Hierarchy of coherent structures and real-space energy transfer in turbulent channel flow

Abstract

By analysing a database (Lozano-Durán & Jiménez, Phys. Fluids, vol. 26, 2014, 011702) of fully developed turbulent channel flow at the friction Reynolds number, we investigate the sustaining mechanism of a hierarchy of coherent structures in the turbulence. For this purpose, we decompose the turbulent fields into different scales by band-pass filters and quantify the real-space energy transfer. Visualizations of the hierarchy of vortices and velocity in the filtered fields show that the largest-scale structures at each distance from the wall are composed of quasi-streamwise vortices and low-speed streaks. These are similar to well known coherent structures in the buffer layer and they are maintained by a hierarchical self-sustaining process. Quantitatively, however, the energy production rate of the largest-scale structures is different in the log and buffer layers. This difference explains the change of the scaling of the Reynolds stress as a function of the Reynolds number. In contrast to the largest-scale structures, vortices smaller than the distance from the wall distribute isotropically, and they are generated by an energy cascading process. The energy of these small-scale structures is transferred predominantly from twice-larger-scale structures and reduced by half-scale ones through the vortex stretching and contraction, respectively. Turbulent advection from the wall hardly contributes to the maintenance of small-scale structures in the log layer.