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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
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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

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