The generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow

Abstract This paper studies the generation of Tollmien–Schlichting waves by free-stream turbulence in transonic flow over a half-infinite flat plate with roughness element using an asymptotic approach. It is assumed that Reynolds number (denoted Re) large, and uniform so it can be modelled as vorticity waves. Close to plate, Blasius boundary layer forms at thickness $$O(\mathrm{{Re}}^{-{1}/{2}})$$ O ( Re - 1 / 2 ) , deformation also present $$O(\mathrm{{Re}}^{-{1}/{4}})$$ 4 . The report shows there no mechanism which penetrate from into classical layer; therefore, transitional introduced between them order prevent discontinuity vorticity. interaction region vicinity then analysed triple-deck model for flow. A novel expansion used analyse upper deck, enables viscous–inviscid problem derived. In make analytical progress, height small, this, we find explicit formula receptivity coefficient wave far downstream roughness.