Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence

Kurien, Susan; Sreenivasan, Katepalli R.

doi:10.1103/physreve.62.2206

Cited by 122 publications

(165 citation statements)

References 11 publications

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“…The anisotropy is large at low Reynolds number and diminishes to a small value at R λ = 970. This observation tends to confirm recent experimental results which indicate that anisotropy may persist to much higher Reynolds numbers than previously believed [19,20].In summary, our measurements indicate that the Heisenberg-Yaglom scaling of acceleration variance is observed for 500 ≤ R λ ≤ 970. At lower Reynolds number, our measurements are consistent with the anomalous scaling observed in DNS [14,16].…”

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confidence: 92%

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Fluid particle accelerations in fully developed turbulence

Porta

Voth

Crawford

et al. 2001

Nature

553

525

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The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport[1, 2], processes in stirred chemical reactors and combustion systems [3], and in the industrial production of nanoparticles[4]. The perspective of particle trajectories has been used successfully to describe mixing and transport in turbulence[3, 5], but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations [6,7], based on the 1941 scaling theory of Kolmogorov[8, 9] (K41). Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that universal K41 scaling of the acceleration variance is attained at high Reynolds numbers. Our data show strong intermittency-particles are observed with accelerations of up to 1,500 times the acceleration of gravity (40 times the root mean square value). Finally, we find that accelerations manifest the anisotropy of the large scale flow at all Reynolds numbers studied.In principle, fluid particle trajectories are easily measured by seeding a turbulent flow with minute tracer particles and following their motions with an imaging system. In practice this can be a very challenging task since we must fully resolve particle motions which take place on times scales of the order of the Kolmogorov time, τ η = (ν/ǫ) 1/2 where ν is the kinematic viscosity and ǫ is the turbulent energy dissipation. This is exemplified in Fig. 1, which shows a measured three-dimensional, time resolved trajectory of a tracer particle undergoing violent accelerations in our turbulent water flow, for which τ η = 0.3 ms. The particle enters the detection volume on the upper right, is pushed to the left by a burst of acceleration and comes nearly to a stop before being rapidly accelerated (1200 times the acceleration of gravity) upward in a cork-screw motion. This trajectory illustrates the difficulty in following tracer particles-a particle's acceleration can go from zero to 30 times its rms value and back to zero in fractions of a millisecond and within distances of hundreds of micrometers.Conventional detector technologies are effective for low Reynolds number flows[10, 11], but do not provide adequate temporal resolution at high Reynolds numbers. However, the requirements are met by the use of silicon strip detectors as optical imaging elements in a particle tracking system. The strip detectors employed in our experiment (See Fig. 2a) were developed to measure particle tracks in the vertex detector of the CLEO III experiment operating at the Cornell Electron Positron Collider [12]. When applied to particle tracking in turbulence (See Fig. 2b) each detector measures a one-dimensional projection of the image of the tracer particles. Using a data acquisition system designed for the turbulence expe...

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supporting

confidence: 92%

supporting

confidence: 91%

Fluid particle accelerations in fully developed turbulence

Porta

Voth

Crawford

et al. 2001

Nature

553

525

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“…Similar discussions exist about possible effects of the flow configuration on otherwise universal motions at small scales. 3,[10][11][12]22 The additivity and the universality have not been confirmed for the coarse-grained energy of the longitudinal velocity u 2 R . Figure 5 shows that our formalism does not reproduce the experiments of some of the flows.…”

Section: Concluding Discussionmentioning

confidence: 99%

Statistical mechanics and large-scale velocity fluctuations of turbulence

et al. 2011

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Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.

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“…By contrast, the understanding of anisotropic, inhomogeneous, compressible, non-stationary, or bound turbulence is only in its infancy (Kurien & Sreenivasan 2000;Biferale et al 2008;Byrne et al 2011;Hansen et al 2011;Biferale et al 2012;Grauer et al 2012). Characterizing our CDL data in terms of structure functions thus is rather exploratory.…”

Section: Structure Functionsmentioning

confidence: 99%

Supersonic turbulence in 3D isothermal flow collision

Folini

Walder

Favre

2014

A&A

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Large scale supersonic bulk flows are present in a wide range of astrophysical objects, from O-star winds to molecular clouds, galactic sheets, accretion, or γ-ray bursts. Associated flow collisions shape observable properties and internal physics alike. Our goal is to shed light on the interplay between large scale aspects of such collision zones and the characteristics of the compressible turbulence they harbor. Our model setup is as simple as can be: 3D hydrodynamical simulations of two head-on colliding, isothermal, and homogeneous flows with identical upstream (subscript u) flow parameters and Mach numbers 2 < M u < 43. The turbulence in the collision zone is driven by the upstream flows, whose kinetic energy is partly dissipated and spatially modulated by the shocks confining the zone. Numerical results are in line with expectations from self-similarity arguments. The spatial scale of modulation grows with the collision zone. The fraction of energy dissipated at the confining shocks decreases with increasing M u . The mean density is ρ m ≈ 20ρ u , independent of M u . The root mean square Mach number is M rms ≈ 0.25M u . Deviations toward weaker turbulence are found as the collision zone thickens and for small M u . The density probability function is not log-normal. The turbulence is inhomogeneous, weaker in the center of the zone than close to the confining shocks. It is also anisotropic: transverse to the upstream flows M rms is always subsonic. We argue that uniform, head-on colliding flows generally disfavor turbulence that is at the same time isothermal, supersonic, and isotropic. The anisotropy carries over to other quantities like the density variance -Mach number relation. Line-of-sight effects thus exist. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. Turbulence characteristics generally deviate markedly from those found for uniformly driven, supersonic, isothermal turbulence in 3D periodic box simulations. We suggest that this should be kept in mind when interpreting turbulence characteristics derived from observations. Our simulations show that even a simple model setup results in a richly structured interaction zone. The robustness of our findings toward more realistic setups remains to be tested.

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Anisotropic scaling contributions to high-order structure functions in high-Reynolds-number turbulence

Cited by 122 publications

References 11 publications

Fluid particle accelerations in fully developed turbulence

Fluid particle accelerations in fully developed turbulence

Statistical mechanics and large-scale velocity fluctuations of turbulence

Supersonic turbulence in 3D isothermal flow collision

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