The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation （DNS）. The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence （FST）, with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting （T-S） wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz＇s measurements, Wu＇s theoretical calculations, and the linear stability theory （LST）.
A high-order numerical method for three-dimensional hydrodynamics is p-resented.The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the k-ǫturbulence model in an orthogonal curvilinear coordinate system.In ad-dition,a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level.The proposed method isfirst validated by its application to simulateflow in a 180◦curved laboratoryflume.It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm.Then the method is applied to study three-dimensional hydrodynamics in a natural river,and the simulated results are in accordance with measurements.
The boundary-layer receptivity under the interaction of free-stream turbu- lence （FST） and localized wall roughness is studied by the direct numerical simulation （DNS） and the fast Fourier transform. The results show that the Tollmien-Schlichting （T-S） wave packets superposed by a group of stability, neutral, and instability T-S waves are generated in the boundary layer. The propagation speeds of the T-S wave packets are calculated. The relation among the boundary-layer receptivity response, the amplitude of the FST, the roughness height, and the roughness width is determined. The results agree well with Dietz＇s experiments. The effect of the roughness geometries on the receptivity is also studied.
