Statistics of the turbulent boundary layers over 3D cube-roughened walls

• To simulate turbulent boundary layers over 3D cube-roughened walls and to see turbulence in the inner and outer fluid layers.
• To compare turbulence statistics with those affected by different wall conditions.
• To propose a suitable geometrical parameter for estimation of turbulence statistics in the inner and outer layers.

Direct numerical simulations (DNSs) of turbulent boundary layers (TBLs) over three-dimensional (3D) cube-roughened walls were performed and the turbulent characteristics in the inner and outer layers were statistically analyzed. The spanwise spacing was varied over pz/k = 2, 3, 4, and 6 (pz is the spanwise spacing between cubes and k is the height of the roughness) to examine the effects of the roughness spacing on the TBLs. The form drag (Cp) reached a maximum at pz/k = 3, whereas the skin-friction drag (Cf) reached a minimum at the same extent. The Reynolds stresses in the outer region were shown to increase with increasing pz/k  , and similar behavior was observed in the wall-normal velocity fluctuations at the roughness crest (vw+). The properties of the turbulence in the inner and outer layers were found to be well represented by the roughness density (λp).