The characteristics of the internal layers of intense shear are examined in a mixing layer and in a jet, in the range of Reynolds numbers 134<Re λ <275. Conditionally averaged profiles of streamwise velocity conditioned on the identified internal layers present strong velocity jumps, which account for approximately 10% of the characteristic large-scale velocity of the flow. The thickness (δw) of the internal layers from the combined analysis of both the mixing layer and the jet scales with (δw)/λReλ-1/2, which suggests a scaling with the Kolmogorov length scale (η), analogous to recent observations on the turbulent/nonturbulent interface (TNTI). The thickness of the internal shear layers within the mixing layer is found to be between 9η and 11η. The concentration of a passive scalar across the internal layers is also examined, at the Schmidt number Sc=1.4. The scalar concentration does not show any jumps across the internal layers, which is an important difference between the internal layers and the TNTI. This can be explained from the analysis of the internal layers of intense scalar gradient, where the flow topology node/saddle/saddle dominates, associated with strain, whereas the internal layers of intense shear are characterized by a prevalence of focus/stretching. A topological content analogous to that obtained in layers of intense scalar gradient is found in proximity to the TNTI, at the boundary between the viscous superlayer and the turbulent sublayer. These observations evidence that the TNTI and the internal layers of intense scalar gradient are similar in several respects.

To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier proper orthogonal decomposition (Fourier-POD) is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analyzed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wave number m=0, associated to the characteristic Kelvin-Helmholtz vortex rings, in the fractal jet modal structures at the fundamental azimuthal wave number m=4 capture the largest amount of energy. In addition, energy is scattered across a wider range of wave numbers than in the round jet. The radial Fourier-POD profiles, however, are nearly insensitive to the orifice geometry, and collapse to a universal distribution when scaled with a characteristic radial length. A similar collapse was recently observed in POD analysis of turbulent structures in pipe flow. However, unlike in pipe flow, the azimuthal-to-radial aspect ratio of the Fourier-POD structures is not constant and varies greatly with the wave number. The second part of the paper focuses on the relationship between streamwise vorticity and streamwise velocity, to characterize the role of the orifice geometry on the lift-up mechanism recently found to be active in turbulent jets [P. Nogueira, A. Cavalieri, P. Jordan, and V. Jaunet, Large-scale streaky structures in turbulent jets, J. Fluid Mech. 873, 211 (2019)JFLSA70022-112010.1017/jfm.2019.365]. The averaging of the streamwise vorticity conditioned on intense positive fluctuations of streamwise velocity reveals a pair of vorticity structures of opposite sign flanking the conditioning point, inducing a radial flow towards the jet periphery. This pair of structures is observed in both jets, even if the azimuthal extent of this pattern is 30% larger in the jet issuing from the circular orifice. The coupling between streamwise vorticity and velocity motions is also examined using Fourier-POD. The analysis reveals that in the jet with a circular orifice lower wave-number modes, corresponding to structures at larger scales, capture a larger fraction of the vorticity-velocity coupling. This evidences that the orifice geometry directly influences the interaction between velocity and vorticity.

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.