Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T23:30:06.080Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the generation of Tollmien-Schlichting waves by sudden surface-curvature change

Published online by Cambridge University Press:  21 April 2006

M. E. Goldstein  and
Lennart S. Hultgren
M. E. Goldstein
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135, USA
Lennart S. Hultgren
Affiliation:
National Aeronautics and Space Administration, Lewis Research Center, Cleveland, OH 44135, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This note is primarily concerned with the generation of spatially growing Tollmien-Schlichting waves by the interaction of very long-wavelength free-stream disturbances with a discontinuity in the curvature of a bounding surface (whose slope may or may not be continuous). The theory is combined with a numerical solution of the local Orr-Sommerfeld equation, and the result is used to predict the Tollmien-Schlichting amplitude in a relevant experiment carried out by Leehey & Shapiro (1980). The calculated results are in satisfactory agreement with their observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 519 - 525
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Goldstein, M. E. 1985 Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry. J. Fluid Mech. 154, 509–529.Google Scholar
Leehey, P. & Shapiro, P. J. 1980 Leading edge effect in laminar boundary layer excitation by sound. In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), pp. 321–331. Springer.
Messiter, A. F. 1970 Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18, 241–257.Google Scholar
Saric, W. S. & Nayfeh, A. H. 1977 Nonparallel stability of boundary layers with pressure gradients and suction. In Laminar-Turbulent Transition, AGARD-CP-224, pp. 6:1–21.
Schlichting, H. 1979 Boundary-Layer Theory (7th edn). McGraw-Hill.
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. 1979 Boundary layers for nonlinear stability of disturbances of various sizes. Proc. R. Soc. Lond.A366, 91–109.Google Scholar
Stewartson, K. 1969 On the flow near the trailing edge of a flat plate. II. Mathematika 16, 106–121.Google Scholar
Stewartson, K. 1970 On laminar boundary layers near corners. Q. J. Mech. Appl. Maths 23, 137–152.Google Scholar
Thomas, A. S. W. & Lekoudis, S. G. 1978 Sound and Tollmien-Schlichting waves in a Blasius boundary layer. Phys. Fluids 21, 2112–2113.Google Scholar