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On the stability of the asymptotic suction boundary-layer profile

Published online by Cambridge University Press:  28 March 2006

T. H. Hughes  and
W. H. Reid
T. H. Hughes
Affiliation:
Department of Mathematics, The University of Chicago Present address: Applied Mathematics Division, Argonne National Laboratory.
W. H. Reid
Affiliation:
Department of Mathematics, The University of Chicago
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Abstract

This paper presents a discussion of some aspects of the linear stability problem for the asymptotic suction profile. An exact solution of the inviscid equation is first obtained in terms of the usual hypergeometric function and its analytical continuation. This exact solution provides both a corrected version of an earlier treatment by Freeman and an independent check on the more general method suggested for solving the inviscid equation numerically. Various approximations to the characteristic equation, and hence to the curve of neutral stability, are then considered. In particular, it is found that, in a consistent asymptotic treatment of the related adjoint problem, at least one viscous correction to the singular inviscid solution must be considered. Based on the present results for the adjoint problem, it is suggested that Tollmien's original treatment of the viscous corrections must be slightly modified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 4 , December 1965 , pp. 715 - 735
Copyright
© 1965 Cambridge University Press

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References

Bussmann, K. & Münz, H. 1942 Jb. dtsch. Luftfahrtf, 1, 36.
Chiarulli, P. & Freeman, J. C. 1948 Tech. Rep. no. F-TR-1197-IA, Headquarters Air Materiel Command, Dayton.
Conte, S. D. & Miles, J. W. 1959 J. Soc. Indust. Appl. Math. 7, 361.
Davis, H. T. 1933 Tables of the Higher Mathematical Functions, vol. I. Bloomington, Indiana: Principia Press.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, G. F. 1953 Higher Transcendental Functions, vol. I. New York: McGraw-Hill Book Co.
Holstein, H. 1950 Z. angew. Math. Mech. 30, 25.
Hughes, T. H. & Reid, W. H. 1965 J. Fluid Mech. 23, 737.
Lewin, L. 1958 Dilogarithms and Associated Functions. London: MacDonald.
Lin, C. C. 1945 Quart. Appl. Math. 3, 117, 218, 277.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Michael, D. H. 1964 J. Fluid Mech. 18, 19.
Miles, J. W. 1960 J. Fluid Mech. 8, 593.
Miles, J. W. 1962 J. Fluid Mech. 13, 427.
Pretsch, J. 1942 Jb. dtsch. Luftfahrtf, 1, 1.
Reid, W. H. 1965 In Basic Developments in Fluid Dynamics, vol. 1 (ed. M. Holt). New York: Academic Press.
Schensted, I. V. 1960 Ph.D. Dissertation, University of Michigan.
Stuart, J. T. 1960 J. Fluid Mech. 9, 353.
Stuart, J. T. 1963 In Laminar Boundary Layers (ed. L. Rosenhead). Oxford: Clarendon Press.
Tollmien, W. 1929 Nachr. Ges. Wiss. Gottingen, Math. Phys. Klasse 21. (Also asNACA Tech. Memo. no. 609, 1931).
Watson, J. 1960 J. Fluid Mech. 9, 371.