Analysis of flow-wall deformation coupling in high Reynolds number compliant wall boundary layers

Interactions of turbulent boundary layers with a compliant surface are investigated experimentally at Re _τ = 3300–8900. Integrating tomographic particle tracking with Mach–Zehnder interferometry enables simultaneous mapping of the compliant wall deformation and the three-dimensional velocity and pressure fields. Our initial study (J. Fluid. Mech. vol. 980, R2) shows that the flow–deformation correlations decrease with increasing Re _τ , despite an order of magnitude increase in deformation amplitude. To elucidate the mechanisms involved, the same velocity, pressure and kinetic energy fields are decomposed to ‘wave-coherent’ and ‘stochastic’ parts using a Hilbert projection method. The phase dependent coherent variables, especially the pressure, are highly correlated with the wave, but decrease with increasing Re _τ . While the coherent energy is 6 %–10 % of the stochastic level, the pressure root mean square is comparable near the wall. The energy flux between the coherent and stochastic parts and the pressure diffusion reverse sign at the critical layer. To explain the Re _τ dependence, the characteristic deformation wavelength (three times the thickness) is compared with the scales of the energy-containing eddies in the boundary layer represented by the k⁻¹ range in the energy spectrum. When the deformation wavelength is matched with the k _x E _uu peak at the present lowest Re _τ , the flow–deformation correlations and coherent pressure become strong, even for submicron deformations. In this case, the flow and wall motion become phase locked, suggesting resonant behaviours. As Re _τ increases, the wall wavelengths and spectral range of attached eddies are no longer matched, resulting in reduced correlations and lower coherent energy and pressure, despite larger deformation.