The Role of a Critical Layer in Interactions of a Turbulent Boundary Layer with a Compliant Surface

Simultaneous measurements of the time-resolved 3D flow and spatial distribution of wall deformation in a compliant wall boundary layer are performed by combining tomographic particle tracking with Mach Zehnder Interferometry. The pressure is computed by spatially integrating the material acceleration. The range of Re_t is 3300 to 8900, and that of E/ρU₀² (E - Young’s modulus) is 2.5 to 20.3. The deformations travel at 0.53U₀, independent of Re_τ, and their wavelength is three times the wall thickness. Conditional statistics shows that the dominant 3D flow structure involves a spanwise vortex with a laterally inward flow above a surface bump inducing a sweeping diverging flow above a dimple located downstream. Data obtained from several references shows that trend of deformation amplitude scaled by the compliant wall thickness collapse when plotted vs. pressure fluctuations scaled by the shear speed. The pressure-deformation correlations peak at the ‘critical layer’, where U(y) is equal to the surface wave speed, U_sw. Below this layer, the pressure and vertical velocity fluctuations are advected at U_sw, and at higher elevations, they are advected at U(y). Hence, the flow and surface waves are coupled below the critical layer, even for deformations much smaller than a wall unit.