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Stability of natural convection in a narrow rotating annulus

Published online by Cambridge University Press:  29 March 2006

Seppo A. Korpela  and
Vedat S. Arpaci
Seppo A. Korpela
Affiliation:
Department of Mechanical Engineering, The Ohio State University, Columbus
Vedat S. Arpaci
Affiliation:
Department of Mechanical Engineering, The University of Michigan, Ann Arbor
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Abstract

The stability of the conduction regime of natural convection of a fluid contained in a narrow rotating annulus with a heated inner wall has been investigated according to the linear theory. The results include computations for Prandtl numbers P = 0, 0·72 and 6·7 over a large range of the rotational parameters. For low rotation rates the instability sets in as multicellular convection with the cell axes horizontal in the absence of rotation but tilting monotonically towards the vertical as the rotation rate is in creased. Two other types of instability were found at high rotation rates. For large Froude numbers the unstable thermal stratification leads to a Bénard type of convection with vertically oriented rolls. For large Taylor numbers, through a mainly hydrodynamic mechanism, a nearly vertically oriented cellular structure develops in the flow which is destabilized as a result of rotation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 75 , Issue 2 , 27 May 1976 , pp. 385 - 399
Copyright
© 1976 Cambridge University Press

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References

Babcilon, V. 1964 J. Atmos. Sci. 21, 291.
Batchelor, G. K. 1954 Quart. Appl. Math. 12, 209.
Bibikh, R. V. 1967 Prikl. Math. Mech. 30, 432.
Birikh, R. V., Gershuni, G. Z. & Zhukhovitskii, E. M. 1965 Prikl. Math. Mech. 29, 93.
Bibikh, R. V., Gershuni, G. Z., Zhukhovitskii, E. M. & Rudakov, R. N. 1973 Prikl. Math. Mech. 36, 707.
Brindley, J. 1960 Phil. Trans. A, 253, 1.
Chandrasekhar, S. 1954 J. Bat. Mech. Anal. 3, 181.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Davies, T. V. 1956 Phil. Trans. A, 249, 27.
Davies, T. V. 1939 J. Fluid Mech. 5, 593.
Dolph, C. L. & Lewis, D. G. 1958 Quart. Appl. Math. 16, 97.
Forsythe, G. E. & Moler, C. B. 1967 Computer Solution of Linear Algrebraic Systems. Prentice-Hall.
Fultz, D. 1951 Compendium of Meteorology. Boston: Am. Met. Soc. publ. 1235.
Fultz, D. 1953 Fluid Models in Geophysics. Proc. 1st Symp. Use of Models in Geophys. Fluid Dyn., Baltimore, p. 27.
Gershuni, G. Z. 1953 Zh. Tech. Fiz. 23, 1838.
Gershuni, G. Z. 1955 Zh. Tech. Fiz. 25, 351.
Gershuni, G. Z. & Zhukhovitskii, E. M. 1969 Prikl. Math. Mech. 33, 830.
Gill, A. E. & Davey, A. 1969 J. Fluid Mech. 35, 775.
Gill, A. E. & Kirkham, C. C. 1970 J. Fluid Mech. 42, 125.
Gotoh, K. & Ikeda, N. 1971a J. Phys. Soc. Japan, 30, 259.
Gotoh, K. & Ikeda, N. 1971b J. Phys. Soc. Japan, 30, 864.
Gotoh, K. & Ikeda, N. 1972 J. Phys. Soc. Japan, 31, 1697.
Gotoh, K. & Satoh, M. 1966 J. Phys. Soc. Japan, 21, 542.
Gøuzüm, D. & Arpaci, V. S. 1974 J. Fluid Mech. 64, 439.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Harris, D. L. & Reid, W. H. 1958 Astrophys. J. Suppl. Ser. 3, 429.
Hart, J. 1971 J. Fluid Mech. 47, 547.
Hide, R. 1953 Quart. J. Roy. Met. Soc. 79, 161.
Hide, E. 1958 Phil. Trans. A, 250, 441.
Korpela, S. A. 1974 Int. J. Heat Mass Transfer, 17, 215.
Korpela, S. A., GÖZÜM, D. & Baxi, C. B. 1973 Int. J. Heat Mass Transfer, 16, 1683.
Kuo, H. L. 1954 J. Met. 11, 399.
Kuo, H. L. 1956 J. Met. 13, 82.
Kuo, H. L. 1957 J. Met. 14, 553.
Lorenz, E. N. 1962 J. Atmos. Sci. 19, 39.
Moler, C. B. & Stewart, G. W. 1973 SIAM J. Numer. Anal. 10, 241.
O'Neil, E. J. 1969 Studies Appl. Math. 48, 227.
Orszag, S. A. 1971 J. Fluid Mech. 50, 689.
Roberts, P. H. 1960 J. Math. Anal. Appl. 1, 195.
Rudakov, R. N. 1967a Prikl. Math. Mech. 30, 439.
Rudakov, R. N. 1967b Prikl. Math. Mech. 31, 376.
Vest, C. M. & Arpaci, V. S. 1969 J. Fluid Mech. 36, 1.
Wilkinson, J. H. 1965 The Algebraic Eigenvalue Problem. Oxford University Press.