Internal layers in turbulent free-shear flows

Abstract

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 /λ ∼ Re −1/2 λ , which suggests a scaling with the Kolmogorov length scale (η), analogous to recent observations on the turbulent/non-turbulent 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 characterised 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 (VSL) and the turbulent sublayer (TSL). These observations evidence that the TNTI and the internal layers of intense scalar gradient are similar in several respects.

The response of small-scale shear layers to perturbations in turbulence

“…The small-scale shear layers in isotropic turbulence are analysed by detecting the shear layers with the triple decomposition of a velocity gradient tensor, as also reported in previous studies of shear layers in turbulent flows (Eisma et al 2015;Watanabe et al 2020;Fiscaletti et al 2021). The DNS databases are analysed with the procedures briefly described below.…”

“…One of the most famous small-scale structures in turbulence is a vortex tube with rotating motion. The radius of vortices is about four to six times the Kolmogorov scale in various turbulent flows (Jiménez et al 1993;Jiménez & Wray 1998;Kida & Miura 1998;Tanahashi, Iwase & Miyauchi 2001;Kang, Tanahashi & Miyauchi 2007;Mouri, Hori & Kawashima 2007;Ganapathisubramani, Lakshminarasimhan & Clemens 2008;da Silva et al 2011;Jahanbakhshi, Vaghefi & Madnia 2015;Ghira, Elsinga & da Silva 2022). Another small-scale structure observed in turbulence is a vortex sheet.…”

“…The details of the triple decomposition can be found in Kolář (2007), which is briefly explained in § 2.2. The shear-layer identification in turbulent flows has been reported with criteria based on the norm or vorticity of ∇u S (Eisma et al 2015;Watanabe, Tanaka & Nagata 2020;Fiscaletti, Buxton & Attili 2021). Gul, Elsinga & Westerweel (2020) have compared shear layers detected with the triple decomposition and the eigenvalue of A ij in a turbulent pipe flow and have found that the same flow regions with intense shear can be identified with both quantities.…”

“…The shear layers in turbulence are formed in a region of biaxial strain. The shear layers are small-scale structures whose mean length scales are characterised by the Kolmogorov scale in isotropic turbulence and turbulent free shear flows (Watanabe et al 2020;Fiscaletti et al 2021;Hayashi, Watanabe & Nagata 2021a). The enstrophy production and strain self-amplification actively occur in the shear layers because of the interaction between the shear and biaxial strain (Watanabe et al 2020;Hayashi et al 2021a).…”

“…Most fundamental studies on shear instability assume a uniform shear layer, whose thickness is much smaller than the length scale in the other directions. However, visualisation of shear layers in turbulence has suggested that this assumption is not valid as they have a pancake or ribbon shape with a finite aspect ratio (Buxton & Ganapathisubramani 2010;Bhatt & Tsuji 2021;Fiscaletti et al 2021;Hayashi et al 2021a). For this reason, it is not clear how the stability analysis of shear flows with an infinite aspect ratio is related to the evolution of small-scale shear layers in turbulence.…”