The excitation of Tollmien-Schlichting waves in low subsonic boundary layers by free-stream sound waves

Abstract

The excitation of Tollmien-Schlichting waves in low subsonic flat-plate boundary layers by sound is investigated theoretically. The problem is formulated mathematically as an inhomogeneous boundary-value problem which is then solved by a Green's-function technique. It is found that the amplitude of the excited Tollmien-Schlichting wave satisfies an inhomogeneous first-order differential equation. The calculated wave amplitude according to this equation exhibits spatial oscillations in the region ahead of the lower branch neutral stable point of the boundary layer. This characteristic feature resembles that observed experimentally by Shapiro (1977). The theoretical value of the coupling constant between incident sound wave and excited Tollmien-Schlichting wave agrees favourably with measured data. Other predictions of the theory also seem to compare well with available experimental measurements.