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Prog. Theor. Phys. Vol. 68 No. 1 (1982) pp. 49-63

[ Full Text PDF : FREE ACCESS (583K) ]

Side Wall Effect on the Pattern Formation of the Rayleigh-Bénard Convection

Hideyuki Kidachi

Osaka Kyoiku University, Osaka 543

(Received September 18, 1981)

Abstract:

The effect of stress-free side walls on the pattern formation of the Rayleigh-Bénard convection is studied for the case in which the mode of the l-roll pattern and the mode of the l + 1-roll pattern bifurcate from the conduction state successively. In this case the mode of the l-roll pattern prevails when the Prandtl number is small and the aspect ratio (ratio of the side length to the height of the fluid layer) is small. The mode interaction is also studied for the case in which rolls of one mode have axes parallel to the x-direction and rolls of the other mode have axes parallel to the y-direction. In this case the mode interaction produces an unstable grid pattern. In this paper a system of equations is derived from the Boussinesq equations by reductive perturbation method to explain this mode interaction.


URL : http://ptp.ipap.jp/link?PTP/68/49/
DOI : 10.1143/PTP.68.49

[ Full Text PDF : FREE ACCESS (583K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 57 (1988) pp. 1650-1661 :
    Electrohydrodynamic Convective Instability in a Horizontal Fluid Layer with Temperature Gradient
    Hyung-Jong Ko and Moon-Uhn Kim
  2. Journal of the Physical Society of Japan 75 (2006) 034401 (5 pages) :
    Folded Solution Branches in Rayleigh–Bénard Convection in the Presence of Avoided Crossings of Neutral Stability Curves
    Yuki Kato and Kaoru Fujimura
  3. Progress of Theoretical Physics Supplement No.161 (2006) pp. 53-67 :
    Nearly Inviscid Faraday Waves in Slightly Rectangular Containers
    María Higuera and Edgar Knobloch

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