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 Rey nolds number scalings at which different terms in the governing equati ons balance. These balances determine which physical mechanisms are op erating under which circumstances and enable a systematic treatment of the various parameter regimes to be carried out. Linear waves can gro w by viscous mechanisms if the velocity profile is noninflexional and both viscous and inviscid instabilities are present for inflexional pr ofiles. When disturbances become nonlinear the resulting dynamics depe nd upon the type of instability and, in particular, on whether the cri tical layer lies within the viscous wall layer or is separate from it. Therefore, the classification of a wave as viscous or inviscid is imp ortant to the theory of transition. However, at finite Reynolds number s the boundaries separating different types of instability become blur red. Moreover, certain asymptotic theories are known to give poor quan titative agreement with experiment while others remain untested by det ailed experimental comparison. This paper is concerned with identifyin g the domains where the different asymptotic theories are most relevan t so as to facilitate their comparison with experiment. Numerical solu tions of the Orr-Sommerfeld equation are presented that indicate that in wind-tunnel experiments the instability driving transition is essen tially 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 larg er in a typical practical situation. (C) Elsevier, Paris.