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Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry

Published online by Cambridge University Press:  20 April 2006

M. E. Goldstein
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, Ohio 44135
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Abstract

By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) we show that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. 0(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien- Schlichting wave. The analysis provides a qualitative explanation of the Leehey & Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin & Polyakov (1979) experiment. It may also explain why small ‘trip wires’ can promote early transition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 154 , May 1985 , pp. 509 - 529
Copyright
© 1985 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. National Bureau of Standards.
Ackerberg, R. C. & Phillips, J. H. 1972 J. Fluid Mech. 51, 137.
Aizin, L. B. & Polyakov, M. F. 1979 Acoustic generation of Tollmien-Schlichting waves over local unevenness of surface immersed in streams (in Russian). Preprint 17, Akad. Nauk USSR, Siberian Div., Inst. Theor. Appl. Mech., Novosibirsk.
Bodonyi, R. J. & Smith, F. T. 1981 Proc. R. Soc. Lond. A 375, 65–92.
Bogdanova, E. V. & Ryzhov, O. S. 1983 Q. J. Mech. Appl. Maths. 36, 271.
Brown, S. N. & Daniels, P. G. 1975 J. Fluid Mech. 67, 743.
Burggraf, O. R. & Smith, F. T. 1985 On the development of large-sized short-scaled disturbances in boundary layers (leading to the Benjamin-Ono, KdV and Burger's equations). To be published in Proc. R. Soc. Lond. A.
Gedney, C. J. 1983 Phys. Fluids 26, 1158.
Goldstein, M. E. 1981 J. Fluid Mech. 104, 217.
Goldstein, M. E. 1983 J. Fluid Mech. 127, 59.
Goldstein, M. E. 1983b Generation of Tollmien-Schlichting waves by free-stream disturbances at low Mach numbers. NASA TM 83026.
Goldstein, M. E. 1984 J. Fluid Mech. 145, 71.
Goldstein, M. E., Sockol, P. M. & Sanz, J. 1983 J. Fluid Mech. 129, 443.
Hall, P. & Smith, F. 1982 Stud. Appl. Maths 66, 000.
Leehey, P. & Shapiro, P. 1979 In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 321–331. Springer.
Lin, C. C. 1946 Q. Appl. Maths 3, 277.
Messiter, A. F. 1970 SIAM J. Appl. Maths 18, 241.
Murdock, J. W. 1980 Proc. R. Soc. Lond. A 372, 517.
Napolitans, Werle, M. & Davis 1979 AIAA J. 17, 000.
Nishioka, M. & Morkovin, M. V. 1985 Boundary-layer receptivity to unsteady pressure gradients: experiments and overview, submitted to J. Fluid Mech.Google Scholar
Ragab & Nayfeh, A. 1980 AIAA Paper 80-0072.
Reid, W. H. 1965 In Basic Developments in Fluid Dynamics, vol. I (ed. M. Holt), pp. 249–307. Academic.
Shapiro, P. J. 1977 The influence of sound upon laminar boundary layer instability. MIT Acoustics and Vibration Lab. Rep. 83458-83560-1.Google Scholar
Smith, F. T. 1973 J. Fluid Mech. 57, 803.
Smith, F. T. 1979 Proc. R. Soc. Lond. A 366, 91.
Smith, F. T., Brighton, P. W. M., Jackson, P. W. & Hunt, J. C. R. 1981 J. Fluid Mech. 113, 123–152.
Smith, F. T. & Daniels, P. G. 1981 J. Fluid Mech. 110, 1–37.
Stewartson, K. 1969 Mathematika 16, 106.
Stewartson, K. 1970 Q. J. Mech. Appl. Maths 23, 137.
Stewartson, K. 1971 Q. J. Mech. Appl. Maths 24, 387.
Sykes, R. I. 1978 Proc. R. Soc. Lond. A 361, 225.
Tam, C. K. W. 1971 J. Fluid Mech. 46, 757.