Wall-attached structures in a turbulent boundary layer over cubical roughness

This study investigates wall-attached structures of streamwise velocity fluctuations (u) that contribute to the logarithmic region of a turbulent boundary layer (TBL) over a staggered array of high cubical roughness elements (k/δ = 0.12), using direct numerical simulation (DNS) data at Re_τ ≈ 700. For comparison, DNS data of a smooth-wall TBL are analyzed. Wall-attached u structures are identified from instantaneous flow fields and classified into y-scaled and δ-scaled structures based on their wall-normal height (l_y). The y-scaled structures are geometrically self-similar, and their turbulence intensity follows a logarithmic variation. Moreover, their 2D spectra show a linear relationship between streamwise and spanwise wavelengths (λ_x and λ_z), reminiscent of self-similarity—distinct from the δ-scaled structure. For λ_z > δ, the smooth wall shows limited spanwise growth, while the rough wall exhibits a linear relationship (λ_x ~ λ_z). The meandering behavior of the identified structures reveals that its magnitude increases over the rough wall, particularly for the δ-scaled structure. Notably, the upper bound of the 2D spectra aligns along λ_x ~ λ_z as meandering strengthens. These results suggest that the enhanced meandering promotes energy distribution toward large λ_z at long λ_x, leading to the emergence of λ_x ~ λ_z ­­behavior in the logarithmic region. Consequently, amplified meandering motions over the rough wall may contribute to the logarithmic variation in the streamwise turbulence intensity.