Exact relationship for third-order structure functions in helical flows

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

Volumn 61, Issue 5, 2000, Pages 5321-5325

  Gomez, T ^a,b   Politano, H ^a   Pouquet, A ^a  

^a CNRS   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

HELICAL FLOWS; LINEAR SCALING; MIXED STRUCTURE; REFLECTIONAL SYMMETRY; STRINGENT TEST; THIRD-ORDER; VELOCITY CORRELATION FUNCTIONS; VORTICITY FIELD;

VORTICITY;

EID: 0003174791     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.5321     Document Type: Article

References (42)

1. R. Kraichnan, Phys. Rev. Lett. 72, 1016 (1994)
2. Phys. Rev. Lett.R. Kraichnan78, 4922 (1997)
3. Phys. Rev. Lett.R. Kraichnan, V. Yakhot, and S. Chen 75, 240 (1995).
4. M. Vergassola, Phys. Rev. E 53, 3021 (1996)
5. see also S. Boldyrev and A. Schekochihin, Phys. Rev. E (to be published) (e-print chaodyn/9907034), for the case of tensors passively advected by a Gaussian velocity field, delta-correlated in time and without the assumption of incompressibility.
6. A. Kolmogorov, Dokl. Akad. Nauk. 32, 16 (1941).
7. R. Antonia, M. Ould-Rouis, F. Anselmet, and Y. Zhu, J. Fluid Mech. 332, 395 (1997)
8. J. Fluid Mech.see also L. Fulachier and R. Dumas, 77, 257 (1976) for the case of the passive scalar.
9. H.K. Moffatt, J. Fluid Mech. 35, 117 (1969)
10. H.K. MoffattPhilos. Trans. R. Soc. London, Ser. A 333, 321 (1990).
11. H.K. Moffatt and A. Tsinober, Annu. Rev. Fluid Mech. 24, 281 (1992).
12. M. Steenbeck, F. Krause, and K. Rädler, Z. Naturforsch. A 21, 369 (1966).
13. R. Kraichnan and R. Panda, Phys. Fluids 31, 2395 (1988).
14. This relationship is written with a dimensional factor containing a length scale (Formula presented) characteristic of the energy-containing range.
15. O. Podvigina and A. Pouquet, Physica D 75, 475 (1994).
16. P. Orlandi, J. Fluid Mech. 9, 2045 (1997).
17. A. Tsinober, in Structure of Turbulence and Drag Reduction, edited by A. Gyr (Springer-Verlag, Berlin, 1990), p. 313.
18. O. Chkhetiani, Plasma Zh. Éksp. Teor. Fiz 63, 768 (1996) [JETP Lett. 63, 808 (1996)
19. see also V. L’vov, E. Podivilov and I. Procaccia, http://xxx.lanl.gov/abs/chao-dyn/9705016 (1997), where a result similar to that of O. Chkhetiani is derived independently. We are thankful to M. Vergassola to have pointed out this second reference to us.
20. G. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, England, 1953).
21. All pseudoscalars (except the total helicity (Formula presented) are denoted in this paper with a tilde symbol in order to distinguish them from scalars.
22. (Formula presented) and (Formula presented) and similarly G and (Formula presented) are unrelated functions of r.
23. H. Robertson, Proc. Cambridge Philos. Soc. 36, 209 (1940).
24. This is because we deal with the temporal evolution of a (pseudo)scalar, the local density of helicity.
25. We choose to ignore here the possibility that the Loitsianskii integral is not invariant, leading to a different behavior in the large scales and consequently to a different decay law of the kinetic energy of a turbulent flow [see P.G. Saffman, Phys. Fluids 10, 1349 (1967)
26. P.G. SaffmanJ. Fluid Mech. 27, 581 (1967).
27. T. von Kármán and L. Howarth, Proc. R. Soc. London, Ser. A 164, 192 (1938).
28. Note that our definition of helicity includes a factor (Formula presented)
29. B. Dernoncourt, J.-F. Pinton, and S. Fauve, Physica D 117, 181 (1998)
30. Physica DC. Baudet, O. Michel and W.J. Williams,, 128, 1 (1999).
31. R. Antonia, Y. Zhu, and H. Shapi, J. Fluid Mech. 323, 173 (1996).
32. R. Antonia, M. Ould-Rouis, Y. Zhu, and F. Anselmet, Phys. Rev. E 57, 5483 (1998).
33. P. Iroshnikov, Sov. Astron. 7, 566 (1963)
34. R.H. Kraichnan, Phys. Fluids 8, 1385 (1965).
35. D. Biskamp and H. Welter, Phys. Fluids B 1, 1964 (1989)
36. Phys. Fluids BH. Politano, A. Pouquet, and P-L. Sulem 1, 2230 (1989).
37. H. Politano, A. Pouquet, and V. Carbone, Europhys. Lett. 43, 516 (1998).
38. J.-F. Pinton, F. Plaza, L. Danaila, P. Legal, and F. Anselmet, Physica D 122, 187 (1998)
39. see also O. Boratav, Phys. Fluids 10, 2122 (1998).
40. T. Gomez, H. Politano, and A. Pouquet, Phys. Fluids 11, 2298 (1999)
41. S. Galtier, T. Gomez, H. Politano and A. Pouquet, in Advances in Turbulence VII, edited by U. Frisch (Kluwer, Dordrecht, 1998), p. 453.
42. The derivation of the equivalent relationship for helical flows but in MHD will be reported elsewhere.