Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-27T16:38:57.282Z Has data issue: false hasContentIssue false
  • English
  • Français

The development of three-dimensional wave packets in a boundary layer

Published online by Cambridge University Press:  28 March 2006

M. Gaster
M. Gaster
Affiliation:
National Physical Laboratory, Teddington
Get access Rights & Permissions [Opens in a new window]

Abstract

The formation and growth of three-dimensional wave packets in a laminar boundary layer is treated as a linear problem. The asymptotic form of the disturbed region developing from a point source is obtained in terms of parameters describing two-dimensional instabilities of the flow. It is shown that a wave caustic forms and limits the lateral spread of growing disturbances whenever the Reynolds number is √2 times the critical value. The analysis is applied to the boundary layer on a flat plate and shapes of the wave-envelope are calculated for various Reynolds numbers. These show that all growing disturbances are contained within a wedge-shaped region of approximately 10° semi-angle.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 1 , 9 April 1968 , pp. 173 - 184
Copyright
© 1968 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

Benjamin, T. B. 1961 J. Fluid Mech. 10, 401.
Criminale, W. O. & Kovasznay, L. S. G. 1962 J. Fluid Mech. 14, 59.
Gaster, M. 1962 J. Fluid Mech. 14, 222.
Gaster, M. 1965 J. Fluid Mech. 22, 433.
Lighthill, M. J. 1965 J. Inst. Maths. Applics. 1, 1.
Schlichting, H. 1933 Nachr. Ges. Wiss. Göttingen. Maths. Phys. Klasse, 181.
Schlichting, H. 1935 Nachr. Ges. Wiss. Göttingen. Maths. Phys. Klasse, 1, 47.
Schubauer, G. B. & Skramstad, H. K. 1947 NACA Tech. Rept. no. 909.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.