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Asymptotic receptivity analysis and the parabolized stability equation: a combined approach to boundary layer transition

Published online by Cambridge University Press:  14 August 2006

M. R. TURNER  and
P. W. HAMMERTON
M. R. TURNER
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
P. W. HAMMERTON
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
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Abstract

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We consider the interaction of free-stream disturbances with the leading edge of a body and its effect on the transition point. We present a method which combines an asymptotic receptivity approach, and a numerical method which marches through the Orr–Sommerfeld region. The asymptotic receptivity analysis produces a three-deck eigensolution which in its far downstream limiting form produces an upstream boundary condition for our numerical parabolized stability equation (PSE). We discuss the advantages of this method compared to existing numerical and asymptotic analysis and present results which justify this method for the case of a semi-infinite flat plate, where asymptotic results exist in the Orr–Sommerfeld region. We also discuss the limitations of the PSE and comment on the validity of the upstream boundary conditions. Good agreement is found between the present results and the numerical results of Haddad & Corke (1998).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 562 , 10 September 2006 , pp. 355 - 381
Copyright
© 2006 Cambridge University Press