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On the first-mode instability in subsonic, supersonic or hypersonic boundary layers

Published online by Cambridge University Press:  21 April 2006

F. T. Smith
F. T. Smith
Affiliation:
Mathematics Department, University College, Gower Street, London, WC1E 6BT, UK
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Abstract

The work, addressing subsonic, supersonic and hypersonic boundary-layer instability, is motivated by the need for more understanding of compressible transition at high global Reynolds numbers Re. In the supersonic case, the so-called ‘first modes’ of instability found/suggested by previous Orr-Sommerfeld computations can be identified as triple-deck oblique ones, directed outside the local wave-Mach-cone directions. Less oblique instability modes inside are not of Orr-Sommerfeld form since they are substantially affected by non-parallel flow effects. The maximum linear growth rates are determined for a range of supersonic and subsonic free-stream Mach numbers M∞, and comparisons are made with previous computations, showing fairly good agreement at moderate Mach numbers. A second mound of unstable wavenumbers and frequencies is also evident. In addition, the nonlinear version is set up and emphasized (with attention drawn to a recent paper by the author (1988a) showing the possibility of nonlinear break-up), and certain extremes are examined including those of transonic and hypersonic boundary layers. In the hypersonic limit a new regime is found (for many conditions, including the insulated plate), namely $M_{\infty \sim Re^{\frac{1}{10}}$, in which non-parallel-flow effects enter to control the main disturbances, and it is concluded that the restriction $M_{\infty \ll Re^{\frac{1}{10}}$ applies to the Orr-Sommerfeld approach. This is a very severe restriction in practice.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 127 - 153
Copyright
1989 Cambridge University Press

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