Opposition-control of the energetic cycle of near wall streaks in wall-bounded turbulence, using numerical approaches, has shown promise for drag reduction. For practical implementation, real-time opposition control is only realizable if there is a degree of coherence between the turbulent velocities passing a sensor and the target point within the flow; for practicality, a sensor (and actuator) should be wall-based to avoid parasitic drag. As such, we here inspect the feasibility of real-time control of the near wall cycle, by considering the coherence between a measurable wall-quantity, being the wall-shear stress fluctuations, and the streamwise and wall-normal velocity fluctuations in a turbulent boundary layer. Synchronized spatial and temporal velocity data from two direct numerical simulations and a fine large eddy simulation at Re_τ≈590 and 2000 are employed. This study shows that the spectral energy of the streamwise velocity fluctuations that is stochastically incoherent with wall signals is independent of Reynolds number in the near wall region (up to the viscous-scaled wall-normal height z⁺≈20). Consequently, the streamwise energy-fraction that is stochastically wall-coherent grows with Reynolds number due to the increasing range of energetic large scales. This thus implies that a wall-based control system has the ability to manipulate a larger portion of the total turbulence energy at off-wall locations, at higher Reynolds numbers, while the efficacy of predicting/targeting the small scales of the near wall cycle remains indifferent with varying Reynolds number. Coherence values of 0.55 and 0.4 were found between the streamwise and wall-normal velocity fluctuations at the near wall peak in the energy spectrogram, respectively, and the streamwise fluctuating friction velocity. These coherence values, which are considerably lower than 1 (maximum possible coherence) suggest that a closed-loop drag reduction scheme targeting near wall cycle streaks alone (based on sensed friction velocity fluctuations) will be of limited success in practice.

This paper examines the recovery of the wall-shear stress of a turbulent boundary layer that has undergone a sudden transition from a rough to a smooth surface. Early work of Antonia & Luxton (J. Fluid Mech., vol. 53, 1972, pp. 737-757) questioned the reliability of standard smooth-wall methods for measuring wall-shear stress in such conditions, and subsequent studies show significant disagreement depending on the approach used to determine the wall-shear stress downstream. Here we address this by utilising a collection of experimental databases at that have access to both 'direct' and 'indirect' measures of the wall-shear stress to understand the recovery to equilibrium conditions of the new surface. Our results reveal that the viscous region recovers almost immediately to an equilibrium state with the new wall conditions; however, the buffer region and beyond takes several boundary layer thicknesses before recovering to equilibrium conditions, which is longer than previously thought. A unique direct numerical simulation database of a wall-bounded flow with a rough-to-smooth wall transition is employed to confirm these findings. In doing so, we present evidence that any estimate of the wall-shear stress from the mean velocity profile in the buffer region or further away from the wall tends to underestimate its magnitude in the near vicinity of the rough-to-smooth transition, and this is likely to be partly responsible for the large scatter of recovery lengths to equilibrium conditions reported in the literature. Our results also reveal that smaller energetic scales in the near-wall region recover to an equilibrium state associated with the new wall conditions within one boundary layer thickness downstream of the transition, while larger energetic scales exhibit an over-energised state for several boundary layer thicknesses downstream of the transition. Based on these observations, an alternative approach to estimating the wall-shear stress from the premultiplied energy spectrum is proposed.