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Article: On fluid flows in precessing spheres in the mantle frame of reference

TitleOn fluid flows in precessing spheres in the mantle frame of reference
Authors
KeywordsAsymptotic solutions
Dimensionless parameters
Ekman numbers
Fluid flow
Frame of reference
Issue Date2010
PublisherAmerican Institute of Physics. The Journal's web site is located at http://ojps.aip.org/phf
Citation
Physics Of Fluids, 2010, v. 22 n. 11, article no. 116604 How to Cite?
AbstractWe investigate, through both asymptotic and numerical analysis, precessionally driven flows of a homogeneous fluid confined in a spherical container that rotates rapidly with angular velocity Ω and precesses slowly with angular velocity Ω p about an axis that is fixed in space. The precessionally driven flows are primarily characterized by two dimensionless parameters: the Ekman number E providing the measure of relative importance between the viscous force and the Coriolis force, and the Poincaré number Po quantifying the strength of the Poincaré forcing. When E is small but fixed and {pipe}Po{pipe} is sufficiently small, we derive a time-dependent asymptotic solution for the weakly precessing flow that satisfies the nonslip boundary condition in the mantle frame of reference. No prior assumption about the spatial-temporal structure of the precessing flow is made in the asymptotic analysis. A solvability condition is derived to determine the spatial structure of the precessing flow, via a selection from a complete spectrum of spherical inertial modes in the mantle frame. The weakly precessing flow within the bulk of the fluid is characterized by an inertial wave moving retrogradely. Direct numerical simulation of the same problem in the same frame of reference shows a satisfactory agreement between the time-dependent asymptotic solution and the nonlinear numerical simulation for sufficiently small Poincaré numbers. © 2010 American Institute of Physics.
Persistent Identifierhttp://hdl.handle.net/10722/135159
ISSN
2015 Impact Factor: 2.017
2015 SCImago Journal Rankings: 1.036
ISI Accession Number ID
Funding AgencyGrant Number
UK STFC/NERC
Hong Kong RGC700308
NSFC10633030
STCSM08XD14052
CAS
Shanghai Supercomputer Center
Funding Information:

K Z expresses his thanks to Professor F H Busse, Professor P H Roberts, and Professor A Tilgner for helpful discussions about the problem K Z is supported by UK STFC/NERC grants, K H C by Hong Kong RGC grant (Grant No 700308), and X L by NSFC (Grant No 10633030), STCSM (Grant No 08XD14052), and CAS grants The numerical computation is supported by Shanghai Supercomputer Center

References

 

DC FieldValueLanguage
dc.contributor.authorZhang, Ken_HK
dc.contributor.authorChan, KHen_HK
dc.contributor.authorLiao, Xen_HK
dc.date.accessioned2011-07-27T01:29:10Z-
dc.date.available2011-07-27T01:29:10Z-
dc.date.issued2010en_HK
dc.identifier.citationPhysics Of Fluids, 2010, v. 22 n. 11, article no. 116604en_HK
dc.identifier.issn1070-6631en_HK
dc.identifier.urihttp://hdl.handle.net/10722/135159-
dc.description.abstractWe investigate, through both asymptotic and numerical analysis, precessionally driven flows of a homogeneous fluid confined in a spherical container that rotates rapidly with angular velocity Ω and precesses slowly with angular velocity Ω p about an axis that is fixed in space. The precessionally driven flows are primarily characterized by two dimensionless parameters: the Ekman number E providing the measure of relative importance between the viscous force and the Coriolis force, and the Poincaré number Po quantifying the strength of the Poincaré forcing. When E is small but fixed and {pipe}Po{pipe} is sufficiently small, we derive a time-dependent asymptotic solution for the weakly precessing flow that satisfies the nonslip boundary condition in the mantle frame of reference. No prior assumption about the spatial-temporal structure of the precessing flow is made in the asymptotic analysis. A solvability condition is derived to determine the spatial structure of the precessing flow, via a selection from a complete spectrum of spherical inertial modes in the mantle frame. The weakly precessing flow within the bulk of the fluid is characterized by an inertial wave moving retrogradely. Direct numerical simulation of the same problem in the same frame of reference shows a satisfactory agreement between the time-dependent asymptotic solution and the nonlinear numerical simulation for sufficiently small Poincaré numbers. © 2010 American Institute of Physics.en_HK
dc.languageengen_US
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 Licenseen_US
dc.rightsAfter publication: Copyright (year) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in (citation of published article) and may be found at (URL/link for published article abstract). Before publication: The following article has been submitted to/accepted by [Name of Journal]. After it is published, it will be found at (URL/link to the entry page of the journal).en_US
dc.subjectAsymptotic solutions-
dc.subjectDimensionless parameters-
dc.subjectEkman numbers-
dc.subjectFluid flow-
dc.subjectFrame of reference-
dc.titleOn fluid flows in precessing spheres in the mantle frame of referenceen_HK
dc.typeArticleen_HK
dc.identifier.emailChan, KH:mkhchan@hku.hken_HK
dc.identifier.authorityChan, KH=rp00664en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1063/1.3515344en_HK
dc.identifier.scopuseid_2-s2.0-79251578039en_HK
dc.identifier.hkuros188097en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-79251578039&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume22en_HK
dc.identifier.issue11en_HK
dc.identifier.spagearticle no. 116604-
dc.identifier.epagearticle no. 116604-
dc.identifier.isiWOS:000285486600063-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridZhang, K=7404451892en_HK
dc.identifier.scopusauthoridChan, KH=7406033542en_HK
dc.identifier.scopusauthoridLiao, X=7202134147en_HK

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