, COen_HK
dc.date.accessioned2010-05-31T03:42:21Z-
dc.date.available2010-05-31T03:42:21Z-
dc.date.issued2008en_HK
dc.identifier.citationJournal Of Engineering Mathematics, 2008, v. 62 n. 3, p. 233-245en_HK
dc.identifier.issn0022-0833en_HK
dc.identifier.urihttp://hdl.handle.net/10722/59069-
dc.description.abstractThe interfacial capillary-gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three- dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier-Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity. © Springer Science+Business Media B.V. 2007.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0022-0833en_HK
dc.relation.ispartofJournal of Engineering Mathematicsen_HK
dc.subjectAsymptotic solutionen_HK
dc.subjectFundamental singularityen_HK
dc.subjectInterfacial waveen_HK
dc.subjectSurface tensionen_HK
dc.subjectViscosityen_HK
dc.titleInterfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluidsen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0022-0833&volume=62&issue=3&spage=233&epage=245&date=2008&atitle=Interfacial+capillary-gravity+waves+due+to+a+fundamental+singularity+in+a+system+of+two+semi-infinite+fluidsen_HK
dc.identifier.emailNg, CO:cong@hku.hken_HK
dc.identifier.authorityNg, CO=rp00224en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s10665-007-9199-6en_HK
dc.identifier.scopuseid_2-s2.0-44449134306en_HK
dc.identifier.hkuros152414en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-44449134306&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume62en_HK
dc.identifier.issue3en_HK
dc.identifier.spage233en_HK
dc.identifier.epage245en_HK
dc.identifier.isiWOS:000259570500003-
dc.publisher.placeNetherlandsen_HK
dc.relation.projectNonlinear interaction between surface gravity waves and non-Newtonian fluid mud-
dc.identifier.scopusauthoridLu, DQ=7403079439en_HK
dc.identifier.scopusauthoridNg, CO=7401705594en_HK

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