Wall-pressure-velocity transfer kernel in high Reynolds number turbulent channel flows

Abstract

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.