Toward an experimental von Kármán dynamo: Numerical studies for an optimized design

Physics of Fluids

Volumn 17, Issue 11, 2005, Pages 1-17

  Ravelet, F ^a   Chiffaudel, Arnaud ^a   Daviaud, F ^a   Leorat J ^b  

^a CEA SACLAY   (France)

^b UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; COMPUTER SIMULATION; FLOW OF FLUIDS; MATHEMATICAL MODELS; OPTIMIZATION; RADIAL FLOW; REYNOLDS NUMBER;

BOUNDARY-LAYER RADIAL VELOCITY SHEAR; KINEMATIC DYNAMO; VON KARMAN FLOW; WATER MODEL EXPERIMENT;

FLUID DYNAMICS;

FLUID DYNAMICS;

EID: 30044435892     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2130745     Document Type: Article

References (45)

1. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, England, 1978).
2. A. Gailitis, O. Lielausis, S. Dement'ev, E. Platacis, and A. Cifersons, "Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.84.4365 84, 4365 (2000).
3. R. Stieglitz and U. Müller, "Experimental demonstration of a homogeneous two-scale dynamo," Phys. Fluids PHFLE61070-663110.1063/ 1.1331315 13, 561 (2001).
4. A. Gailitis, O. Lielausis, E. Platacis, S. Dement'ev, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, and G. Will, "Magnetic field saturation in the Riga dynamo experiment," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.86.3024 86, 3024 (2001).
5. A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, and F. Stefani, "Colloquium: Laboratory experiments on hydromagnetic dynamos," Rev. Mod. Phys. RMPHAT0034-686110.1103/RevModPhys.74.973 (2002).
6. U. Müller, R. Stieglitz, and S. Horanyi, "A two-scale hydromagnetic dynamo experiment," J. Fluid Mech. JFLSA70022-112010.1017/S0022112003006700 498, 31 (2004).
7. F. Stefani, G. Gerbeth, and A. Gailitis, "Velocity profile optimization for the Riga dynamo experiment," Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows, edited by A. Alemany, Ph. Marty, and J.-P. Thibault (Kluwer Academic, Dordrecht, The Netherlands, 1999), pp. 31-44.
8. A. Tilgner, "Numerical simulation of the onset of dynamo action in an experimental two-scale dynamo," Phys. Fluids PHFLE61070-663110.1063/1.1513156 14, 4092 (2002).
9. A. Tilgner and F. H. Busse, "Simulation of the bifurcation diagram of the Karlsruhe dynamo," Magnetohydrodynamics MAGIAI0025-0015 38, 35 (2002).
10. F. Plunian and K.-H. Rädler, "Subharmonic dynamo action in the Roberts flow," Geophys. Astrophys. Fluid Dyn. GAFDD30309-192910.1080/03091920290004506 96, 115 (2002).
11. D. Sweet, E. Ott, J. M. Finn, T. M. Antonsen, and D. P. Lathrop, "Blowout bifurcations and the onset of magnetic activity in turbulent dynamos," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.63.066211 63, 066211 (2001).
12. A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, and F. Stefani, "The Riga dynamo experiment," Surv. Geophys. SUGEEC0169-329810.1023/A:1024851818821 24, 247 (2003).
13. F. Cattaneo, D. W. Hughes, and E.-J. Kim, "Suppression of chaos in a simplified nonlinear dynamo model," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.76.2057 76, 2057 (1996).
14. F. Pétrélis and S. Fauve, "Saturation of the magnetic field above the dynamo threshold," Eur. Phys. J. BEPJBFY1434-602810.1007/s100510170103 22, 273 (2001).
15. Y. Ponty, H. Politano, and J.-F. Pinton, "Simulation of induction at low magnetic Prandtl number," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.92.144503 92, 144503 (2004).
16. F. Pétrélis, "Effet dynamo: Etude des mécanismes d'instabilité et de saturation du champ magnétique," Ph.D. thesis, Université Paris VI (2002).
17. S. Fauve and F. Pétrélis, "The dynamo effect," in Peyresq Lectures on Nonlinear Phenomena, edited by J.-A. Sepulchre (World Scientific, Singapore, 2003), Vol. II.
