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Interferometric study of two-dimensional Bénard convection cells

Published online by Cambridge University Press:  29 March 2006

R. Farhadieh  and
R. S. Tankin
R. Farhadieh
Affiliation:
Gas Dynamics Laboratory, Northwestern University, Evanston, Illinois 60201
R. S. Tankin
Affiliation:
Gas Dynamics Laboratory, Northwestern University, Evanston, Illinois 60201
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Abstract

A Mach-Zehnder interferometer was used to stud two-dimensional Bénard convection cells. The experiments were performed with distilled water and sea water in the region where density is a linear function of temperature. Two-dimensional convection rolls were formed with Rayleigh numbers as great as 23400. Reversal in the temperature profile was obtained for R/Rc ≥ 3·8, and an overshoot of about 6% was observed at R/Rc = 9·2 and 13·8. This agrees with the values predicted theoretically by Veronis (1966) for stress-free boundaries and Royal (1969) for rigid boundaries. This disagrees with the experimental results of Gille (1967), who reports an overshoot of only 1 ½% at R/Rc = 16. Many of the other results agree with those of other experimenters, such as the relation between the cell height-to-width ratio and Rayleigh number, the relation between the Nusselt number and Rayleigh number, and the value of the critical Rayleigh number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 4 , 11 December 1974 , pp. 739 - 752
Copyright
© 1974 Cambridge University Press

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References

Bénard, H. 1901 Ann. Chim. Phys. 23, 62–144.
Busse, F. H. 1967 J. Math. & Phys. 46, 140–150.
Busse, F. H. & Whitehead, J. A. 1971 J. Fluid Mech. 47, 305–320.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Davies-Jones, R. P. 1971 J. Fluid Mech. 44, 695–704.
Davis, S. 1967 J. Fluid Mech. 30, 465–478.
Gille, J. 1967 J. Fluid Mech. 30, 371–384.
Montgomery, R. B. 1955 American Institute of Physics Handbook, 2nd ed., pp. 2–123.
Pellew, A. & Southwell, R. V. 1940 Proc. Roy. Soc A 176, 312–343.
Rayleigh, Lord 1916 Phil. Mag. 32, 529–546.
Rossby, H. T. 1969 J. Fluid Mech. 36, 309–335.
Royal, J. W. 1969 Dissertation Boston University.
Schmidt, R. J. & Milverton, S. W. 1935 Proc. Roy. Soc A 152, 586–594.
Schneck, P. & Veronis, G. 1967 Phys. Fluids, 10, 927–930.
Segel, L. A. 1969 J. Fluid Mech. 38, 203–224.
Silveston, P. L. 1958 Forsch. Ing. Wes. 24, 29–32, 59–69.
Stork, K. & Müller, U. 1972 J. Fluid Mech. 54, 599–611.
Tilton, L. W. & Taylor, J. K. 1938 J. Res. Nat. Bur. Stand. 20, 419–465.
Veronis, G. 1966 J. Fluid Mech. 26, 49–68.
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 J. Fluid Mech. 54, 351–367.