Experimental Study of the Bottleneck in Fully Developed Turbulence

Küchler, Christian; Bewley, Gregory P.; Bodenschatz, Eberhard

doi:10.1007/s10955-019-02251-1

Cited by 37 publications

(40 citation statements)

References 58 publications

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“…However, with increasing R λ and the scale range, the energy transfer across the scales is better facilitated, leading to the diminution of the bottleneck and a simultaneous rise in spectral density in NDR. Recent experimental results [31] have confirmed the decay of the bottleneck even up to R λ ≈ 4000. Based on this behavior, we may infer that the exponent in this part of NDR will likely continue to decrease at least up to R λ = 4000; however, if the trend in Fig.…”

mentioning

confidence: 80%

“…2(b).] In the first, corresponding to the region immediately past the bottleneck (known to occur around kη ≈ 0.1 [30,31]) to kη 0.5, data for all R λ exhibit a spectral collapse, with the exponent ranging from 0.68 ± 0.03 for R λ = 140 to 0.67 ± 0.01 for R λ = 1300, effectively 2/3. This value of γ is in agreement with the theoretical prediction from NPRG [14] (though a precise wave-number range is not obtainable from the theory).…”

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confidence: 99%

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Dissipation range of the energy spectrum in high Reynolds number turbulence

Buaria

Sreenivasan

2020

Phys. Rev. Fluids

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We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to R λ = 650, with excellent small-scale resolution of k max η ≈ 6, and additionally at R λ = 1300 with k max η ≈ 3, where k max is the maximum resolved wave number and η is the Kolmogorov length scale. We find that for a limited range of wave numbers k past the bottleneck, in the range 0.15 kη 0.5, the spectra for all R λ display a universal stretched exponential behavior of the form exp(−k 2/3), in rough accordance with recent theoretical predictions. In contrast, the stretched exponential fit does not possess a unique exponent in the near dissipation range 1 kη 4, but one that persistently decreases with increasing R λ. This region serves as the intermediate dissipation range between the exp(−k 2/3) region and the far dissipation range kη 1 where analytical arguments as well as DNS data with superfine resolution [S. Khurshid et al., Phys. Rev. Fluids 3, 082601 (2018)] suggest a simple exp(−kη) dependence. We briefly discuss our results in connection to the multifractal model.

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confidence: 80%

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confidence: 99%

Dissipation range of the energy spectrum in high Reynolds number turbulence

Buaria

Sreenivasan

2020

Phys. Rev. Fluids

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“…Inviscid simulations such as those shown in [104,105] assume an infinite Reynolds number for which the ideal k −5/3 -law should hold for arbitrary high Reynolds numbers. At finite Reynolds numbers deviations from the k −5/3 -law are to be expected, and a bottleneck effect is also seen in experiments [107]. However, it is difficult to say whether the appearance of the bottleneck effect in underresolved simulations bears any physical meaning.…”

Section: Vortical Structuresmentioning

confidence: 98%

“…In laboratory experiments the effect is difficult to study as it requires sufficiently high Reynolds numbers and is visible only for extremely high wave numbers. To overcome the experimental difficulties, Küchler et al [107] employed a very sophisticated experimental setup using sulphurhexaflouride at pressures of up to 15 bar in order to obtain Taylor micro-scale Reynolds numbers of up to 1600 and Kolmogorov scales of ten microns. This provides sufficient measurement accuracy to investigate the bottleneck effect.…”

Section: Vortical Structuresmentioning

confidence: 99%

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

Geier

Lenz

Schönherr

et al. 2020

Theor. Comput. Fluid Dyn.

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We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ($${\hbox {Re}}=160{,}000$$ Re = 160 , 000 ) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.

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“…The bottleneck effect is an accumulation of the cascading energy at wavenumbers just below the dissipation range, leading to a change in the power-law behavior of the energy spectrum. The bottleneck effect exists even for ordinary viscosity and has been the subject of many studies in turbulence [8][9][10][11][12]. With the use of hyper-viscosity, the bottleneck becomes more pronounced, even leading to a non-monotonic behavior of the energy spectrum.…”

Section: Introductionmentioning

confidence: 99%

Turbulent cascade, bottleneck, and thermalized spectrum in hyperviscous flows

et al. 2020

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In many simulations of turbulent flows the viscous forces ν∇ 2 u are replaced by a hyper-viscous term −νp(−∇ 2 ) p u in order to suppress the effect of viscosity at the large scales. In this work we examine the effect of hyper-viscosity on decaying turbulence for values of p ranging from p = 1 (regular viscosity) up to p = 100. Our study is based on direct numerical simulations of the Taylor-Green vortex for resolutions from 512 3 to 2048 3 . Our results demonstrate that the evolution of the total energy E and the energy dissipation remain almost unaffected by the order of the hyper-viscosity used. However, as the order of the hyper-viscosity is increased, the energy spectrum develops a more pronounced bottleneck that contaminates the inertial range. At the largest values of p examined, the spectrum at the bottleneck range has a positive power-law behavior E(k) ∝ k α with the power-law exponent α approaching the value obtained in flows at thermal equilibrium α = 2. This agrees with the prediction of Frisch et al. [Phys. Rev. Lett. 101, 144501 (2008)] who suggested that at high values of p, the flow should behave like the truncated Euler equations (TEE). Nonetheless, despite the thermalization of the spectrum, the flow retains a finite dissipation rate up to the examined order, which disagrees with the predictions of the TEE system implying suppression of energy dissipation. We reconcile the two apparently contradictory results, predicting the value of p for which the hyper-viscous Navier-Stokes goes over to the TEE system and we discuss why thermalization appears at smaller values of p.

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Experimental Study of the Bottleneck in Fully Developed Turbulence

Cited by 37 publications

References 58 publications

Dissipation range of the energy spectrum in high Reynolds number turbulence

Dissipation range of the energy spectrum in high Reynolds number turbulence

Under-resolved and large eddy simulations of a decaying Taylor–Green vortex with the cumulant lattice Boltzmann method

Turbulent cascade, bottleneck, and thermalized spectrum in hyperviscous flows

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