Turbulent Statistics of the Turbulent Boundary Layer over a Cube-Roughened Wall

Abstract

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 px/k=8 and pz/k=2, where px and pz are the streamwise and spanwise spacings of the cubes; the roughness height (k) was k=1.5θin, where θin 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