Transition at dissipative scales in large-Reynolds-number turbulence

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 6, 2002, Pages

  Tabeling, Patrick ^a   Willaime, Herve ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DATA ACQUISITION; DATA REDUCTION; PHASE TRANSITIONS; REYNOLDS NUMBER; STATISTICAL METHODS; TURBULENT FLOW;

INTERMITTENCY EFFECTS; LARGE-REYNOLDS-NUMBER TURBULENCE; STANDARD DEVIATION; SUB-KOLMOGOROV STRUCTURES;

TURBULENCE;

EID: 41349098983     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.066301     Document Type: Article

References (21)

1. A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 301 (1941).
2. H. L. Grant, R. W. Stewart, and A. Moillet, J. Fluid Mech. 41, 153 (1962).
3. U. Frisch, Turbulence (Cambridge University Press, Cambridge, 1995).
4. K. R. Sreenivasan and R. A. Antonia, Annu. Rev. Fluid Mech. 29, 435 (1997).
5. M. Nelkin, Adv. Phys. 43, 143 (1994).
6. P. Tabeling, G. Zocchi, F. Belin, J. Maurer, and H. Willaime, Phys. Rev. E 53, 1613 (1996).
7. F. Belin, J. Maurer, P. Tabeling, and H. Willaime, Phys. Fluids 9, 12 (1997);
8. Phys. FluidsF. BelinJ. MaurerP. TabelingH. Willaime9, 3843 (1997).
9. V. Emsellem, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 322, 11 (1996).
10. V. Emsellem, D. Lohse, P. Tabeling, L. Kadanoff, and J. Wang, Phys. Rev. E 55, 2672 (1997).
11. The review of Ref. 4 raises a criticism on our flatness measurements above (Formula presented), as published in Ref. 6. These measurements were corrected and completed one year after 7; the criticism does not concern the range of (Formula presented) where the transition takes place; unfortunately, the distinction between the two ranges was not clearly made in the review, and consequently, an impression was left that the whole set of our flatness measurements could be subjected to caution.
12. The review of Ref. 4 considers as an established fact that the hyperflatnesses of orders 5 and 6 monotically increase with the Reynolds number, referring to a study by Antonia et al. [Boundary-Layer Meteorol. 21, 15 (1981)] to support this statement. Data in the above reference are scarce, and it seems difficult to use this paper to draw out any accurate conclusion about the evolution of the aforementioned factors. Our hyperflatness measurements, published in Ref. 7 are much more detailed, and clearly shows a transitional behavior.
13. F. Moisy, P. Tabeling, and H. Willaime, Phys. Rev. Lett. 82, 3994 (1999).
14. H. Willaime, F. Moisy, J. Maurer, and P. Tabeling, Eur. Phys. J. B 18, 363 (2000).
15. B. Pearson (unpublished).
16. In here, the term “breakdown” is used in a vague sense (while in the current understanding, vortex breakdown refers to an accurately described phenomenon [see, for instance, H. Liebovitch, Annu. Rev. Fluid Mech. 10, 221 (1978)]),. In the present paper, vortex breakdown refers to an instability which substantially changes the internal structure of the worms. Speculating that this instability is closely similar to an ordinary vortex breakdown is a possibility one may not necessarily rule out at the moment.
17. J. Jimenez, P. Wray, P. G. Saffman, and R. S. Rogallo, J. Fluid Mech. 255, 65 (1993).
18. F. Moisy and J. Jimenez (unpublished).
19. G. Stolovitsky, K. R. Sreenivasan, and A. Jueneja, Phys. Rev. E 48, 3217 (1993).
20. F. Belin, P. Tabeling, and H. Willaime, Physica D 93, 52 (1996).
21. A tentative way to estimate the characteristics of the debris would be to assume they have the form of vortex filaments, immerged in a background field of intensity (Formula presented) and subjected to a strain, locally generated by the worm, on the order of (Formula presented). In such a situation, the limiting width of these subfilaments would be on the order of (Formula presented) (in which (Formula presented) is the kinematic viscosity, (Formula presented) is the Kolmogorov scale, and L is the large scale)], and the corresponding internal Reynolds number would be on the order of (Formula presented); the debris thus define intense subkolmogorovian structures. Because their internal Reynolds number increases with (Formula presented) these subfilaments are in turn expected to burst as (Formula presented) is further increased. One may iterate the argument for the next generations of debris; the reasoning leads to defining a hierarchy of subkolmogorovian structures, which successively become unstable as (Formula presented) is increased. A similar hierarchy was obtained by 16. However, in their paper the authors conclude the system ultimately becomes stable at infinite Reynolds numbers.