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On fluid motion in librating ellipsoids with moderate equatorial eccentricity

Published online by Cambridge University Press:  15 March 2011

KEKE ZHANG ,
KIT H. CHAN  and
XINHAO LIAO
KEKE ZHANG*
Affiliation:
Department of Mathematical Sciences, University of Exeter, Exeter EX4 4QF, UK
KIT H. CHAN
Affiliation:
Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong
XINHAO LIAO
Affiliation:
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
*
†Email address for correspondence: kzhang@ex.ac.uk
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Abstract

The motion of a homogeneous fluid of viscosity ν confined in a librating ellipsoidal cavity with semi-axes a and moderate equatorial eccentricity is investigated. The ellipsoid rotates with an angular velocity Ω0(1 + δsint), where Ω0 is the mean rate of rotation, is the libration frequency and Ω0δ represents the amplitude of longitudinal libration. When δ ≪2 and E1/2 ≪ 2 ≪ 1, where E is the Ekman number defined as E = ν/(a2Ω0), an explicit analytical solution describing fluid motion in librating ellipsoids is derived for any size of the libration frequency . Three-dimensional numerical simulations of the same problem are also performed, revealing the generation of mean zonal flow in librating ellipsoidal cavities and showing a satisfactory agreement between the asymptotic and numerical analyses.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 673 , 25 April 2011 , pp. 468 - 479
Copyright
Copyright © Cambridge University Press 2011

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References

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