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On flow in weakly precessing cylinders: the general asymptotic solution

Published online by Cambridge University Press:  24 August 2012

Xinhao Liao  and
Keke Zhang
Xinhao Liao
Affiliation:
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
Keke Zhang*
Affiliation:
Department of Mathematical Sciences, University of Exeter, Exeter EX4 4QE, UK
*
†Email address for correspondence: kzhang@ex.ac.uk
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Abstract

We investigate, through both asymptotic and numerical analysis, precessionally driven flow of a homogeneous fluid confined in a fluid-filled circular cylinder that rotates rapidly about its symmetry axis and precesses slowly about a different axis that is fixed in space. After demonstrating that the inviscid approximation is always divergent even far away from resonance, we derive a general asymptotic solution for an asymptotically small Ekman number in the rotating frame of reference describing the weakly precessing flow that satisfies the no-slip boundary condition and that is valid at or near or away from resonance. Numerical analysis of the same problem using the Galerkin method in terms of a Chebyshev polynomial expansion is also carried out, showing satisfactory agreement between the general asymptotic solution and the corresponding numerical solution at or near or away from resonance.

JFM classification

Boundary Layers: Boundary layer structure Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 709 , 25 October 2012 , pp. 610 - 621
Copyright
Copyright © Cambridge University Press 2012

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