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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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References

REFERENCES

Busse, F. H. & Simitev, R. 2004 Inertial convection in rotating fluid spheres. J. Fluid Mech. 498, 23–30.CrossRefGoogle Scholar
Davies-Jones, R. P. & Gilman, P. A. 1971 Convection in a rotating annulus uniformly heated from below. J. Fluid Mech. 46, 65–81.CrossRefGoogle Scholar
Herrmann, J. & Busse, F. H. 1993 Asymptotic theory of wall-localized convection in a rotating fluid layer. J. Fluid Mech. 255, 183–194.CrossRefGoogle Scholar
Goldstein, H. F., Knobloch, E., Mercader, I. & Net, M. 1993 Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers. J. Fluid Mech. 248, 583–604.CrossRefGoogle Scholar
Goldstein, H. F., Knobloch, E., Mercader, I. & Net, M. 1994 Convection in a rotating cylinder. Part 2. Linear theory for small Prandtl numbers. J. Fluid Mech. 248, 583–604.CrossRefGoogle Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Kerswell, R. R. & Barenghi, C. F. 1995 On the viscous decay-rates of inertial waves in rotating circular cylinder. J. Fluid Mech. 285, 215–247.CrossRefGoogle Scholar
Kuo, E. Y. & Cross, M. C. 1993 Travelling-wave wall states in rotating Rayleigh-Benard convection. Phys. Rev. E 47, 2245–2248.CrossRefGoogle Scholar
Liao, X., Zhang, K. & Chang, Y. 2005 Convection in rotating annular channels heated from below. Part 1. Linear stability and weakly nonlinear mean flows. Geophys. Astrophys. Fluid Dyn. 99, 445–465.CrossRefGoogle Scholar
Liao, X., Zhang, K. & Chang, Y. 2006 On boundary-layer convection in a rotating fluid layer. J. Fluid Mech. 549, 375–384.CrossRefGoogle Scholar
Liu, Y. & Ecke, R. E. 1999 Nonlinear traveling waves in rotating Rayleigh-Bénard convection: Stability boundaries and phase diffusion. Phys. Rev. E 59, 4091–4105CrossRefGoogle Scholar
Marqués, F. 1990 On boundary conditions for velocity potentials in confined flows: Application to Couette flow. Phys. Fluids A 2, 729–737CrossRefGoogle Scholar
Plaut, E. 2003 Nonlinear dynamics of travelling Rayleigh-Bénard convection: effects of the boundary conditions and of the topology. Phys. Rev. E 67, 046303Google ScholarPubMed
Zhang, K. 1994 On coupling between the Poincaré equation and the heat equation. J. Fluid Mech. 268, 211–229CrossRefGoogle Scholar
Zhang, K., Earnshaw, P., Liao, X. & Busse, F. H. 2001 On inertial waves in a rotating fluid sphere. J. Fluid Mech. 437, 103–119.CrossRefGoogle Scholar
Zhang, K. & Liao, X. 2004 A new asymptotic method for the analysis of convection in a rotating sphere. J. Fluid Mech. 518, 319–346.CrossRefGoogle Scholar
Zhong, F., Ecke, R. E. & Steinberg, V. 1991 Asymmetric modes and the transition to vortex structure in rotating Rayleigh-Benard convection. Phys. Rev. Lett. 67, 2473–2476.CrossRefGoogle ScholarPubMed