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Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics
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10.1063/1.4829450
    + View Affiliations - Hide Affiliations
    Affiliations:
    1 Mathematics Applications Consortium for Science and Industry (MACSI), Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland
    2 Research Center for Compact Chemical Processes, National Institute of Advanced Industrial Science and Technology, 4-2-1 Nigatake, Miyagino-ku, Sendai 983-8551, Japan
    a) Author to whom correspondence should be addressed. Electronic mail: michael.vynnycky@ul.ie. Tel.: +353 61 233735.
    Phys. Fluids 25, 113602 (2013); http://dx.doi.org/10.1063/1.4829450
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View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Geometry of the flow.

Image of FIG. 2.
FIG. 2.

Multi-region asymptotic structure of a steady Rayleigh-Bénard convection cell as → ∞ when no-shear conditions are prescribed on all boundaries.

Image of FIG. 3.
FIG. 3.

Multi-region asymptotic structure of a steady Rayleigh-Bénard convection cell as → ∞ when no-slip conditions are prescribed on the horizontal boundaries (and no-shear conditions on the vertical boundaries).

Image of FIG. 4.
FIG. 4.

1/3 vs. λ for = 107, 108, 109 and comparison with Ref. 11 .

Image of FIG. 5.
FIG. 5.

1/3 vs. for λ = 0.2, 1, and 2.

Image of FIG. 6.
FIG. 6.

(−θ)/ 1/3 vs. for = 107, 108, 109 with λ = 3/2 and no-shear boundary conditions at = 0, 1.

Image of FIG. 7.
FIG. 7.

1/5 vs. λ for = 106, 5 × 106, 107.

Image of FIG. 8.
FIG. 8.

1/5 vs. for = 107, λ = 1.3.

Image of FIG. 9.
FIG. 9.

Proposed solution structure in (λ, )-space for the no-slip case.

Image of FIG. 10.
FIG. 10.

1/5 vs. λ for = 107, 108 and comparison with Ref. 10 .

Image of FIG. 11.
FIG. 11.

χ vs. λ for our asymptotic solution.

Image of FIG. 12.
FIG. 12.

1/5 vs. for λ = 0.2, 1, and 2.

Image of FIG. 13.
FIG. 13.

(−θ)/ 1/5 vs. for = 107 and 108 with λ = 1 and no-slip boundary conditions at = 0, 1.

Image of FIG. 14.
FIG. 14.

Streamfunction, ψ, for the upper solution for = 107 with λ = 1 and no-slip boundary conditions at = 0, 1 (−100 ⩽ ψ ⩽ 0 with Δψ = 10). The flow is anti-clockwise.

Image of FIG. 15.
FIG. 15.

Streamfunction, ψ, for the lower solution for = 107 with λ = 1.6 and no-slip boundary conditions at = 0, 1 (−180 ⩽ ψ ⩽ 0 with Δψ = 30). The flow is anti-clockwise.

Image of FIG. 16.
FIG. 16.

Streamfunction, for the core solution with λ = 1.

Image of FIG. 17.
FIG. 17.

Streamfunction, for the core solution with λ = 1.6.

Image of FIG. 18.
FIG. 18.

−ω1/2 vs. /λ for λ = 0.2, 1, 2.

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2013-11-12
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/11/10.1063/1.4829450
10.1063/1.4829450
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