The organized motion of characterized turbulent flow at low Reynolds number in a straight square duct

We study the self-sustaining turbulent flow at minimal frictional Reynolds number in a straight square duct using direct numerical simulation. The flow in the square duct is maintained through a constant pressure gradient in the stream-wise direction. The computational investigation of the flow phenomenon for minimal, marginal and fully turbulent flow is studied using organized motion and dynamics of coherent structures. The central theme of the present work is to demonstrate the organized motion of the flow regimes below the frictional Reynolds number of the fully turbulent flow. The controlled direct numerical simulation study and vortex-detection technique unveil hairpin vortices in fully and minimal turbulent flow in the square duct for the first time. Bursting of streaks is detected with variable interval time average, and the evolution of hairpin vortices is also addressed. Turbulent intensities and energy spectra are reported and compared between the minimal, marginal and fully turbulent flow. The minimal turbulence in a square duct indicates transitional turbulent flow characteristics like lesser occurrence of ejection and sweep, intermittent bursting events, and a steeper variation of energy spectrum as compared to fully turbulent energy spectrum distribution.