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Direct numerical simulation (DNS) of a turbulent boundary layer with moderate Reynolds number was performed to scrutinize streamwise-coherence of hairpin packet motions. The Reynolds number based on the momentum thickness (θ in) and free-stream velocity (U ∞) was varied in the range Re θ =1410~2540 which was higher than the previous numerical simulations in the turbulent boundary layer. In order to include the groups of hairpin packets existing in the outer layer, large computational domain was used (more than 50δ o , where δ o is the boundary layer thickness at the inlet in the streamwise domain). Characteristics of packet motions were investigated by using instantaneous flow fields, two-point correlation and conditional average flow fields in xy-plane. The present results showed that a train of hairpin packet motions was propagating coherently along the downstream and these structures induced the very large-scale motions in the turbulent boundary layer.

Direct numerical simulation (DNS) of a spatially developing turbulent boundary layer (TBL) with regularly arrayed cubical roughness elements was performed to investigate the effects of three-dimensional (3D) surface elements. The staggered cubes downstream were periodically arranged in the streamwise and spanwise directions with pitches of p x /k=8 and p z /k=2, where p x and p z are the streamwise and spanwise spacings of the cubes; the roughness height (k) was k=1.5θ in , where θ in is the momentum thickness at the inlet. Spatially developing characteristics over the 3D cubical roughness were compared with the data obtained from the DNS over the two-dimensional (2D) rod roughened wall and smooth wall. Introduction of the cubical roughness on the TBL affected the turbulent Reynolds stresses not only in the roughness sublayer but also in the outer layer; and these effects are consistent with those observed over the 2D rough wall.

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