Coherent structures and associated sub-grid scale energy transfer in a rough-wall turbulent channel flow

Our earlier study has revealed spectral bumps and enhanced dissipation of turbulent kinetic energy (TKE) by roughness scale eddies in the outer parts of a rough wall channel flows at Re$_{\tau }$=3520-5360. Here, conditional averaging of PIV data, based on high subgrid-scale (SGS) energy flux, shows an inclined large structure with negative spanwise vorticity in streamwise-wall-normal (\textit{xy}) planes, and two pairs of counter-rotating vortices in streamwise-spanwise (\textit{xz}) planes, both near the wall and in the outer-layer. In instantaneous snapshots, this structure consists of periodic bundles of roughness-scale eddies spaced by a roughness wavelength, resulting from lifting and re-orientation of near-wall, quasi-streamwise vortices. Near the wall, the peak of SGS energy flux occur at the intersection of the quasi-streamwise eddies, while in the outer-layer, elevated flux occurs within the large structure owing to interaction among eddies in a bundle. At the conditioning point, the SGS kinetic energy peaks, but the resolved TKE has a minimum. The location of the resolved TKE maximum varies with elevation due to the increasing impact of ejections with distance from the wall.