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A new inviscid mode of instability in compressible boundary-layer flows

Published online by Cambridge University Press:  23 November 2015

Adam P. Tunney ,
James P. Denier ,
Trent W. Mattner  and
John E. Cater
Adam P. Tunney*
Affiliation:
Department of Engineering Science, University of Auckland, Auckland 1142, New Zealand
James P. Denier
Affiliation:
Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia
Trent W. Mattner
Affiliation:
School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia
John E. Cater
Affiliation:
Department of Engineering Science, University of Auckland, Auckland 1142, New Zealand
*
†Email address for correspondence: a.tunney@auckland.ac.nz
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Abstract

The stability of an almost inviscid compressible fluid flowing over a rigid heated surface is considered. We focus on the boundary layer that arises. The effect of surface heating is known to induce a streamwise acceleration in the boundary layer near the surface. This manifests in a streamwise velocity which exhibits a maximum larger than the free-stream velocity (i.e. the streamwise velocity exhibits an ‘overshoot’ region). We explore the impact of this overshoot on the stability of the boundary layer, demonstrating that the compressible form of the classical Rayleigh equation (which governs the development of short wavelength instabilities) possesses a new unstable mode that is a direct consequence of this overshoot. The structure of this new class of modes in the small wavenumber limit is detailed, providing a valuable confirmation of our numerical results obtained from the full inviscid eigenvalue problem.

JFM classification

Boundary Layers: Boundary layer stability Compressible Flows: Compressible boundary layers Aerodynamics: High-speed flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 301 - 323
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Copyright
© 2015 Cambridge University Press 

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