On alignments and small scale structure in turbulent pipe flow

The data base of an extensive DNS of turbulent flow in a pipe (Eggels et al. J. Fluid Mech. 268 (1994) 175) at Re = 7000, based on the pipe diameter and the centerline velocity or Reτ = 360 based on the friction velocity uτ, has been used to study some of the alignments discovered recently in quasi-isotropic and shear turbulent flows and attracted considerable attention. These are the alignments between the velocity u and vorticity vectors ω, between the vorticity ω and the eigenvectors of the rate of strain tensor sij, and between ω and the vortex stretching vector Wi = ωj sij. Comparison of these alignments strongly indicates that the quasi-two-dimensional (QTD) state of turbulent pipe flow in regions of strong alignment between ω and the intermediate eigenvector λint of the rate of strain tensor sij is qualitatevly different from purely two-dimensional one. This is manifested in stronger alignments between ω and W in these regions as well as in larger enstrophy generation ⟨ωiωjsij⟩ ≡ ⟨ωiWi⟩ and large ⟨W2⟩, which are identically zero for a purely two-dimensional flow. The same is true of regions with concentrated vorticity, most of which are embedded into the regions with strong alignment between ω and λint.