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Physics of Fluids / Volume 7 / Issue 1

Phys. Fluids 7, 92 (1995); http://dx.doi.org/10.1063/1.868768 (6 pages)

Convection rolls and their instabilities in the presence of a nearly insulating upper boundary

R. M. Clever and F. H. Busse

Institute of Geophysics and Planetary Physics, University of California at Los Angeles

(Received 21 June 1994; accepted 13 September 1994)

The problem of steady convection rolls and their instabilities in a fluid layer heated from below is studied numerically in the case of a highly conducting, rigid lower and a nearly insulating, stress‐free upper boundary. A Galerkin method is used to obtain two‐dimensional solutions in dependence on the Rayleigh number R and the wave number α for different values of the Prandtl number P. Their stability is analyzed through the superposition of general three‐dimensional infinitesimal disturbances. Most instabilities correspond qualitatively to those found in the case of symmetric highly conducting, rigid boundaries. A new instability, the subharmonic varicose instability, is found, however, which restricts the region of stable rolls toward a higher Rayleigh number in the case of moderate Prandtl numbers. © 1995 American Institute of Physics.

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KEYWORDS and PACS

Keywords

CONVECTIVE INSTABILITIES, HEATING, GALERKIN−PETROV METHOD, RAYLEIGH NUMBER, PRANDTL NUMBER, BOUNDARY CONDITIONS, ASYMMETRY, TEMPERATURE GRADIENTS, BOUSSINESQ EQUATIONS

PACS

  • 47.20.Bp

    Buoyancy-driven instabilities (e.g., Rayleigh-Benard)

  • 47.20.Ky

    Nonlinearity, bifurcation, and symmetry breaking

  • 47.20.Lz

    Secondary instabilities

  • 47.27.T-

    Turbulent transport processes

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.868768

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

For access to fully linked references, you need to log in.
    R. M. Clever and F. H. Busse, “Convection in a fluid layer with asymmetric boundary conditions,” Phys. Fluids A 5, 99 (1993PFADEB000005000001000099000001).

    F. H. Busse and M. Auer, “Undulating rolls and domain instability,” Phys. Rev. Lett. 72, 3178 (1994).

    Q. Ouyang, G. H. Gunaratne, and H. L. Swinney, “Rhombic patterns: Broken hexagonal symmetry,” Chaos 3, 707 (1993CHAOEH000003000004000707000001).

    V. Dufiet and J. Boissonade, “Conventional and unconventional Turing patterns,” J. Chem. Phys. 96, 664 (1992JCPSA6000096000001000664000001).

    G. H. Gunaratne, “Complex spatial patterns on planar continua,” Phys. Rev. Lett. 71, 1367 (1993)
    Comment on “Complex spatial patterns on planar continua” by A. A. Nepomnyashchy and L. M. Pismen, Phys. Rev. Lett. 72, 944 (1994).


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