Characteristics of small-scale shear layers in a temporally evolving turbulent planar jet

Hayashi, Miki; Watanabe, Tomoaki; Nagata, Koji

doi:10.1017/jfm.2021.459

Cited by 12 publications

(41 citation statements)

References 68 publications

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“…This enables us to adapt a large time increment at a late time because the instantaneous velocity becomes small with time. Initial velocity perturbations are obtained by the method that generates spatially correlated fluctuations from random numbers (Watanabe, Zhang & Nagata 2019 b ; Hayashi, Watanabe & Nagata 2021; Watanabe & Nagata 2021). The characteristic length scale of is and the initial r.m.s.…”

Section: Direct Numerical Simulations Of Temporally Evolving Stably S...mentioning

confidence: 99%

The decay of stably stratified grid turbulence in a viscosity-affected stratified flow regime

2022

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The decay of stably stratified turbulence generated by a towed rake of vertical plates is investigated by direct numerical simulations (DNS) of temporally evolving grid turbulence in a linearly stratified fluid. The Reynolds number $Re_M=U_0M/\nu$ is 5000 or 10 000 while the Froude number $Fr_M=U_0/MN$ is between 0.1 and 6 ( $U_0$ : towing speed; $M$ : mesh size; $\nu$ : kinematic viscosity; $N$ : Brunt–Väisälä frequency). The DNS results are compared with the theory of stably stratified axisymmetric Saffman turbulence. Here, the theory is extended to a viscosity-affected stratified flow regime with low buoyancy Reynolds number $Re_b$ , and power laws are derived for the temporal variations of the horizontal velocity scale ( $U_H$ ) and the horizontal and vertical integral length scales ( $L_H$ and $L_V$ ). Temporal grid turbulence initialized with the mean velocity deficit of wakes exhibits a $k^{2}$ energy spectrum at a low-wavenumber range and invariance of $U_H^2L_H^2L_V$ , which are the signatures of axisymmetric Saffman turbulence. The decay of various quantities follows the power laws predicted for low- $Re_b$ Saffman turbulence when $Fr_M$ is sufficiently small. However, the decay of $U_H^2$ at $Fr_M=6$ is no longer expressed by a power law with a constant exponent. This behaviour is related to the scaling of kinetic energy dissipation rate $\varepsilon$ , for which $\alpha =\varepsilon /(U_H^3/L_H)$ is constant during the decay for $Fr_M\leq 1$ while it varies with time for $Fr_M=6$ . We also examine the experimental data of towed-grid experiments by Praud et al. (J. Fluid Mech., vol. 522, 2005, pp. 1–33), which is shown to agree with the theory of low- $Re_b$ Saffman turbulence.

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Section: Direct Numerical Simulations Of Temporally Evolving Stably S...mentioning

confidence: 99%

The decay of stably stratified grid turbulence in a viscosity-affected stratified flow regime

2022

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“…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).…”

Section: Introductionmentioning

confidence: 99%

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

Watanabe

Nagata

2023

J. Fluid Mech.

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The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$ . Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$ . Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

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“…To distinguish rigid-body rotation from straining motions, various decomposition based on the velocity gradient tensor have been proposed (Kolář 2007; Li, Zhang & He 2014; Gao & Liu 2018; Keylock 2018; Nagata et al. 2020; Watanabe, Tanaka & Nagata 2020; Hayashi, Watanabe & Nagata 2021). Here, we apply to our state-of-the-art experimental datasets the new rortex–shear (RS) decomposition proposed by Liu et al.…”

Section: Introductionmentioning

confidence: 99%

“…In the shear-driven flows of interest in this paper, it is meaningful to define vortical structures after an appropriate treatment of the 'contaminating' shear (Shrestha et al 2021). To distinguish rigid-body rotation from straining motions, various decomposition based on the velocity gradient tensor have been proposed (Kolář 2007;Li, Zhang & He 2014;Keylock 2018;Nagata et al 2020;Watanabe, Tanaka & Nagata 2020;Hayashi, Watanabe & Nagata 2021). Here, we apply to our state-of-the-art experimental datasets the new rortex-shear (RS) decomposition proposed by Liu et al (2018) and Xu et al (2019) to decompose the three-dimensional (3-D) vorticity vector into a rigid-body rotation vector, the 'rortex' vector R, and a shear vector S. In some literature (e.g.…”

Section: Introductionmentioning

confidence: 99%

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

et al. 2022

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We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment (SID). We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the rortex–shear decomposition of the local vorticity vectors into a rortex vector capturing rigid-body rotation and a shear vector. We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. The pair of legs for each hairpin are counter-rotating and entrain fluid laterally and vertically, whereas their arched-up ‘heads’, which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, whereas vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

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Characteristics of small-scale shear layers in a temporally evolving turbulent planar jet

Abstract: Abstract

Cited by 12 publications

References 68 publications

The decay of stably stratified grid turbulence in a viscosity-affected stratified flow regime

The decay of stably stratified grid turbulence in a viscosity-affected stratified flow regime

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

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

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