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Wavenumber selection in large-amplitude axisymmetric convection

Phys. Fluids 29, 23 (1986); doi:10.1063/1.865980

Issue Date: January 1986

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Jeffrey C. Buell and Ivan Catton
Department of Mechanical, Aerospace, and Nuclear Engineering, University of California, Los Angeles, California 90024
Unique wavenumbers are calculated for axisymmetric Rayleigh–Bénard convection as a function of the Rayleigh number (R) up to the second critical value for several different Prandtl numbers. The analysis assumes slightly bent rolls (large radius of curvature) and that there exists a horizontal pressure gradient strong enough to force the net mean flow induced by curvature to be zero. The assumptions are satisfied for axisymmetric convection in a large aspect ratio cylinder (however, this may not be the only case). Manneville and Piquemal [Phys. Rev. A 28, 1774 (1983)] found the initial slope of the selected wavenumber with respect to Rayleigh number (using an analytic solution valid for small amplitude solutions) and our calculations agree with theirs. This initial slope is sensitive to the Prandtl number (P), but at moderate to large R the selected wavenumber is approximately independent of P when P>3. For smaller P larger wavenumbers are found, but this does not contradict any available experimental evidence. Physics of Fluids is copyrighted by The American Institute of Physics.
History: Received 17 June 1985; accepted 1 October 1985
Permalink: http://dx.doi.org/10.1063/1.865980
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KEYWORDS and PACS

Keywords
PACS
  • 47.25.Qv
    Fluid dynamics Turbulent flows, convection, and heat transfer Convection and heat transfer
  • 47.20.-k
    Fluid dynamics Hydrodynamic stability
  • 02.60.+y
    Mathematical methods in physics Numerical approximation and analysis
  • YEAR: 1986

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ISSN:
0031-9171 (print)   1089-7666 (online)
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