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The response of a laminar boundary layer in supersonic flow to small-amplitude progressive waves

Published online by Cambridge University Press:  26 April 2006

P. W. Duck
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
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Abstract

In this paper the effect of a small-amplitude progressive wave on the laminar boundary layer on a semi-infinite flat plate, due to a uniform supersonic free-stream flow is considered. The perturbation to the flow caused by the wave divides into two streamwise zones. In the first, relatively close to the leading edge of the plate, on a transverse scale comparable with the boundary-layer thickness, the perturbation flow is described by a form of the unsteady linearized compressible boundary-layer equations. In the free stream, this component of flow is governed by the wave equation, the solution of which provides the outer velocity conditions for the boundary layer. This boundary-layer system is solved numerically, and also the asymptotic structure in the far downstream limit is studied. This reveals a breakdown and a subsequent second streamwise zone, where the flow disturbance is predominantly inviscid. The two zones are shown to match in a proper asymptotic sense.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 423 - 448
Copyright
© 1990 Cambridge University Press

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