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Article: Vortex arrays for sinh-Poisson equation of two-dimensional fluids: Equilibria and stability

TitleVortex arrays for sinh-Poisson equation of two-dimensional fluids: Equilibria and stability
Authors
KeywordsPhysics
Issue Date2004
PublisherAmerican Institute of Physics. The Journal's web site is located at http://ojps.aip.org/phf
Citation
Physics Of Fluids, 2004, v. 16 n. 9, p. 3296-3305 How to Cite?
AbstractThe sinh-Poisson equation describes a stream function configuration of a stationary two-dimensional (2D) Euler flow. We study two classes of its exact solutions for doubly periodic domains (or doubly periodic vortex arrays in the plane). Both types contain vortex dipoles of different configurations, an elongated "cat-eye" pattern, and a "diagonal" (symmetric) configuration. We derive two new solutions, one for each class. The first one is a generalization of the Mallier-Maslowe vortices, while the second one consists of two corotating vortices in a square cell. Next, we examine the dynamic stability of such vortex dipoles to initial perturbations, by numerical simulations of the 2D Euler flows on periodic domains. One typical member from each class is chosen for analysis. The diagonally symmetric equilibrium maintains stability for all (even strong) perturbations, whereas the cat-eye pattern relaxes to a more stable dipole of the diagonal type. © 2004 American Institute of Physics.
Persistent Identifierhttp://hdl.handle.net/10722/43069
ISSN
2015 Impact Factor: 2.017
2015 SCImago Journal Rankings: 1.036
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorGurarie, Den_HK
dc.contributor.authorChow, KWen_HK
dc.date.accessioned2007-03-23T04:38:05Z-
dc.date.available2007-03-23T04:38:05Z-
dc.date.issued2004en_HK
dc.identifier.citationPhysics Of Fluids, 2004, v. 16 n. 9, p. 3296-3305en_HK
dc.identifier.issn1070-6631en_HK
dc.identifier.urihttp://hdl.handle.net/10722/43069-
dc.description.abstractThe sinh-Poisson equation describes a stream function configuration of a stationary two-dimensional (2D) Euler flow. We study two classes of its exact solutions for doubly periodic domains (or doubly periodic vortex arrays in the plane). Both types contain vortex dipoles of different configurations, an elongated "cat-eye" pattern, and a "diagonal" (symmetric) configuration. We derive two new solutions, one for each class. The first one is a generalization of the Mallier-Maslowe vortices, while the second one consists of two corotating vortices in a square cell. Next, we examine the dynamic stability of such vortex dipoles to initial perturbations, by numerical simulations of the 2D Euler flows on periodic domains. One typical member from each class is chosen for analysis. The diagonally symmetric equilibrium maintains stability for all (even strong) perturbations, whereas the cat-eye pattern relaxes to a more stable dipole of the diagonal type. © 2004 American Institute of Physics.en_HK
dc.format.extent1172861 bytes-
dc.format.extent26624 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
dc.languageengen_HK
dc.publisherAmerican Institute of Physics. The Journal's web site is located at http://ojps.aip.org/phfen_HK
dc.relation.ispartofPhysics of Fluidsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectPhysicsen_HK
dc.titleVortex arrays for sinh-Poisson equation of two-dimensional fluids: Equilibria and stabilityen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1070-6631&volume=16&issue=9&spage=3296&epage=3305&date=2004&atitle=Vortex+arrays+for+sinh-Poisson+equation+of+two-dimensional+fluids:+Equilibria+and+stabilityen_HK
dc.identifier.emailChow, KW:kwchow@hku.hken_HK
dc.identifier.authorityChow, KW=rp00112en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1063/1.1772331en_HK
dc.identifier.scopuseid_2-s2.0-4544250686en_HK
dc.identifier.hkuros98218-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-4544250686&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume16en_HK
dc.identifier.issue9en_HK
dc.identifier.spage3296en_HK
dc.identifier.epage3305en_HK
dc.identifier.isiWOS:000223273600011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridGurarie, D=6602858506en_HK
dc.identifier.scopusauthoridChow, KW=13605209900en_HK

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