Numerical Study of Local Receptivity in the Boundary Layer

The research on local receptivity in the boundary layer is very important for the prediction and control of the laminar-turbulent transition, and especially the study on the formation mechanism of 3D Tollmien-Schlichting (T-S) waves is meaningful in theory. The high-order high-resolution non-uniform compact finite difference schemes were utilized to study the local receptivity under the interaction of free-stream turbulence and 2D localized wall roughness. The numerical results verify the exsistance of the local receptivity under the interaction of free-stream turbulence and 2D localized wall roughness, and the streamwise vorticity forms and gets stronger downstream as the excited 3D T-S wave packets evolve in the streamwise direction. The numerical results also show that the propagation direction of the excited 3D T-S wave packets is influenced by the propagation direction of the free-stream turbulence, and the propagation speed is close to 1/3 of the free-stream velocity; the wave-length conversion mechanism only changes streamwise wave number α, whereas spanwise wave number β keeps unchanged. In addition, the relation between the free-stream amplitude and incident angle, the localized wall roughness height and length, and the local receptivity, is confirmed. The in-depth research on this subject is helpful for further understanding of the laminar-turbulent transition and tubulence formation.