Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-21T08:11:10.611Z Has data issue: false hasContentIssue false
  • English
  • Français

Excitation of instability waves in a two-dimensional shear layer by sound

Published online by Cambridge University Press:  19 April 2006

Christopher K. W. Tam
Christopher K. W. Tam
Affiliation:
Department of Mathematics, Florida State University; Tallahassee
Get access Rights & Permissions [Opens in a new window]

Abstract

The excitation of instability waves in a plane compressible shear layer by sound waves is studied. The problem is formulated mathematically as an inhomogeneous boundary-value problem. A general solution for arbitrary incident sound wave is found by first constructing the Green's function of the problem. Numerical values of the coupling constants between incident sound waves and excited instability waves for a range of flow Mach numbers are calculated. The effect of the angle of incidence in the case of a beam of acoustic waves is analysed. It is found that for moderate subsonic Mach numbers a narrow beam aiming at an angle between 50 to 80° to the flow direction is most effective in exciting instability waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 89 , Issue 2 , 28 November 1978 , pp. 357 - 371
Copyright
© 1978 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

Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas. M.I.T. Press.
Chan, Y. Y. 1974a, b Spatial waves in turbulent jets. Phys. Fluids, 17, 46–53, 1667–1670.Google Scholar
Freymuth, P. 1966 On transition in a separated laminar boundary layer. J. Fluid Mech. 25, 683–704.Google Scholar
Kendall, J. M. 1975 Wind tunnel experiments relating to supersonic and hypersonic boundary layer transition. A.I.A.A. J. 13, 290–299.Google Scholar
Mack, L. M. 1975 Linear stability theory and the problem of supersonic boundary layer transition. A.I.A.A. J. 13, 278–289.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Miksad, R. W. 1973 Experiments on nonlinear interactions in the transition of a free shear layer. J. Fluid Mech. 59, 1–21.Google Scholar
Moore, C. J. 1977 The role of shear layer instability waves in jet exhaust noise. J. Fluid Mech. 80, 321–367.Google Scholar
Reshotko, E. 1976 Boundary layer stability and transition. Ann. Rev. Fluid Mech. 8, 311–349.Google Scholar
Sato, H. 1970 An experimental study of nonlinear interaction of velocity fluctuations in the transition region of a two-dimensional wake. J. Fluid Mech. 44, 741–765.Google Scholar
Tam, C. K. W. 1971 Directional acoustic radiation from a supersonic jet generated by shear layer instability. J. Fluid Mech. 46, 757–768.Google Scholar