Self-similarity of turbulent jet flows with internal and external intermittency

Gauding, Michael; Bode, Mathis; Brahami, Y.; Varéa, Emilien; Danaila, Luminita

doi:10.1017/jfm.2021.399

Cited by 16 publications

(22 citation statements)

References 80 publications

(155 reference statements)

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“…Note that this is different from R 0 ∼ u 2 0 , which is the assumption made in Townsend (1949), Tennekes & Lumley (1972) and Gauding et al (2021). We do not use this assumption here (but the results (2.19) and (2.20) of our analysis confirm it in this very particular flow case).…”

Section: Mean Flow Scalingsmentioning

confidence: 76%

“…In spatially developing self-similar turbulent jets and wakes, the turbulence dissipation scaling impacts on the TNTI propagation speed via its relation to the jet/wake width growth (Zhou & Vassilicos 2017;Cafiero & Vassilicos 2020), and the jet/wake width growth rate is obtained from mass, momentum and turbulent kinetic energy balances (Townsend 1976;George 1989;Dairay, Obligado & Vassilicos 2015;Cafiero & Vassilicos 2019). This approach to the estimation of the jet/wake width does not seem to have ever been applied to temporally developing turbulent flows, even though Gauding et al (2021) did apply to temporally developing turbulent planar jets the self-similar theory of Townsend (1949) (see also Tennekes & Lumley 1972), which uses only momentum balance (but no mass and turbulent kinetic energy balances), and a hypothesis on the relation between mean flow and Reynolds shear stress profiles that is now known not to be generally true (e.g. Dairay et al 2015;Cafiero & Vassilicos 2019).…”

Section: Introductionmentioning

confidence: 99%

“…This approach to the estimation of the jet/wake width does not seem to have ever been applied to temporally developing turbulent flows, even though Gauding et al. (2021) did apply to temporally developing turbulent planar jets the self-similar theory of Townsend (1949) (see also Tennekes & Lumley 1972), which uses only momentum balance (but no mass and turbulent kinetic energy balances), and a hypothesis on the relation between mean flow and Reynolds shear stress profiles that is now known not to be generally true (e.g. Dairay et al.…”

Section: Introductionmentioning

confidence: 99%

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Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

Er,

Laval,

Vassilicos

2023

J. Fluid Mech.

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The temporally developing self-similar turbulent jet is fundamentally different from its spatially developing namesake because the former conserves volume flux and has zero cross-stream mean flow velocity whereas the latter conserves momentum flux and does not have zero cross-stream mean flow velocity. It follows that, irrespective of the turbulent dissipation's power-law scalings, the time-local Reynolds number remains constant, and the jet half-width $\delta$ , the Kolmogorov length $\eta$ and the Taylor length $\lambda$ grow identically as the square root of time during the temporally developing self-similar planar jet's evolution. We predict theoretically and confirm numerically by direct numerical simulations that the mean centreline velocity, the Kolmogorov velocity and the mean propagation speed of the turbulent/non-turbulent interface (TNTI) of this planar jet decay identically as the inverse square root of time. The TNTI has an inner structure over a wide range of closely spatially packed iso-enstrophy surfaces with fractal dimensions that are well defined over a range of scales between $\lambda$ and $\delta$ , and that decrease with decreasing iso-enstrophy towards values close to $2$ at the viscous superlayer. The smallest scale on these isosurfaces is approximately $\eta$ , and the length scales between $\eta$ and $\lambda$ contribute significantly to the surface area of the iso-enstrophy surfaces without being characterised by a well-defined fractal dimension. A simple model is sketched for the mean propagation speeds of the iso-enstrophy surfaces within the TNTI of temporally developing self-similar turbulent planar jets. This model is based on a generalised Corrsin length, on the multiscale geometrical properties of the TNTI, and on a proportionality between the turbulent jet volume's growth rate and the growth rate of $\delta$ . A prediction of this model is that the mean propagation speed at the outer edge of the viscous superlayer is proportional to the Kolmogorov velocity multiplied by the $1/4$ th power of the global Reynolds number.

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Section: Mean Flow Scalingsmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

Er,

Laval,

Vassilicos

2023

J. Fluid Mech.

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“…In future studies, the present inhomogeneous seeding approach could be extended to address higher-order turbulent statistics in self-similar jets. For instance, investigating the Eulerian structure functions of the nozzle seeded flow compared with those of the global jet could help in disentangling the roles of internal and external intermittency in self-similar jets (Gauding et al 2021). From a more Lagrangian perspective, having access to longer trajectories (especially through numerical simulations) would enable one to study separately the temporal dynamics of the nozzle seeded particles (from the nozzle to the core of the jet) and of the entrained particles (from outside to inside the jet).…”

Section: Discussionmentioning

confidence: 99%

Entrainment, diffusion and effective compressibility in a self-similar turbulent jet

et al. 2022

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An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle$ , is found to be essentially indistinguishable from the global mean velocity field of the jet, $\langle \boldsymbol {U} \rangle$ , for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which $\boldsymbol {\nabla }\boldsymbol {\cdot } \langle \boldsymbol {U}_{\boldsymbol {\varphi }} \rangle \neq 0$ even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated with entrained fluid particles. By considering a classical advection–diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity $K_T$ ) and momentum (through the turbulent viscosity $\nu _T$ ) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $\nu _T$ (and hence of the turbulent Prandtl number $\sigma _T = \nu _T/K_T$ ) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets.

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“…2020; Gauding et al. 2021). This deviation from K41 theory is referred to as anomalous (multifractal) scaling and, together with non-Gaussian p.d.f.s of field increments at small scales, is a measure of small-scale intermittency (Kolmogorov 1962).…”

Section: Introductionmentioning

confidence: 99%

Multifield intermittency of dust storm turbulence in the atmospheric surface layer

2023

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Dust storms are typical dispersed two-phase atmospheric turbulence involving electrified charged dust particles. Previous observations have demonstrated that clean-air atmospheric turbulence is strongly intermittent. However, the intermittency of the wind velocity, concentration of dust particles with a diameter smaller than $10\ \mathrm {\mu }{\rm m}$ (PM10) and electric fields, known as multifield intermittency, has not been reported or characterized yet. Here, we quantify the small-scale multifield intermittency of dust storms using datasets obtained from the Qingtu Lake Observation Array and a wavelet-based data analysis technique. The results indicate that the probability density functions of the multifield increments are scale dependent, and the scaling exponents of the multifield structure functions exhibit anomalous scaling, suggesting that the multiple fields in dust storms are also highly intermittent. Specifically, the wind velocity during dust storms appears to be more intermittent as compared with clean-air conditions. Among the multiple fields, the small-scale intermittency is strongest for PM10 dust concentration, moderate for electric fields and weakest for wind velocity. Furthermore, the anomalous scaling of multiple fields is well described by the hierarchical structure theory of turbulence. It is theoretically predicted that the wind velocity displays a one-dimensional filamentary structure, while the PM10 dust concentration and electric fields display two-dimensional sheet-like structures. Finally, after removing the coherent components of the observed time series by the proposed wavelet conditioning statistics, Kolmogorov linear scaling is recovered for the multiple fields, suggesting that small-scale multifield intermittency is caused by the presence of small-scale coherent structures.

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Self-similarity of turbulent jet flows with internal and external intermittency

Abstract: Abstract

Cited by 16 publications

References 80 publications

Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

Length scales and the turbulent/non-turbulent interface of a temporally developing turbulent jet

Entrainment, diffusion and effective compressibility in a self-similar turbulent jet

Multifield intermittency of dust storm turbulence in the atmospheric surface layer

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