Direct numerical simulations of the turbulent boundary layers over the rough walls

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Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over two-dimensional (2-D) and rod and three-dimensional (3-D) cube rough walls were performed to investigate the effects of streamwise spacing on the properties of the TBL The 2-D and 3-D roughness were periodically arranged in the downstream direction with pitches of px/k=2, 3, 4, 6, 8 and 10 and for the cube, the spanwise spacing is fixed to pz/k=2 with staggered array, where px and pz are the streamwise and spanwise spacings of the roughness and k is the roughness height. Inspection of the Reynolds stresses showed that except for px/k=2 and 3 over the 2-D rough walls, the effects of the surface roughness extend to the outer layer over the 2-D and 3-D rough walls and the magnitude of the Reynolds shear stress in the outer layer is increased with proportion to px/k. However, such results are contrary to the trends of form drag, roughness junction and roughness length against px/k, which showed the maximum values at px/k=8 and 4 over the 2-D and 3-D rough walls respectively.