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On precessing flow in an oblate spheroid of arbitrary eccentricity
Zhang, Keke1; Chan, Kit H.2; Liao, Xinhao3
2014-03-01
Source PublicationJOURNAL OF FLUID MECHANICS
ISSN0022-1120
Volume743Pages:358-384
Corresponding AuthorZhang, Keke(kzhang@ex.ac.uk)
AbstractWe consider a homogeneous fluid of viscosity nu confined within an oblate spheroidal cavity of arbitrary eccentricity E marked by the equatorial radius d and the polar radius d root 1-E-2 with 0 < E < 1. The spheroidal container rotates rapidly with an angular velocity Omega(0) about its symmetry axis and precesses slowly with an angular velocity Omega(p) about an axis that is fixed in space. It is through both topographical and viscous effects that the spheroidal container and the viscous fluid are coupled together, driving precessing flow against viscous dissipation. The precessionally driven flow is characterized by three dimensionless parameters: the shape parameter E, the Ekman number Ek = nu/(d(2)vertical bar Omega(0)vertical bar) and the Poincare number Po = +/-vertical bar Omega(p)vertical bar/vertical bar Omega(0)vertical bar. We derive a time-dependent asymptotic solution for the weakly precessing flow in the mantle frame of reference satisfying the no-slip boundary condition and valid for a spheroidal cavity of arbitrary eccentricity at Ek << 1. No prior assumptions about the spatial-temporal structure of the precessing flow are made in the asymptotic analysis. We also carry out direct numerical simulation for both the weakly and the strongly precessing flow in the same frame of reference using a finite-element method that is particularly suitable for non-spherical geometry. A satisfactory agreement between the asymptotic solution and direct numerical simulation is achieved for sufficiently small Ekman and Poincare numbers. When the nonlinear effect is weak with vertical bar Po vertical bar << 1, the precessing flow in an oblate spheroid is characterized by an azimuthally travelling wave without having a mean azimuthal flow. Stronger nonlinear effects with increasing vertical bar Po vertical bar produce a large-amplitude, time-independent mean azimuthal flow that is always westward in the mantle frame of reference. Implications of the precessionally driven flow for the westward motion observed in the Earth's fluid core are also discussed.
Keywordgeophysical and geological flows rotating flows
DOI10.1017/jfm.2014.58
WOS KeywordDYNAMO DRIVEN ; FLUID-FLOW ; RIGID BODY ; LIQUID ; SHELLS ; INSTABILITIES ; CAVITIES ; MOTION ; EARTH ; CORE
Indexed BySCI
Language英语
WOS Research AreaMechanics ; Physics
WOS SubjectMechanics ; Physics, Fluids & Plasmas
WOS IDWOS:000332844200017
PublisherCAMBRIDGE UNIV PRESS
Citation statistics
Cited Times:13[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://libir.pmo.ac.cn/handle/332002/27837
Collection中国科学院紫金山天文台
Corresponding AuthorZhang, Keke
Affiliation1.Univ Exeter, Dept Math Sci, Exeter EX4 4QF, Devon, England
2.Univ Hong Kong, Dept Math, Pokfulam, Hong Kong, Peoples R China
3.Chinese Acad Sci, Shanghai Astron Observ, Key Lab Planetary Sci, Shanghai 200030, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Keke,Chan, Kit H.,Liao, Xinhao. On precessing flow in an oblate spheroid of arbitrary eccentricity[J]. JOURNAL OF FLUID MECHANICS,2014,743:358-384.
APA Zhang, Keke,Chan, Kit H.,&Liao, Xinhao.(2014).On precessing flow in an oblate spheroid of arbitrary eccentricity.JOURNAL OF FLUID MECHANICS,743,358-384.
MLA Zhang, Keke,et al."On precessing flow in an oblate spheroid of arbitrary eccentricity".JOURNAL OF FLUID MECHANICS 743(2014):358-384.
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