Characterizing boundary-layer instability at finite Reynolds numbers

When the Reynolds number is treated as an asymptotically large number in a boundary-layer stability analysis, it is possible to identify Reynolds number scalings at which different terms in the governing equations balance. These balances determine which physical mechanisms are operating under which circumstances and enable a systematic treatment of the various parameter regimes to be carried out. Linear waves can grow by viscous mechanisms if the velocity profile is noninflexional and both viscous and inviscid instabilities are present for inflexional profiles. When disturbances become nonlinear the resulting dynamics depend upon the type of instability and, in particular, on whether the critical layer lies within the viscous wall layer or is separate from it. Therefore, the classification of a wave as viscous or inviscid is important to the theory of transition. However, at finite Reynolds numbers the boundaries separating different types of instability become blurred. Moreover, certain asymptotic theories are known to give poor quantitative agreement with experiment while others remain untested by detailed experimental comparison. This paper is concerned with identifying the domains where the different asymptotic theories are most relevant so as to facilitate their comparison with experiment. Numerical solutions of the Orr-Sommerfeld equation are presented that indicate that in wind-tunnel experiments the instability driving transition is essentially viscous even for adverse pressure gradient boundary layers, and that inviscid instability waves would be difficult to observe. For an inviscid wave near the upper branch there could he a lower frequency viscous wave at the same point in the how with amplitude 50 times larger in a typical practical situation. (C) Elsevier, Paris.