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Asymptotic theory for torsional convection in rotating fluid spheres

Published online by Cambridge University Press:  19 January 2017

Keke Zhang ,
Kameng Lam  and
Dali Kong
Keke Zhang*
Affiliation:
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QE, UK Lunar and Planetary Science Laboratory, Macau University of Science and Technology, Macau
Kameng Lam
Affiliation:
Lunar and Planetary Science Laboratory, Macau University of Science and Technology, Macau
Dali Kong
Affiliation:
College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QE, UK
*
†Email address for correspondence: kzhang@ex.ac.uk
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Abstract

This paper is concerned with the classical, well-studied problem of convective instabilities in rapidly rotating, self-gravitating, internally heated Boussinesq fluid spheres. Sanchez et al. (J. Fluid Mech., vol. 791, 2016, R1) recently found, unexpectedly via careful numerical simulation, that non-magnetic convection in the form of axially symmetric, equatorially antisymmetric torsional oscillation is physically preferred in a special range of small Prandtl number for rapidly rotating fluid spheres with the stress-free boundary condition. We derive an asymptotic solution describing convection-driven torsional oscillation – whose flow velocity and pressure are fully analytical and in closed form – that confirms the result of the numerical analysis and is in quantitative agreement with the numerical solution. We also demonstrate, through the derivation of a different asymptotic solution, that convection-driven torsional oscillation cannot occur in rapidly rotating fluid spheres with the no-slip boundary condition.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection Geophysical and Geological Flows: Geophysical and Geological Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , R2
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Copyright
© 2017 Cambridge University Press 

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