(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
The mechanisms of the laminar-turbulent transition and the turbulent formation are always one of the important issues in the fields of fluid mechanics, and the boundary-layer receptivity plays a key role in the laminar-turbulent transition. Although there have been plenty of achievements on the boundary-layer receptivity, it is rarely to see the study about the boundary-layer receptivity excited by the interaction of free-stream turbulence and three-dimensional localized wall roughness, which is one of the urgent problems for the prediction of the laminar-turbulent transition in engineering practice. Hence, this problem is studied in this paper by direct numerical simulation. Can the wave packet structures comprised by the two- and three-dimensional T-S waves be discovered in the boundary layer? If so, and how do the group speed and propagation direction of the excited wave packet change? Subsequently, it can prove whether the boundary-layer receptivity exists. Then, the relations between the boundary-layer receptivity and the free-stream turbulence intensity, and the length, width and height of the three-dimensional localized wall roughness are established. Above all, these researches are able to promote the theoretical foundations of the hydrodynamic stability theory and turbulence formation.