Magnetic field transport and kinematic dynamo effect: A Lagrangian interpretation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2065, 2006, Pages 137-147

  Celani, A ^a   Mazzino, A ^b,c   Vincenzi, D ^d,e  

^a INSTITUT NON LINÉAIRE DE NICE   (France)

^b UNIVERSITY OF GENOA   (Italy)

^c INFN SEZIONE DI GENOVA   (Italy)

^d MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

^e Department of Molecular Biology and Genetics   (United States)

Author keywords

Dynamo effect; Lagrangian dynamics; Statistical conservation laws

Indexed keywords

EID: 33750167632     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1561     Document Type: Article

References (29)

1. Arad, I., Biferale, L., Celani, A., Procaccia, I. & Vergassola, M. 2001 Statistical conservation laws in turbulent transport. Phys. Rev. Lett. 87, 164 502. (doi:10.1103/PhysRevLett.87.164502)
2. Bernard, D., Gawȩdzki, K. & Kupiainen, A. 1998 Slow modes in passive advection. J. Stat. Phys. 90, 519-569.
3. Biferale, L. & Procaccia, I. 2005 Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414, 43-164. (doi:10.1016/j.physrep.2005.04. 001)
4. Boldyrev, S. & Cattaneo, F. 2004 Magnetic-field generation in Kolmogorov-turbulence. Phys. Rev. Lett. 92, 144501. (doi:10.1103/PhysRevLett.92. 144501)
5. Celani, A. & Vergassola, M. 2001 Statistical geometry in scalar turbulence. Phys. Rev. Lett. 80, 424-427. (doi:10.1103/PhysRevLett.86.424)
6. Chertkov, M., Falkovich, G., Kolokolov, I. & Lebedev, V. 1995 Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar. Phys. Rev. E 52, 4924-4941. (doi:10.1103/PhysRevE.52. 4924)
7. Chertkov, M., Falkovich, G., Kolokolov, I. & Vergassola, M. 1999 Small-scale turbulent dynamo. Phys. Rev. Lett. 83, 4065-4068. (doi:10.1103/PhysRevLett.83.4065)
8. Childress, S. & Gilbert, A. D. 1995 Stretch, twist, fold: the fast dynamo. Lecture Notes in Physics, vol. 37. Berlin: Springer.
9. Cocke, W. J. 1969 Turbulent hydrodynamic line stretching. Consequences of isotropy. Phys. Fluids 12, 2488-2492. (doi:10.1063/1.1692385)
10. Falkovich, G., Gawȩdzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913-975. (doi:10.1103/RevModPhys.73.913)
11. Frisch, U., Mazzino, A. & Vergassola, M. 1998 Intermittency in passive scalar advection. Phys. Rev. Lett. 80, 5532-5535. (doi:10.1103/ PhysRevLett.80.5532)
12. Gawȩdzki, K. & Kupiainen, A. 1995 Anomalous scaling of the passive scalar. Phys. Rev. Lett. 75, 3834-3837. (doi:10.1103/PhysRevLett.75. 3834)
13. Horvai, P. In preparation. Finite-scale effects in the Kraichnan-Kazantsev dynamo.
14. Kazantsev, A. P. 1967 Enhancement of a magnetic field by a conducting fluid. Zh. Eksp. Teor. Fiz. 53, 1806-1813.
15. [Transl. 1968 Sov. Phys. JETP 26, 1031-1034.]
16. Klyatskin, V. I. 2005 Dynamics of stochastic systems, 1st edn, ch. 5. Amsterdam: Elsevier.
17. Kraichnan, R. H. 1968 Small-scale structure of a scalar field convected by turbulence. Phys. Fluids 11, 945-963. (doi:10.1063/1.1692063)
18. Lanotte, A. & Mazzino, A. 1999 Anisotropic nonperturbative zero modes for passively advected magnetic fields. Phys. Rev. E 60, R3483-R3486. (doi:10.1103/PhysRevE.60.R3483)
19. Moffatt, H. K. 1978 Magnetic field generation in electrically conducting fluids. Cambridge: Cambridge University Press.
20. Monin, A. A. Yaglom, A. M. 1975 Statistical fluid mechanics, vol. 2, p. 40. Cambridge, MA: MIT Press.
21. Ponty, Y., Mininni, P. D., Montgomery, D. C., Pinton, J. F., Politano, H. & Pouquet, A. 2005 Numerical study of dynamo action at low magnetic Prandt1 numbers. Phys. Rev. Lett. 94, 104-502. (doi:10.1103/PhysRevLett.94.164502)
22. Schekochihin, A. A., Cowley, S. C., Taylor, S. F., Maron, J. L. & McWilliams, J. C. 2004 Simulations of the small-scale turbulent dynamo. Astrophys. J. 612, 276-307. (doi:10.1086/422547)
23. Shraiman, B. I. & Siggia, E. 1995 Anomalous scaling of a passive scalar in turbulent flow. C.R. Acad. Sci. Paris Ser. II 321, 279-284.
24. Shraiman, B. I. & Siggia, E. 2000 Scalar turbulence. Nature 405, 039-646. (doi:10.1038/35015000)
25. Sreenivasan, K. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. A 434, 165-182.
26. Taylor, G. I. 1921 Diffusion by continuous movements. Proc. Math. Soc. 20, 196-212.
27. Vergassola, M. 1996 Anomalous scaling for passively advected magnetic fields. Phys. Rev. E 53, R3021-R3024. (doi:10.1103/PhysRevE.53.R3021)
28. Vincenzi, D. 2002 The Kraichnan-Kazantsev dynamo. J. Stat. Phys. 106, 1073-1091. (doi:10.1023/A:1014089820881)
29. Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203-240. (doi:10. 1146/annurev.fluid.32.1.203)