Non-parallel stability analysis of three-dimensional boundary layers alongan infinite attachment line

Instability of a non-parallel similar-boundary-layer flow to small and wavy disturbances is governed by partial differential equations with respect to the non-dimensional vertical coordinate zeta and the local Reynolds number R-1 based on chordwise velocity of external stream and a boundary-layer th ickness. In the particular case of swept Hiemenz flow, the equations admit a series solution expanded in inverse powers of R-1(2) and then are decompo sed into an infinite sequence of ordinary differential systems with the lea ding one posing an eigenvalue problem to determine the first approximation to the complex dispersion relation. Numerical estimation of the series solu tion indicates a much lower critical Reynolds number of the so-called obliq ue-wave instability than the classical value R-c = 583 of the spanwise-trav eling Tollmien-Schlichting instability. Extension of the formulation to gen eral Falkner-Skan-Cooke boundary layers is proposed in the form of a double power series with respect to 1/R-1(2) and a small parameter epsilon denoti ng the difference of the Falkner-Skan parameter m from the attachment-line value m = 1. (C) 2000 The Japan Society of Fluid Mechanics and Elsevier Sci ence B.V. All rights reserved.