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Article: Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids
Title | Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids | ||||||||||
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Authors | |||||||||||
Keywords | Asymptotic solution Fundamental singularity Interfacial wave Surface tension Viscosity | ||||||||||
Issue Date | 2008 | ||||||||||
Publisher | Springer 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? | ||||||||||
Abstract | The 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 Identifier | http://hdl.handle.net/10722/59069 | ||||||||||
ISSN | 2015 Impact Factor: 0.665 2015 SCImago Journal Rankings: 0.347 | ||||||||||
ISI Accession Number ID |
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. | ||||||||||
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Grants |
DC Field | Value | Language |
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dc.contributor.author | Lu, DQ | en_HK |
dc.contributor.author | Ng, CO | en_HK |
dc.date.accessioned | 2010-05-31T03:42:21Z | - |
dc.date.available | 2010-05-31T03:42:21Z | - |
dc.date.issued | 2008 | en_HK |
dc.identifier.citation | Journal Of Engineering Mathematics, 2008, v. 62 n. 3, p. 233-245 | en_HK |
dc.identifier.issn | 0022-0833 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/59069 | - |
dc.description.abstract | The 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.language | eng | en_HK |
dc.publisher | Springer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0022-0833 | en_HK |
dc.relation.ispartof | Journal of Engineering Mathematics | en_HK |
dc.subject | Asymptotic solution | en_HK |
dc.subject | Fundamental singularity | en_HK |
dc.subject | Interfacial wave | en_HK |
dc.subject | Surface tension | en_HK |
dc.subject | Viscosity | en_HK |
dc.title | Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+fluids | en_HK |
dc.identifier.email | Ng, CO:cong@hku.hk | en_HK |
dc.identifier.authority | Ng, CO=rp00224 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s10665-007-9199-6 | en_HK |
dc.identifier.scopus | eid_2-s2.0-44449134306 | en_HK |
dc.identifier.hkuros | 152414 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-44449134306&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 62 | en_HK |
dc.identifier.issue | 3 | en_HK |
dc.identifier.spage | 233 | en_HK |
dc.identifier.epage | 245 | en_HK |
dc.identifier.isi | WOS:000259570500003 | - |
dc.publisher.place | Netherlands | en_HK |
dc.relation.project | Nonlinear interaction between surface gravity waves and non-Newtonian fluid mud | - |
dc.identifier.scopusauthorid | Lu, DQ=7403079439 | en_HK |
dc.identifier.scopusauthorid | Ng, CO=7401705594 | en_HK |