The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ei, with the vorticity vector ω, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors |ei⋅ˆω| are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e1, in contrast to the global tendency for ω to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between ω and nonlocal e1 and that the strongly swirling worms are kinematically significant to this process.@en

The interaction between the large and the small scales of turbulence is investigated in a mixing layer, at a Reynolds number based on the Taylor microscale of , via direct numerical simulations. The analysis is performed in physical space, and the local vorticity root-mean-square (r.m.s.) is taken as a measure of the small-scale activity. It is found that positive large-scale velocity fluctuations correspond to large vorticity r.m.s. on the low-speed side of the mixing layer, whereas, they correspond to low vorticity r.m.s. on the high-speed side. The relationship between large and small scales thus depends on position if the vorticity r.m.s. is correlated with the large-scale velocity fluctuations. On the contrary, the correlation coefficient is nearly constant throughout the mixing layer and close to unity if the vorticity r.m.s. is correlated with the large-scale velocity gradients. Therefore, the small-scale activity appears closely related to large-scale gradients, while the correlation between the small-scale activity and the large-scale velocity fluctuations is shown to reflect a property of the large scales. Furthermore, the vorticity from unfiltered (small scales) and from low pass filtered (large scales) velocity fields tend to be aligned when examined within vortical tubes. These results provide evidence for the so-called 'scale invariance' (Meneveau & Katz, Annu. Rev. Fluid Mech., vol. 32, 2000, pp. 1-32), and suggest that some of the large-scale characteristics are not lost at the small scales, at least at the Reynolds number achieved in the present simulation.@en

The interaction between the small and large scales of turbulence is investigated in a mixing layer achieving a Reynolds number based on the Taylor microscale (Reλ) of 250. Positive fluctuations of the large-scale velocity correspond to large vorticity rms on the low-speed side of the mixing layer and to low vorticity rms on the high-speed side, respectively. The relationship between large and small scales thus depends on the position if the vorticity rms is correlated with the large-scale velocity fluctuations. However, when correlating the vorticity rms with the large-scale velocity gradients, the correlation coefficient is nearly constant throughout the mixing layer and close to unity. This observation reveals that large and small scales are characterized by a strong interaction independent of the flow position when the large-scale velocity gradients are considered instead of the large-scale velocity fluctuations usually employed in the existing literature on amplitude modulation. The vorticity from unfiltered (small scales) and from low-pass filtered velocity fields tend to be aligned when examined within vortical tubes, suggesting that part of the large-scale characteristics is not lost at the smallest scales.@en