Coherent structures in turbulent square duct flow

The current work investigates coherent structures in a direct numerical simulation of turbulent flow in a square duct at a Reynolds number of 3800. The flow is investigated using proper orthogonal decomposition (POD). The higher order POD modes reveal corner structures spanning a wide range of scales, supporting the hypothesis that the secondary motions are composed of a superposition of contributions from instantaneous organized motions of different scales. The lower order POD modes are identified as representing the turbulence coherent structures. The streamwise evolution of the structures is investigated using conditional modes, which resolve structures similar to the large-scale motions found in other wall-bounded turbulent flows. These large-scale structures have a streamwise length O(5−8h), similar to what has been observed experimentally and numerically in circular pipe flow. The evolution is characterized by a wall-normal growth followed by a wall-detachment, after which the transition to a new structure occurs. It appears that there is a transition between a symmetric and anti-symmetric mode, resulting in in-phase and out-of-phase motions at the opposing walls.