Measurements of Instantaneous Wall Shear Stresses and Near-wall Structures Using Digital Holographic Microscopy

Flow measurements are conducted near the wall of a square channel at Re$_{h}$=60,000 using Digital Holographic Microscopy. Instantaneous 3D velocity distributions are obtained over a volume of 1.5 x 2.5 x 1.5 mm$^{3}$, corresponding to x$^{+}$=50, y$^{+}$=83, z$^{+}$=50, y being the wall normal direction. The (pixel) displacement resolution is 0.7$\mu $m in the streamwise and spanwise directions and 10$\mu $m in the wall-normal directions. Using PIV guided particle tracking, each reconstructed hologram provides 2000 -- 6000 vectors. The distributions of 2 $\mu $m particles are not uniform, and they tend to cluster in layers at 2$<$y$^{+}<$5, and at 20$<$y$^{+}<$50. Local distributions of wall shear stresses are computed directly from the instantaneous velocity gradients in the viscous sub-layer (0$<$y$^{+}<$5). Preliminary analyses reveal clear correlations between the distribution of local wall-shear stresses and the presence of streamwise flow structures in the buffer layer (5$<$y$^{+}<$50). Current on-going analysis examines the effects of these buffer-layer structures, the local 3-D vorticity distribution and alignment of the strain tensor eigenvectors on the distribution of wall-shear stresses.