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On the instability of a three-dimensional attachment-line boundary layer: weakly nonlinear theory and a numerical approach

Published online by Cambridge University Press:  21 April 2006

Philip Hall  and
Mujeeb R. Malik
Philip Hall
Affiliation:
Mathematics Department, University of Exeter, North Park Road, Exeter, England
Mujeeb R. Malik
Affiliation:
High Technology Corporation, Hampton, VA 23666
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Abstract

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier–Stokes equations for the attachment-line flow have been solved using a Fourier–Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 257 - 282
Copyright
© 1986 Cambridge University Press

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