On precessing flow in an oblate spheroid of arbitrary eccentricity

doi:10.1017/jfm.2014.58

	On precessing flow in an oblate spheroid of arbitrary eccentricity
	Zhang, Keke 1; Chan, Kit H.2; Liao, Xinhao 3
刊名	JOURNAL OF FLUID MECHANICS
	2014-03-01
卷号	743 页码:358-384
关键词	geophysical and geological flows rotating flows
ISSN号	0022-1120
DOI	10.1017/jfm.2014.58
通讯作者	Zhang, Keke(kzhang@ex.ac.uk)
英文摘要	We 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.
WOS关键词	DYNAMO DRIVEN ; FLUID-FLOW ; RIGID BODY ; LIQUID ; SHELLS ; INSTABILITIES ; CAVITIES ; MOTION ; EARTH ; CORE
WOS研究方向	Mechanics ; Physics
语种	英语
出版者	CAMBRIDGE UNIV PRESS
WOS记录号	WOS:000332844200017
内容类型	期刊论文
源URL	[http://libir.pmo.ac.cn/handle/332002/27795]
专题	中国科学院紫金山天文台
通讯作者	Zhang, Keke
作者单位	1.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
推荐引用方式 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.