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Bénard convection in a finite box: secondary and imperfect bifurcations

Published online by Cambridge University Press:  19 April 2006

P. Hall  and
I. C. Walton
P. Hall
Affiliation:
Department of Mathematics, Imperial College, London
I. C. Walton
Affiliation:
Department of Mathematics, Imperial College, London
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Abstract

In the solution given by Hall & Walton (1977) for Bénard convection in a two-dimensional box with slightly imperfectly insulated side walls it was shown that there were certain critical values 2Lc of the length 2L of the box at which two modes became unstable simultaneously. In this paper we show that in the neighbourhood of Lc a secondary transition takes place which may be a bifurcation or a smooth transition depending on the boundary conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 2 , 29 January 1979 , pp. 377 - 395
Copyright
© 1979 Cambridge University Press

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References

Daniels, P. G. 1977 The effect of distant sidewalls on finite amplitude Bénard convection. Proc. Roy. Soc. A 358, 173–197.Google Scholar
Drazin, P. G. 1975 On the effects of side walls on Bénard convection. Z. angew. Math. Phys. 27, 239–243.Google Scholar
Hall, P. & Walton, I. C. 1977 The smooth transition to a convective regime in a two-dimensional box. Proc. Roy. Soc. A 358, 199–221.Google Scholar
Keener, J. P. 1976 Secondary bifurcations in non-linear diffusion reaction equations. Stud. Appl. Math. 55, 187–211.Google Scholar
Kelly, R. E. & Pal, D. 1976 Thermal convection induced between non-uniformly heated horizontal surfaces. Proc. 1976 Heat Transfer Fluid Mech. Inst. pp. 1–17. Stanford University Press.