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Linear growth rates for the Rayleigh-Bénard instability in cylindrical geometry

Published online by Cambridge University Press:  20 April 2006

J. N. Shaumeyer ,
R. P. Behringer  and
Ralph Baierlein
J. N. Shaumeyer
Affiliation:
Department of Physics, Wesleyan University, Middletown, Connecticut 06457 U.S.A.
R. P. Behringer
Affiliation:
Department of Physics, Wesleyan University, Middletown, Connecticut 06457 U.S.A.
Ralph Baierlein
Affiliation:
Department of Physics, Wesleyan University, Middletown, Connecticut 06457 U.S.A.
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Abstract

We report theoretical growth rates for the Rayleigh–Bénard instability when the fluid layer is contained by non-slip walls in a cylindrical geometry with diameter D and height L. Our results are for the growth rates of the first two axisymmetric modes as functions of the Prandtl number P and the aspect ratio γ≡D/2L. We have considered the two extreme cases of ideally insulating and ideally conducting side walls, and found that the growth rate is relatively insensitive to the choice of the thermal boundary conditions on the side walls. Our results are useful in understanding recent experimental measurements of the convective time-scale.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 109 , August 1981 , pp. 339 - 348
Copyright
© 1981 Cambridge University Press

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References

Ahlers, G. 1975 In Fluctuations, Instabilities, and Phase Transitions (ed. T. Riste). Plenum.
Ahlers, G., Cross, M. C., Hohenberg, P. C. & Safran, S. 1980 J. Fluid Mech. (to appear).
Behringer, R. P. & Ahlers, G. 1977 Phys. Lett. A 62, 329.
Bergé, P. & Dubois, M. 1974 Phys. Rev. Lett. 32, 1041.
Brown, S. N. & Stewartson, K. 1978 Proc. Roy. Soc. A 360, 455.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Charlson, G. S. & Sani, R. L. 1970 J. Heat Mass Transfer 13, 1479.
Charlson, G. S. & Sani, R. L. 1971 J. Heat Mass Transfer 14, 2157.
Charlson, G. S. & Sani, R. L. 1975 J. Fluid Mech. 71, 210.
Daniels, P. G. 1977 Proc. Roy. Soc. A 358, 173.
Daniels, P. G. 1978 Mathematika 25, 216.
Davey, A. 1962 J. Fluid Mech. 14, 336.
Davis, S. H. 1967 J. Fluid Mech. 30, 465.
Hall, P. & Walton, I. C. 1977 Proc. Roy. Soc. A 358, 199.
Joseph, D. D. 1976 Stability of Fluid Motions. Springer.
Koschmieder, E. L. 1974 Adv. Chem. Phys. 26, 177.
Koschmieder, E. L. & Pallas, S. G. 1974 J. Heat Mass Transfer 17, 991.
Krishnamurti, R. 1970 J. Fluid Mech. 42, 309.
Liang, S. F., Vidal, A. & Acrivos, A. 1969 J. Fluid Mech. 36, 239.
Newell, A. C. & Whitehead, J. A. 1969 J. Fluid Mech. 38, 279.
Rossby, H. T. 1969 J. Fluid Mech. 36, 309.
Schlüter, A., Lortz, D.& Busse, F. 1965 J. Fluid Mech. 23, 129.
Segel, L. A. 1969 J. Fluid Mech. 38, 203.
Stewartson, K. & Weinstein, M. 1979 Phys. Fluids 22, 1421.
Wesfreid, J., Pomeau, Y., Dubois, M., Normand, C. & Bergé, P. 1978 J. Phys. Lett. 39, 725.