Three-dimensional measurements of flow structure and turbulence around a pair of cubic roughness elements embedded in the inner part of a turbulent channel

The 3D flow and turbulence around a pair of roughness cubes embedded in the inner part of a turbulent channel flow (\textit{Re}$_{\mathrm{\tau }}=$2500) are measured using microscopic tomographic holography accelerated using GPU-based algorithms. The cube height, $a=$1 mm, is 90 wall units. ${\rm T}$he cubes decrease the near-wall velocity and generate secondary flows as far as 3$a$ upstream. Horseshoe vortices form at the front surface, and propagate asymmetrically around the cubes, generating secondary vortices along the side surfaces. Each cube and its near wake are engulfed by a vortical canopy dominated by wall-normal vorticity along the sides and spanwise vorticity above the cube. Merging of the ``tip vortices'' developing along the cube upper edge, horseshoe and secondary vortices occurs downstream at locations that decrease with the spacing. They form a large streamwise vortex behind each cube, which rotates in the same direction as the inner leg of the horseshoe vortex. With decreasing spacing, the flow accelerates faster between cubes, but also decelerates faster in the near wake. Streamwise velocity fluctuations of 40{\%} of the freestream velocity and negative Reynolds shear stress develop near the front upper corner of the cube. The turbulence remains high around the entire surface and near wake.