Direct numerical simulation of turbulent boundary layer over hemispherical rough walls

Direct numerical simulations (DNSs) were performed to investigate the effects of hemispherical roughness on the properties of the spatially developing turbulent boundary layer (TBL). To resolve the hemispherical roughness element, an immersed boundary method was employed. The hemispheres were staggered in the downstream direction and arranged periodically in the streamwise and spanwise directions with spacing of px/d = 2, 4, 8 and pz/d = 2 (where px and pz are the streamwise and spanwise spacings of the hemispheres, and d is the diameter). The effects of different streamwise spacing on the turbulent statistics and coherent structures were examined. Inspection of the Reynolds stress profiles shows that the outer-layer similarity is not established for current conditions, and it is significantly dependent on the roughness types. The introduction of the roughness affects the coherent structure and the eject- and sweep-events not only in the roughness sublayer but also in the outer layer. With the decrement of the streamwise spacing, the effects become more obvious. By contrast, the Reynolds stress anisotropic tensor in the outer layer is rarely affected by the surface roughness. The influences mainly concentrate in the roughness sublayer, and are significantly related to the streamwise spacing.