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Convection in a box: on the dependence of preferred wave-number upon the Rayleigh number at finite amplitude

  • Stephen H. Davis (a1)

Abstract

Using Stuart's shape assumption and a condition of maximum heat transport it is found that the preferred number of finite roll cells present in Bénard convection in a three-dimensional rectangular box tends to decrease with increasing supercritical Rayleigh number in contradiction to the behaviour in an infinite layer but in accordance with experimental observation.

This ‘end effect’ might explain the similar observation of wave-number decrease in the Taylor instability between rotating cylinders.

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References

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Coles, D. 1965 J. Fluid. Mech. 21, 3.
Davey, A. 1962 J. Fluid Mech. 14, 3.
Davis, S. H. 1967 J. Fluid Mech. 30, 465.
Koschmieder, E. L. 1966 Beitr. Phys. Atmos. 39, 1.
Krishnamurti, R. 1967 Doctoral dissertation, Institute of Geophysics and Planetary Physics, U.C.L.A., Los Angeles, California.
SCHLÜTER, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 1.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1.
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Convection in a box: on the dependence of preferred wave-number upon the Rayleigh number at finite amplitude

  • Stephen H. Davis (a1)

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