On the generation of Tollmien-Schlichting waves in the boundary layer of a flat plate by the disturbances in the free stream

Abstract

A model is proposed for the problem of ‘receptivity’ of the boundary layer of a flat plate to the free-stream turbulence. The basic idea is that two harmonic components of the turbulent velocity spectrum may generate Tollmien-Schlichting waves in the boundary layer through nonlinear interaction. The numerical calculations based on this model show that Tollmien-Schlichting waves can actually be generated and the amplitudes may have the same order of magnitude as the disturbance amplitude in the free stream, at least for certain ranges of the Reynolds number, wavenumber and frequency.