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Article: Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration
Title | Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration | ||||||||||||||||||||||
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Authors | |||||||||||||||||||||||
Keywords | Asymptotic solutions Asymptotic theories Ekman numbers Fluid motions Geophysical and geological flows | ||||||||||||||||||||||
Issue Date | 2012 | ||||||||||||||||||||||
Publisher | Cambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=FLM | ||||||||||||||||||||||
Citation | Journal of Fluid Mechanics, 2012, v. 692, p. 420-445 How to Cite? | ||||||||||||||||||||||
Abstract | Abstract We consider a homogeneous fluid of viscosity u confined within an oblate spheroidal cavity, x 2/a 2 + y 2/a 2 + z 2/(a 2 (1-E 2))= 1, with eccentricity 0 | ||||||||||||||||||||||
Persistent Identifier | http://hdl.handle.net/10722/156282 | ||||||||||||||||||||||
ISSN | 2015 Impact Factor: 2.514 2015 SCImago Journal Rankings: 1.450 | ||||||||||||||||||||||
ISI Accession Number ID |
Funding Information: K.Z. would like to thank J. M. Aurnou, F. H. Busse, J. L. Margot and J. Noir for helpful discussions. In particular, J. Noir pointed out that the term. Po/(omega) over cap) cos(Omega<INF>0</INF>(omega) over capt)(y) over cap x u in (2.3) is physically required because the rotation vector Omega<INF>0</INF> in planetary latitudinal libration is fixed in the inertial frame. K.Z. is supported by UK NERC, STFC and Leverhulme Trust grants. Part of this work (K.Z.) was carried out at, and supported by, the Institute of Mathematical Sciences, the Chinese University of Hong Kong. K. H. C. is supported by Hong Kong RGC grant/700310 and X. L. is supported by NSFC/10633030 and CAS grants. The parallel computation is supported by Shanghai Supercomputer Center and Swiss National Supercomputing Center. | ||||||||||||||||||||||
References |
DC Field | Value | Language |
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dc.contributor.author | Zhang, K | en_US |
dc.contributor.author | Chan, KH | en_US |
dc.contributor.author | Liao, X | en_US |
dc.date.accessioned | 2012-08-08T08:41:10Z | - |
dc.date.available | 2012-08-08T08:41:10Z | - |
dc.date.issued | 2012 | en_US |
dc.identifier.citation | Journal of Fluid Mechanics, 2012, v. 692, p. 420-445 | en_US |
dc.identifier.issn | 0022-1120 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156282 | - |
dc.description.abstract | Abstract We consider a homogeneous fluid of viscosity u confined within an oblate spheroidal cavity, x 2/a 2 + y 2/a 2 + z 2/(a 2 (1-E 2))= 1, with eccentricity 0 <E < 1. The spheroidal container rotates rapidly with an angular velocity Ω 0, which is fixed in an inertial frame and defines a small Ekman number E= u/(a 2Ω 0), and undergoes weak latitudinal libration with frequency ω |Ω 0| and amplitude Po|Ω 0|, where Po is the Poincaré number quantifying the strength of Poincaré force resulting from latitudinal libration. We investigate, via both asymptotic and numerical analysis, fluid motion in the spheroidal cavity driven by latitudinal libration. When |ω-2/(2-E 2)| < O(E 1/2), an asymptotic solution for E > 1 and Po > 1 in oblate spheroidal coordinates satisfying the no-slip boundary condition is derived for a spheroidal cavity of arbitrary eccentricity without making any prior assumptions about the spatial-temporal structure of the librating flow. In this case, the librationally driven flow is non-axisymmetric with amplitude O(Po), and the role of the viscous boundary layer is primarily passive such that the flow satisfies the no-slip boundary condition. When |ω-2/(2-E 2)| > O(E 1/2), the librationally driven flow is also non-axisymmetric but latitudinal libration resonates with a spheroidal inertial mode that is in the form of an azimuthally travelling wave in the retrograde direction. The amplitude of the flow becomes O(Po/E 1/2) at E > 1 and the role of the viscous boundary layer becomes active in determining the key property of the flow. An asymptotic solution for E > 1 describing the librationally resonant flow is also derived for an oblate spheroidal cavity of arbitrary eccentricity. Three-dimensional direct numerical simulation in an oblate spheroidal cavity is performed to demonstrate that, in both the non-resonant and resonant cases, a satisfactory agreement is achieved between the asymptotic solution and numerical simulation at E > 1. © 2012 Cambridge University Press. | en_US |
dc.language | eng | en_US |
dc.publisher | Cambridge University Press. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=FLM | en_US |
dc.relation.ispartof | Journal of Fluid Mechanics | en_US |
dc.rights | Journal of Fluid Mechanics. Copyright © Cambridge University Press. | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Asymptotic solutions | en_US |
dc.subject | Asymptotic theories | en_US |
dc.subject | Ekman numbers | - |
dc.subject | Fluid motions | - |
dc.subject | Geophysical and geological flows | - |
dc.title | Asymptotic theory of resonant flow in a spheroidal cavity driven by latitudinal libration | en_US |
dc.type | Article | en_US |
dc.identifier.email | Chan, KH: mkhchan@hku.hk | en_US |
dc.identifier.authority | Chan, KH=rp00664 | en_US |
dc.description.nature | published_or_final_version | en_US |
dc.identifier.doi | 10.1017/jfm.2011.521 | en_US |
dc.identifier.scopus | eid_2-s2.0-84857344390 | en_US |
dc.identifier.hkuros | 202756 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-84857344390&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 692 | en_US |
dc.identifier.spage | 420 | en_US |
dc.identifier.epage | 445 | en_US |
dc.identifier.eissn | 1469-7645 | - |
dc.identifier.isi | WOS:000299883400019 | - |
dc.publisher.place | United Kingdom | en_US |
dc.identifier.scopusauthorid | Liao, X=7202134147 | en_US |
dc.identifier.scopusauthorid | Chan, KH=7406033542 | en_US |
dc.identifier.scopusauthorid | Zhang, K=7404451892 | en_US |