A FINITE REYNOLDS-NUMBER APPROACH FOR THE PREDICTION OF BOUNDARY-LAYER RECEPTIVITY IN LOCALIZED REGIONS

Earlier theoretical work on the boundary-layer receptivity problem utilized the triple-deck framework, and typically produced only the leading-order asymptotic result. The applicability of these predictions was limited to the generation of Tollmien-Schlichting-type (viscosity-conditioned) instabilities and rather high values of an appropriate Reynolds number. Generalizing the concepts behind the asymptotic theory of Goldstein and Ruban, the classical Orr-Sommerfeld theory is utilized to predict the receptivity due to small-amplitude surface nonuniformities. This approach accounts for the finite Reynolds-number effects, and can also be extended easily to problems involving other types of instabilities. It is illustrated here for the case of the Tollmien-Schlichting wave generation in a Blasius boundary layer, due to the interaction of a free-stream acoustic wave with a region of short-scale variation in one of the surface boundary conditions. The type of surface disturbances examined include regions of short-scale variations in wall suction, wall admittance, and wall geometry (roughness). Results from the finite Reynolds-number approach are compared in detail with previous asymptotic predictions, as well as the available experimental data.