Free-stream disturbances, continuous eigenfunctions, boundary-layer instability and transition

Abstract

A rational foundation is provided for the application of the linear stability theory of parallel shear flows to transition prediction. An explicit method is given for carrying out the necessary calculations. The expansions are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbance in the inner boundary layer near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer, in that the amplitudes of the discrete Tollmein-Schlichting waves are an extremely small fraction of the amplitude of the disturbance.