Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T23:56:49.360Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-localized receptivity of boundary layers

Published online by Cambridge University Press:  26 April 2006

J. D. Crouch
J. D. Crouch
Affiliation:
Naval Research Laboratory, Washington, DC. USA Present address: Boeing Commercial Airplane Group, Seattle, WA 98124-2207, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A perturbation scheme is developed to analyse the disturbance field produced by acoustic forcing over a flat plate with non-localized surface irregularities. Both the amplitude of the forcing and the height of the irregularity are assumed to be small. At first order, two modes are calculated: a Stokes mode resulting from the acoustic forcing, and a wall mode resulting from the surface irregularity. These modes interact at second order to produce a forced travelling wave with the frequency of the acoustic wave and a wavenumber associated with the surface irregularity. Streamwise variations in the mean flow mediate a distiibuted energy transfer between the forced mode and the eigenmode. Sufficiently far downstream, the forced-mode amplitude becomes small and the total disturbance is dominated by the resulting eigenmode. Receptivity amplitudes, expressed in terms of effective branch I values, are O(10) for a broad range of surface wavenumbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 567 - 581
Copyright
© 1992 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

Aizin, L. B. & Polyakov M. F. 1979 Acoustic generation of Tollmien-Schlichting waves over local unevenness of surfaces immersed in streams. Preprint 17. Akad. Nauk USSR, Siberian Div., Inst. Theor. Appl. Mech., Novosibirsk (in Russian).
Bertolotti F. P., Herbert, Th. & Spalart P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441–474.Google Scholar
Corke T. C., Bar Sever, A. & Morkovin, M. V. 1986 Experiments on transition enhancement by distributed roughness. Phys. Fluids 29, 3199–3213.Google Scholar
Fasel, H. & Konzelmann. U. 1990 Non-parallel stability of a flat-plate boundary layer using the complete Navier-Stokes equations. J. Fluid Mech. 221, 311–347.Google Scholar
Gaster M. 1974 On the effects of boundary-layer growth on flow stability. J. Fluid Mech. 66, 465–480.Google Scholar
Goldstein M. E. 1983 The evolution of Tollmien-Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.Google Scholar
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
Goldstein, M. E. & Hultgren L. S. 1987 A note on the generation of Tollmien-Schlichting waves by sudden surface curvature change. J. Fluid Mech. 181, 519–525.Google Scholar
Goldstein, M. E. & Hultgren L. S. 1989 Boundary-layer receptivity to long-wave free-stream disturbances. Ann. Rev. Fluid Mech. 21, 137–166.Google Scholar
Herbert, Th. & Bertolotti F. P. 1987 Stability analysis of nonparallel boundary layers. Bull. Am. Phys. Soc. 32, 2079.Google Scholar
Kerschen E. J. 1989 Boundary layer receptivity. AIAA paper 89–1109.Google Scholar
Leehey, P. & Shapiro P. J. 1980 Leading edge effect in laminar boundary layer excitation by sound. In Laminar-Turbulent Transition, IUTAM Symposium, Stuttgart, Germany, September 1979 (ed. R. Eppler & H. Fasel), pp. 321–331. Springer.
Lessen, M. & Gangwani S. T. 1976 Effect of small amplitude wall waviness upon the stability of the laminar boundary layer. Phys. Fluids 19, 510–513.Google Scholar
Lighthill M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity Proc. R. Soc. Lond. A 224, 1–23.Google Scholar
Mack L. M. 1975 Linear stability theory and the problem of supersonic boundary-layer transition. AIAA J. 13, 278–289.Google Scholar
Reshotko E. 1976 Boundary-layer stability and transition. Ann. Rev. Fluid Mech. 8, 311–349.Google Scholar
Reshotko E. 1984 Disturbances in a laminar boundary layer due to distributed roughness. In Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), pp. 39–46. Elsevier.
Reshotko, E. & Leventhal L. 1981 Preliminary experimental study of disturbances in a laminar boundary layer due to distributed surface roughness. AIAA paper 81–1224.Google Scholar
Rogler, H. L. & Reshotko E. 1975 Disturbances in a boundary layer introduced by a low intensity array of vortices. SIAM J. Appl. Maths 28, 431–462.Google Scholar
Saric, W. S. & Nayfeh A. H. 1975 Non-parallel stability of boundary layer flows. Phys. Fluids 18, 945–950.Google Scholar
Tam C. K. W. 1981 The excitation of Tollmien-Schlichting waves in low subsonic boundary layers by free-stream sound waves. J. Fluid Mech. 109, 483–501.Google Scholar