Unsteady Disturbance Generation and Amplification in the Boundary-layer Flow behind a Medium-sized Roughness Element

In the present work we investigate receptivity and disturbance amplification behind a circular roughness element in a zero-pressure-gradient flat-plate boundary layer with the aim to identify and understand the basic mechanisms at work. The low disturbance background and the high repeatability of the direct numerical simulations allow to evaluate the different contributions of acoustic-roughness receptivity and of local disturbance amplification. A distinct feature of the boundary-layer flow with roughness element are streamwise streaks which develop from the spanwise edges of the roughness. Small-scale three-dimensional disturbances develop and amplify within these streaks both by instability and by receptivity. For the present small amplitude unsteady forcing however, they remain confined to these areas. In contrast to this, the far-field receptivity result is similar to a wave train generated by periodic suction and blowing at the wall.