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 Re-T=360 based on the friction velocity u(T) 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 w, between the velocity w and the eigenvectors of the rate of strain tensor s(ij), and between w and the vortex stretching vector W-i=w(j) s(ij). Comparison of these alignments strongly indicates that the quasi-two-dimensional (QTD) state of turbulent pipe flow in regions of strong alignment between w and the intermediate eigenvector lambda(int) of the rate of strain tensor s(ij) is qualitatively different from purely two-dimensional one. This is manifested in stronger alignments between w and W in these regions as well as in larger enstrophy generation (w(i)w(j)s(ij))equivalent to (w(i)W(i)) and large (W-2), 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 w and lambda(int).