Dynamical organization around turbulent bursts

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

Volumn 57, Issue 6, 1998, Pages 6643-6646

  Okkels, Fridolin ^a   Jensen, Mogens H ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000629723     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.6643     Document Type: Article

References (24)

1. U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
2. A.N. Kolmogorov, C. R. Acad. Sci. USSR30, 301 (1941)
3. C. R. Acad. Sci. USSRA.N. Kolmogorov 32, 16 (1941).
4. C. Tang, K. Wiesenfeld, P. Bak, S. Coppersmith, and P. Littlewood, Phys. Rev. Lett. 58, 1161 (1987).PRLTAO
5. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).PRLTAO
6. T. Bohr, M. H. Jensen, G. Paladin, and A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, in press).
7. L. Kadanoff, D. Lohse, and N. Schörghofer, Physica D 100, 165 (1997).PDNPDT
8. E. B. Gledzer, Sov. Phys. Dokl. 18, 216 (1973).SPHDA9
9. M. Yamada and K. Ohkitani, J. Phys. Soc. Jpn. 56, 4210 (1987)
10. M. YamadaK. OhkitaniProg. Theor. Phys. 79, 1265 (1988).
11. M. H. Jensen, G. Paladin, and A. Vulpiani, Phys. Rev. A 43, 798 (1991).PLRAAN
12. R. Benzi, L. Biferale, and G. Parisi, Physica D 65, 163 (1993).PDNPDT
13. D. Pisarenko, L. Biferale, D. Courvasier, U. Frisch, and M. Vergassola, Phys. Fluids A 65, 2533 (1993).PFADEB
14. L. Kadanoff, D. Lohse, J. Wang, and R. Benzi, Phys. Fluids 7, 617 (1995).PHFLE6
15. L. Biferale, A. Lambert, R. Lima, and G. Paladin, Physica D 80, 105 (1995).PDNPDT
16. N. Schörghofer, L. Kadanoff, and D. Lohse, Physica D 88, 40 (1995).PDNPDT
17. F. Anselmet, Y. Gagne, E.J. Hopfinger, and R.A. Antonia, J. Fluid Mech. 140, 63 (1984).JFLSA7
18. C. Meneveau and K.R. Sreenivasan, Nucl. Phys. B, Proc. Suppl. 2, 49 (1987).NPBSE7
19. J. Herweijer and W. van de Water, Phys. Rev. Lett. 74, 4651 (1995).PRLTAO
20. T. Dombre and J.-L. Gilson, Physica D 111, 265 (1998).PDNPDT
21. F. Okkels, Master thesis, CATS, University of Copenhagen, Denmark, 1997.
22. O. Gat, I. Procaccia, and R. Zeitak, Phys. Rev. E 51, 1148 (1995).PLEEE8
23. We note that the picture and analysis based on Eq. (7) is local in the sense that only the dynamics of shell n is considered even though the coupling term Cn incorporates the values of amplitudes in the four neighboring shells. A complete picture of the dynamics around the fixed point rn=0, n=1,…,N, can be obtained from the center-manifold relating the shells with high viscosity (high n) to the shells with basically no viscosity (marginal modes corresponding to low n). This more mathematical treatment will be presented by the authors in a forthcoming publication. We are grateful to Tomas Bohr for pointing this structure out.
24. R. Camussi and G. Guj, J. Fluid Mech. 348, 177 (1998). JFLSA7