• journal/journal.article
• aip/pof2
• /content/aip/journal/pof2/25/11/10.1063/1.4829450
• pof.aip.org
1887
No data available.
No metrics data to plot.
The attempt to plot a graph for these metrics has failed.
Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics
USD
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)
/content/aip/journal/pof2/25/11/10.1063/1.4829450
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/11/10.1063/1.4829450
View: Figures

## Figures

FIG. 1.

Geometry of the flow.

FIG. 2.

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

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).

FIG. 4.

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

FIG. 5.

1/3 vs. for λ = 0.2, 1, and 2.

FIG. 6.

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

FIG. 7.

1/5 vs. λ for = 106, 5 × 106, 107.

FIG. 8.

1/5 vs. for = 107, λ = 1.3.

FIG. 9.

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

FIG. 10.

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

FIG. 11.

χ vs. λ for our asymptotic solution.

FIG. 12.

1/5 vs. for λ = 0.2, 1, and 2.

FIG. 13.

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

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.

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.

FIG. 16.

Streamfunction, for the core solution with λ = 1.

FIG. 17.

Streamfunction, for the core solution with λ = 1.6.

FIG. 18.

−ω1/2 vs. /λ for λ = 0.2, 1, 2.

/content/aip/journal/pof2/25/11/10.1063/1.4829450
2013-11-12
2014-04-25

Article
content/aip/journal/pof2
Journal
5
3

### Most cited this month

More Less
This is a required field