Generation of Tollmien–Schlichting waves by convecting gusts interacting with sound

Abstract

A new mechanism is proposed for the generation of Tollmien–Schlichting (T–S) waves by free-stream turbulence. For definiteness and self-consistency, the mechanism is described mathematically by using a triple-deck formalism. The free-stream turbulence is represented by convecting gusts consisting of the so-called vortical and entropy waves of small amplitude. We show that suitable convecting gusts can interact with sound waves in the free stream to produce a forcing that has the same time and length scales as those of the T–S waves, thereby exciting such waves in the vicinity of the lower branch of the neutral stability curve. The T–S waves so produced have the order of magnitude of ε2R5/16, where ε is the amplitude of the free-stream disturbance and R the global Reynolds number. The scale conversion is achieved without resorting to any non-homogeneity on the wall, and hence the mechanism operates in a flat boundary layer. Furthermore, the T–S waves so generated do not undergo any immediate decay, as they may do in some other receptivity processes. For homogeneous isotropic free-stream turbulence, the spectrum of the T–S waves is obtained. The efficiency of the receptivity mechanism is assessed by parametric studies.