Experimental test of the crossover between the inertial and the dissipative range in a turbulent swirling flow

Debue, Paul; Kuzzay, Denis; Saw, Ewe-Wei; Daviaud, François; Dubrulle, Bérengère; Canet, Léonie; Rossetto, Vincent; Wschebor, Nicolás

doi:10.1103/physrevfluids.3.024602

Cited by 26 publications

(31 citation statements)

References 33 publications

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“…with µ a non-universal constant. This prediction was precisely confirmed in direct numerical simulation of NS equation [9], and also observed in experiments on turbulent swirling flows [53].…”

Section: A Small Time Delayssupporting

confidence: 76%

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

2018

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In this paper, we present theoretical results on the statistical properties of stationary, homogeneous and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the Non-Perturbative Renormalization Group, we derive a closed renormalization flow equation for a generic n-point correlation (and response) function for large wave-numbers with respect to the inverse integral scale. The closure is obtained from a controlled expansion and relies on extended symmetries of the Navier-Stokes field theory. It yields the exact leading behavior of the flow equation at large wave-numbers | pi|, and for arbitrary time differences ti in the stationary state. Furthermore, we obtain the form of the general solution of the corresponding fixed point equation, which yields the analytical form of the leading wave-number and time dependence of n-point correlation functions, for large wave-numbers and both for small ti and in the limit ti → ∞. At small ti, the leading contribution at large wave-number is logarithmically equivalent to −α(εL) 2/3 | ti pi| 2 , where α is a non universal constant, L the integral scale and ε the mean energy injection rate. For the 2-point function, the (tp) 2 dependence is known to originate from the sweeping effect. The derived formula embodies the generalization of the effect of sweeping to n−point correlation functions. At large wave-number and large ti, we show that the t 2 i dependence in the leading order contribution crosses over to a |ti| dependence. The expression of the correlation functions in this regime was not derived before, even for the 2-point function. Both predictions can be tested in direct numerical simulations and in experiments.

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Section: A Small Time Delayssupporting

confidence: 76%

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

2018

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“…We shall also interpret the findings in terms of two recent theoretical predictions; the first, resulting from ideas based on distributed chaos, predicts γ = 3/4 or 2/3 depending on a particular choice of parameters [23]; and the second, emerging from a nonperturbative renormalization group (NPRG) approach, predicts that γ = 2/3 [14]. Both references have claimed an agreement in their respective inspections with experimental or DNS data [14,16,23,24] but, as mentioned earlier, the data were restricted to either low R λ or limited resolution. We assess these claims and show that there exists an intermediate bridging region between the stretched exponential and the FDR, on which we shall remark only briefly.…”

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confidence: 54%

“…In contrast to the results of Refs. [16,24], Fig. 1(b) at higher R λ shows that the energy spectra in NDR cannot be described by one single value of γ .…”

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confidence: 93%

“…TABLE I. Simulation parameters for the DNS runs used in the current work: the Taylor-scale Reynolds number (R λ ), the number of grid points (N 3 ), spatial resolution (k max η), ratio of large-eddy turnover time (T E ) to Kolmogorov timescale (τ K ), the simulation time (T sim ) in a statistically stationary state, and the number of three-dimensional snapshots (N s ) used for each run to obtain the statistics. Many attempts have been made over the years to characterize f using both experiments and direct numerical simulations (DNS) [8][9][10][11][12][13][14][15][16], all of which suggest the following general form,…”

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confidence: 99%

“…Other methods for extracting γ are also possible, e.g., see Refs. [16,24], but as described in the Appendix, they are not very robust and can lead to incorrect conclusions, especially when the R λ is low. Figure 2(a) shows log-log plots of −φ(kη) vs kη and confirms that the log-derivative exhibits two regions of distinct power laws.…”

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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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Universal Behaviors in the Diffusive Epidemic Process and in Fully Developed Turbulence

Tarpin

2020

Springer Theses

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Experimental test of the crossover between the inertial and the dissipative range in a turbulent swirling flow

Cited by 26 publications

References 33 publications

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

Dissipation range of the energy spectrum in high Reynolds number turbulence

Universal Behaviors in the Diffusive Epidemic Process and in Fully Developed Turbulence

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