Experimental investigation of turbulent channel flow over a compliant wall using tomographic PIV and Mach-Zehnder interferometry*

The time-resolved 3D flow field and 2D distribution of wall-normal deformation in turbulent channel flow over a compliant surface are simultaneously measured by a combination of tomographic PIV (TPIV) and Mach-Zehnder Interferometry (MZI). The compliant wall is made of PDMS, and the friction Reynolds number is $2.3\times 10^{3}$. The mean velocity profile in the log layer is consistent with that of a channel flow over a smooth rigid wall. The flow resolution of the TPIV measurement is enhanced using single-pixel ensemble correlations to resolve the buffer layer. Extensive calibrations of the MZI system show a wall-normal resolution of deformation in the order of 10 nm. The power spectral density of the surface deformation indicates a wide range of the time-scales. The streamwise wavenumber-frequency spectrum displays two main features: (i) An inclined band corresponding to deformations advected with the flow at approximately 80{\%} of the freestream speed, i.e. the velocity in the log layer. Their amplitudes are in the submicron range. (ii) Non advected, low frequency (\textless 500 Hz) events that are larger than the field-of-view, and have much higher amplitudes, up to 100 $\mu $m. Ongoing analyses examine the deformation-velocity and deformation-pressure correlations to identify structures that influence the interactions with the compliant wall.