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Asymptotic theory of inertial convection in a rotating cylinder

Published online by Cambridge University Press:  07 March 2007

KEKE ZHANG ,
XINHAO LIAO  and
F. H. BUSSE
KEKE ZHANG
Affiliation:
Department of Mathematical Sciences, University of Exeter, EX4 4QE, UK
XINHAO LIAO
Affiliation:
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
F. H. BUSSE
Affiliation:
Institute of Physics, University of Bayreuth, D-95440 Bayreuth, Germany
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Abstract

Inertial convection in a fluid contained in a rotating cylinder heated uniformly from below is investigated on the basis of the assumption that convection at leading order can be represented by a single or several inertial wave modes which propagate either in the prograde or retrograde direction. Buoyancy forces appear at the next order to drive inertial convection against the effect of viscous damping. Asymptotic expressions for inertial convection for four different combinations of the sidewall boundary condition are derived for a cylinder of arbitrary aspect ratio. New convection patterns in rotating cylinders are revealed by the asymptotic analysis. A fully numerical solution of the same problem is also carried out, demonstrating a quantitative agreement between the asymptotic and numerical analysis.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 449 - 471
Copyright
Copyright © Cambridge University Press 2007

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