Interaction between Tollmien-Schlichting waves and free-stream disturbances in boundary-layer flows

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small freestream disturbance and a small localized variation of the surface geometry has been carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T-S waves generated by the interaction between the freestream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the Tollmien-Schlichting waves.