“Superstructures” in turbulent boundary layers over rough walls up Re_τ = 3,000

The existence of large-scale structures, also known as "superstructures", in the instantaneous velocity field at high wall-normal distances has been reported by many studies in the literature so far, for both pipe and boundary layer configurations through primarily experimental studies. Computational works observing similar structures mainly rely on channel-flow configurations or boundary layers at relatively low Re_τ, which thus do not allow for direct comparisons to the experimental datasets. In the present study we report evidence of "superstructures" in spatially developing boundary layers of at least 60δ streamwise extent over both regular and irregular rough-walls by performing direct numerical simulations (DNS) up to Re_τ = 3,000. Rough-wall cases are compared to a refence smooth wall case at the same inflow Re_τ. Detailed evolutions of the "superstructures’" lengthscales, as well as the corresponding time-scales are reported as a function of the streamwise and wall-normal distance through autocorrelation functions of the instantaneous velocity field. Results suggest that the structures formed over the rough-wall cases grow faster following the more rapid boundary layer evolution. Furthermore, "superstructures" have found to be clearly flanked by pairs of counter-rotating vortices when reduced order models (ROM) are constructed. Finally, the impact of "superstructures" to the instantaneous wall shear stress is reported, alongside the differences between the smooth and rough wall cases.