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The stability of a viscous fluid between rotating cylinders with an axial flow

Published online by Cambridge University Press:  28 March 2006

E. R. Krueger  and
R. C. Di Prima
E. R. Krueger
Affiliation:
Army Mathematics Research Centre, University of Wisconsin
Now at the Department of Applied Mathematics, University of Colorado, Boulder, Colorado.
R. C. Di Prima
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York
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Abstract

The stability of viscous flow between rotating cylinders with an axial flow has been investigated theoretically by Goldstein (1937), Chandrasekhar (1960, 1962), and Di Prima (1960); and experimentally by Cornish (1933), Fage (1938), Kaye & Elgar (1957), Donnelly & Fultz (1960) and Snyder (1962a). As was pointed out by Di Prima (1960) there were a number of discrepancies in the early work of the 1930's which were clarified in part by the papers of the 1960's. In turn, there appear to be certain small detailed differences in the more recent papers. In part it is these differences with which the present paper is concerned. In addition, the results of the previous theoretical investigations which are limited to the case in which the cylinders rotate in the same direction, are extended to the case of counter rotation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 19 , Issue 4 , August 1964 , pp. 528 - 538
Copyright
© 1964 Cambridge University Press

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References

Chandrasekhar, S. 1960 Hydrodynamic and Hydromagnetic Stability. Proc. Nat. Acad. Sci., Wash., 46, 141–3.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Chandrashekar, S. 1962 Proc. Roy. Soc. A, 265, 188–97.
Cornish, R. J. 1933 Proc. Roy. Soc. A, 140, 227–40.
Di Prima, R. C. 1960 J. Fluid Mech. 9, 621–31.
Donnelly, R. & Fultz, D. 1960 Proc. Nat. Acad. Sci., Wash., 46, 1150–4.
Fage, A. 1938 Proc. Roy. Soc. A, 165, 501–29.
Goldstein, S. 1937 Proc. Camb. Phil. Soc. 33, 41–61.
Kaye, J. & Elgar, E. C. 1957 Trans. Amer. Soc. Mech. Engrs, 80, 753–65.
Krueger, E. R. & Diprima, R. C. 1963 Mathematics Research Centre Tech. Rep. 430, University of Wisconsin.
Reid, W. & Harris, D. 1958 Astrophys. J. Suppl. 3, 429–52.
Schwarz, K., Springett, B. E. & Donnelly, R. 1963 Private communication.
Snyder, H. 1962a Proc. Roy. Soc. A, 265, 198.
Snyder, H. 1962b Private communication.
Walowit, J., Tsao, S. & Di Prima, R. C. 1964 J. Appl. Mech. (in the Press).