A New Technique of Tollmien-Schlichting Wave Cancellation in a Sound-Exposed Boundary Layer

Abstract

It is well know that sound can reduce the laminar portion of a boundary layer. Sound reflects from a wing surface and generates unstable waves (Tollmien-Schlichting waves) which undergo linear amplification and non-linear interactions, and eventually lead to turbulence. Acoustic disturbances excite T.-S. waves via scattering by longitudinal inhomogeneities in the boundary layer, such as in the vicinity of the wing leading edge or because of unevenness on the wing surface. Unstable wave generation near the leading edge of a wing was investigated experimentally by Shapiro (1977). The generation over unevenness was investigated experimentally by Aizin & Polyakov (1984) and theoretically by Ruban (1984) and Goldstein (1985). Of course the second mechanism of unstable wave generation may be removed by smoothing the wing surface, but the leading edge inhomogeneity is not removable. The methods of boundary layer flow laminarization proposed here are based upon mutual cancellation of T.-S. waves excited near the leading edge and over artificial unevenness. Such cancellation is achieved by a special choice of unevenness. The paper is devoted to mathematical justification of such methods.