SECONDARY INSTABILITY MODES GENERATED BY A TOLLMIEN-SCHLICHTING WAVE SCATTERING FROM A BUMP

The plane finite-amplitude Tollmien-Schlichting wave interaction with a three-dimensional bump on a wall is considered for plane channel flo w. The scattering of this wave leads to the production of unsteady thr ee-dimensional disturbances which transform into growing secondary ins tability modes. The generation of such modes is studied assuming the t hree-dimensional disturbances to be small in comparison with the prima ry plane instability wave. The solution predicts that secondary distur bance amplification takes place only within a narrow wedge downstream of the bump. The qualitative comparison of results with experiments on turbulent wedge origination at an isolated roughness in a boundary la yer is presented.