Insight into the coupling between wall—pressure—velocity (and wall-shear-stress—velocity) is crucial for designing a controller that 1) relies on wall-based sensing and 2) targets specific velocity structures in wall-bounded turbulence. In this context, data in the Reynolds-number range 550 < Reτ < 46k were examined, sourced from DNS and low- and high-Reτ experiments conducted at the Delft University, the University of Melbourne, and the University of Bologna (CICLoPE). Maxima in the statistical-coupling of u-velocity and WSS fluctuations adhere to a Reτ -invariant distance-from-the-wall scaling, with a streamwise/wall-normal ratio of λx/y ≈ 14. While correlations of u- and v-fluctuations with wall-pressure follow a comparable self-similar scaling, achieving accurate off-the- wall velocity estimates require inclusion of the quadratic wall-pressure term. Overall, it is showcased that an experimental implementation of real-time control of wall-bounded turbulence—using wall-pressure sensing—is feasible across a vast range of Reτ .
Assistant Professor in Aerodynamics and Aeroacoustics, Delft University of Technology