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Wave interactions in a three-dimensional attachment-line boundary layer

Published online by Cambridge University Press:  26 April 2006

Philip Hall  and
Sharon O. Seddougui
Philip Hall
Affiliation:
Department of Mathematics, Exeter University, North Park Road, Exeter, Devon EX4 4QE, UK
Sharon O. Seddougui
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Centre, Hampton, VA 23665, USA
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Abstract

The three-dimensional boundary layer on a swept wing can support different types of hydrodynamic instability. Here attention is focused on the so-called ‘spanwise instability’ problem which occurs when the attachment-line boundary layer on the leading edge becomes unstable to Tollmien–Schlichting waves. In order to gain insight into the interactions that are important in that problem a simplified basic state is considered. This simplified flow corresponds to the swept attachment-line boundary layer on an infinite flat plate. The basic flow here is an exact solution of the Navier–Stokes equations and its stability to two-dimensional waves propagating along the attachment line can be considered exactly at finite Reynolds number. This has been done in the linear and weakly nonlinear regimes by Hall, Malik & Poll (1984) and Hall & Malik (1986). Here the corresponding problem is studied for oblique waves and their interaction with two-dimensional waves is investigated. In fact oblique modes cannot be described exactly at finite Reynolds number so it is necessary to make a high-Reynolds-number approximation and use triple-deck theory. It is shown that there are two types of oblique wave which, if excited, cause the destabilization of the two-dimensional mode and the breakdown of the disturbed flow at a finite distance from the leading edge. First a low-frequency mode closely related to the viscous stationary crossflow mode discussed by Hall (1986) and MacKerrell (1987) is a possible cause of breakdown. Secondly a class of oblique wave with frequency comparable with that of the two-dimensional mode is another cause of breakdown. It is shown that the relative importance of the modes depends on the distance from the attachment line.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 367 - 390
Copyright
© 1990 Cambridge University Press

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