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On the non-linear stability of plane Couette flow

Published online by Cambridge University Press:  29 March 2006

T. Ellingsen ,
B. Gjevik  and
E. Palm
T. Ellingsen
Affiliation:
Department of Mechanics, University of Oslo
B. Gjevik
Affiliation:
Department of Mechanics, University of Oslo
E. Palm
Affiliation:
Department of Mechanics, University of Oslo
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Abstract

In the present paper the stability of plane Couette flow is studied. The stream function and distribution of vorticity and the Reynolds stresses for the linearized solution are computed. The stability effect of the non-linear terms are also discussed and it is found that for small amplitudes, the non-linear terms are destabilizing. A neutral curve determining the necessary amplitude in order to get instability, is found. The convergence of the expansion in the latter case is, however, somewhat uncertain and the result should therefore only be considered as a first, rough approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 40 , Issue 1 , 14 January 1970 , pp. 97 - 112
Copyright
© 1970 Cambridge University Press

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References

Dikii, L. A. 1964 J. Appl. Math. Mech. 28, 479.
Eckhaus, W. 1965 Studies in Non-linear Stability Theory Berlin: Springer.
Gallagher, A. P. & Mercer, A. McD. 1962 J. Fluid Mech. 13, 91.
Grohne, D. 1954 Z. angew. Math. Mech. 34, 344.
Hopf, L. 1914 Ann. Phys. 44, 1.
Kuwabara, S. 1967 Phys. Fluids Suppl. 115.
Landau, L. 1944 C.R. Acad. Sci. U.R.S.S. 44, 311.
Meksyn, D. & Stuart, J. T. 1951 Proc. Roy. Soc. Lond. A 208, 517.
Pekeris, C. L. & Shkoller, B. 1967 J. Fluid Mech. 29, 31.
Reichardt, H. 1956 Z. angew. Math. Mech. S, 26.
Reynolds, W. C. & Potter, M. C. 1967 J. Fluid Mech. 27, 465.
Riis, E. 1962 Geof. Publ. 23, no. 4.
Southwell, R. V. & Chitty, L. 1930 Phil. Trans. Lond. A 229, 205.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Watson, J. 1960 J. Fluid Mech. 9, 371.