Universality of small-scale motions within the turbulent/non-turbulent interface layer

• Published in: Journal of fluid mechanics Vol. 916
• Main Authors: Zecchetto, Marco, da Silva, Carlos B.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 06.04.2021
• Subjects: Boundary layers; Computational fluid dynamics; Dimensional analysis; Direct numerical simulation; Entrainment; Fluid flow; Fronts; Investigations; JFM Papers; Mixing layers (fluids); Reynolds number; Shear; Shear flow; Statistical methods; Statistics; Tensors; Turbulent boundary layer; Turbulent entrainment; Turbulent jets; Velocity; Velocity gradient; Velocity gradients; Viscosity; Vortices; Vorticity; Wakes; shear layer turbulence; turbulence simulation
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2021.168

The universality of the statistics of small-scale motions within the turbulent/non-turbulent interface (TNTI) layer that exists at the edges of turbulent free shear flows (i.e. mixing layers) and in turbulent boundary layers is analysed using direct numerical simulations of turbulent jets, wakes and in turbulent fronts evolving without mean shear. The Taylor based Reynolds number of the simulations is $Re_{\lambda } \gtrsim 200$ while the resolution is comparable to the Kolmogorov micro-scale ${\rm \Delta} x \approx \eta$. It is shown that, when properly normalised by using the local Kolmogorov velocity and length scales, the statistics of the vorticity, strain and related quantities, such as the invariants of the velocity gradient tensor, are universal, i.e. virtually equal for the same position within the TNTI layer, which implies the universality of the small-scale ‘nibbling’ associated with the turbulent entrainment mechanism. The results show that the small scales of motion near the TNTI layer are statistically very close to homogeneous, except for a distance of about 10 Kolmogorov micro-scales from the outer surface of the TNTI layer. The proposed normalisation allows for a much more clear identification of the viscous superlayer and the turbulent sublayer within the TNTI layer.