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Effect of streamwise vortices on Tollmien-Schlichting waves

Published online by Cambridge University Press:  20 April 2006

Ali H. Nayfeh
Ali H. Nayfeh
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Present address: Yarmouk University, Irbid, Jordan.
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Abstract

The method of multiple scales is used to determine a first-order uniform expansion for the effect of counter-rotating steady streamwise vortices in growing boundary layers on oblique Tollmien–Schlichting waves. The results show that such vortices have a strong tendency to amplify oblique Tollmien-Schlichting waves having a spanwise wavelength that is twice the wavelength of the vortices. An analytical expression is derived for the growth rates of these waves. These exponential growth rates increase linearly with increasing amplitudes of the vortices. Numerical results are presented. They suggest that this mechanism may dominate the instability.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 107 , June 1981 , pp. 441 - 453
Copyright
© 1981 Cambridge University Press

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References

Aihara, Y. 1962 Bull. Aero. Res. Inst., Tokyo Univ. 3, 195.
Aihara, Y. 1976 Phys. Fluids 19, 1655.
Antar, B. N. & Collins, F. G. 1975 Phys. Fluids 18, 289.
Benney, D. J. & Lin, C. C. 1960 Phys. Fluids 3, 656.
Bippes, H. 1978 NASA TM-75243.
Bippes, H. & Görtler, H. 1972 Acta Mech. 14, 251.
Bradshaw, P. 1965 J. Fluid Mech. 22, 679.
Crow, S. C. 1966 J. Fluid Mech. 24, 153.
Floryan, J. M. & Saric, W. S. 1979 A.I.A.A. Paper no. 79–1497.
Gregory, N. & walker, W. S. 1956 ARC Rep.M 2779.
Görtler, H. 1941 Z. angew. Math. Mech. 21, 250.
Klebanoff, P. S. & Tidstrom, K. D. 1959 N.A.S.A. TN D 195.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 J. Fluid Mech. 12, 1.
Nayfeh, A. H. 1973 Perturbation Methods. Wiley.
Nayfeh, A. H. 1981 Introduction to Perturbation Techniques. Wiley.
Nayfeh, A. H. & Padhye, A. 1979 A.I.A.A. J. 17, 1084.
Ragab, S. A. & Nayfeh, A. H. 1980 A.I.A.A. Paper no. 80–1377.
Smith, A. M. O. 1955 Quart. Appl. Math. 13, 233.
Tani, I. 1961 Adv. Aero Sci. 3, 143.
Tani, I. 1962 J. Geophys. Res. 67, 3075.
Tani, I. & Aihara, Y. 1969 Z. angew. Math. Phys. 39, 609.
Tani, I. & Sakagami, J. 1962 Proc. Int. Counc. Aero. Sci., Stockholm, Spartan, p. 391.
Wortmann, F. X. 1964 Proc. XI Int. Cong. Appl. Mech., p. 815.
Wortmann, F. X. 1969 J. Fluid Mech. 38, 473.