Superstructure impact on instantaneous wall-shear stress

Superstructures have been studied for long over a wide range of Reynolds numbers and over some limited number of rough-wall conditions. However, few is known regarding their impact on the instantaneous wall-shear stress (WSS). Direct measurement of the instantaneous wall-shear stress remains challenging for the experimental community even in the case of smooth-walls, since it requires the deployment of non-intrusive methods that constitute an even greater challenge at high Reynolds number flows. On the other hand, direct numerical simulations that can overcome such limitations are confined in low Reynolds numbers and primarily in channel-flows configurations, where the existence of superstructures is somehow ambiguous. In the present study we utilize two-dimensional time-series signals of the instantaneous wall-shear stress extracted from direct numerical simulations (DNS) performed in boundary layers configurations over highly irregular surfaces up to Re_τ≈3,150. Two-point statistics are employed to investigate the WSS structure, as well as its correlation to the fluctuating velocity field, incarnating the superstructures. Furthermore, pre-multiplied energy spectra of the WSS are computed in both planar directions and are directly associated with the superstructure length-scales estimated via autocorrelation functions performed at various wall-normal locations. Results suggest that superstructures found in the outer-part of the boundary layer have a significant impact on the WSS, which is found to be more amplified in the presence of roughness.