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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.
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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

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