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Asymptotic receptivity and the Parabolized Stability Equation: a combined approach to boundary layer transition

By M R Turner and P W Hammerton

Abstract

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

Publisher: Cambridge University Press
Year: 2006
DOI identifier: 10.1017/S0022112006001108
OAI identifier: oai:epubs.surrey.ac.uk:2887

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