Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure-velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of (and for the wall-normal velocity). When extending the analysis to both homogeneous directions in and, the peak coherence is centred at and for and, and and, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of 0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation - e.g. for use in real-time control of wall-bounded turbulence - has merit in terms of its realization at a range of Reynolds numbers.

Since wall-pressure fluctuations would form a practically-robust input to a real-time active controller of wall-bounded turbulence, it is of high practical interest to study the scaling behavior of the wall-pressure-velocity coupling. This work investigates the coupling of the wall-pressure fluctuations with the streamwise and wall-normal velocity fluctuations. Both the gain (or coherence) and phase spectra of the wall-pressure-velocity transfer kernel are assessed using a comprehensive database, available from direct numerical simulations of turbulent channel flow. With data spanning a decade in friction Reynolds number Re_τ ∼ 550-5200, a 1D analysis (in terms of the streamwise wavelength, λ_x) reveals that the streamwise velocity and wall-pressure are most strongly coupled at a self-similar wall-scaling of λ_x/y ≈ 14. For the wall-normal velocity component, the strongest coupling appears at approximately half this ratio (λ_x/y ≈ 8.5). An analysis of the kernel's phase demonstrates that both the coherent fluctuations of streamwise and wall-normal velocity obey a forward-leaning inclination angle of α ≈ 30^◦. When extending the analysis to 2D (as a function of λ_x and λ_z), the peak-coherence for p_w and u still resides close to λ_x/y ≈ 14 and is reasonably symmetric around λ_x/λ_z = 2.3. The 2D coherence for pw and v peaks around λ_x/λ_z = 1.0. Both the 2D coherence for pw and u, and p_w and v, adhere to a wall-scaling with y. Scaling behaviours identified in this work will aid the efficacy of real-time controllers, by for instance the implementation of data-derived FIR filters to only control velocity structures that are captured through wall-pressure measurements.