18. Dynamo and Dynamics, a Mathematical Challenge, Cargèse (France) August 21-26, 2000, edited by P. Chossat, D. Armbruster, and I. Oprea, NATO ASI series (Kluwer Academic, Dordrecht, The Netherlands, 2001).
19. L. Marié, F. Pétrélis, M. Bourgoin, J. Burguete, A. Chiffaudel, F. Daviaud, S. Fauve, P. Odier, and J.-F. Pinton, "Open questions about homogeneous fluid dynamos: The VKS experiment," Magnetohydrodynamics MAGIAI0025-0015 38, 156 (2002).
20. M. Bourgoin, L. Marié, F. Pétrélis, C. Gasquet, A. Guigon, J.-B. Luciani, M. Moulin, F. Namer, J. Burguete, A. Chiffaudel, F. Daviaud, S. Fauve, P. Odier, and J.-F. Pinton, "MHD measurements in the von Kármán sodium experiment," Phys. Fluids PHFLE61070-663110.1063/1.1497376 14, 3046 (2002).
21. F. Pétrélis, M. Bourgoin, L. Marié, J. Burguete, A. Chiffaudel, F. Daviaud, S. Fauve, P. Odier, and J.-F. Pinton, "Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.90.174501 90, 174501 (2003).
22. L. Marié, J. Burguete, F. Daviaud, and J. Léorat, "Numerical study of homogeneous dynamo based on experimental von Kármán type flows," Eur. Phys. J. BEPJBFY1434-602810.1140/epjb/e2003-00187-2 33, 469 (2003).
23. N. L. Dudley and R. W. James, "Time-dependent kinematic dynamos with stationary flows," Proc. R. Soc. London, Ser. APRLAAZ1364-5021 425, 407 (1989).
24. C. B. Forest, R. O'Connell, R. Kendrick, E. Spence, and M. D. Nornberg, "Hydrodynamic and numerical modeling of a spherical homogeneous dynamo experiment," Magnetohydrodynamics MAGIAI0025-0015 38, 107 (2002).
25. E. C. Bullard and D. Gubbins, "Generation of magnetic fields by fluid motions of global scale," Geophys. Astrophys. Fluid Dyn. GAFDD30309-1929 8, 43 (1977).
26. A. B. Reighard and M. R. Brown, "Turbulent conductivity measurements in a spherical liquid sodium flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.86.2794 86, 2794 (2001).
27. F. Krause and K. H. Rädler, Mean Field MHD and Dynamo Theory (Pergamon, New York, 1980).
28. L. Marié and F. Daviaud, "Experimental measurement of the scale-by-scale momentum transport budget in a turbulent shear flow," Phys. Fluids PHFLE61070-663110.1063/1.1637602 16, 457 (2004).
29. L. Marié, "Transport de moment cinétique et de champ magnétique par un écoulement tourbillonaire turbulent: influence de la rotation," Ph.D. thesis, Université Paris VII (2003).
30. U. Frisch, Turbulence-The Legacy of A. N. Kolmogorov (Cambridge University Press, New York, 1995).
31. F. Ravelet, "Etude expérimentale de l'eacute;coulement tourbillonnaire de von Kármán et application à l'effet dynamo," M.S. thesis, Université Paris VI (2002).
32. J. Léorat, "Numerical simulations of cylindrical dynamos: Scope and method," in Progress in Turbulence Research, Progress in Astronautics and Aeronautics, Vol. 162 (AIAA, Washington, 1994), pp. 282-292.
33. E. Knobloch, "Symmetry and instability in rotating hydrodynamic and magnetohydrodynamic flows," Phys. Fluids PHFLE61070-663110.1063/ 1.868921 8, 1446 (1996).
34. E. C. Bullard and H. Gellman, "Homogeneous dynamos and terrestrial magnetism," Philos. Trans. R. Soc. London, Ser. APTRMAD0962-8428 247, 213 (1954).
35. G. E. Backus, "A class of self-sustaining dissipative spherical dynamos," Ann. Phys. ANPYA20003-380410.1016/0003-4916(58)90054-X (Leipzig) 4, 372 (1958).
36. J.J. Love and D. Gubbins, "Dynamos driven by poloidal flow exist," Geophys. Res. Lett. GPRLAJ0094-827610.1029/96GL00846 23, 857 (1996).
37. M.R.E. Proctor, "An extension of the toroidal theorem," Geophys. Astrophys. Fluid Dyn. GAFDD30309-192910.1080/ 030919209410001659272 98, 235 (2004).
38. M. Lesieur, Turbulence in Fluids, 2nd ed. (Kluwer Academic, Dordrecht, The Netherlands, 1990).
39. R. Kaiser and A. Tilgner, "Kinematic dynamos surrounded by a stationary conductor," Phys. Rev. EPLEEE81063-651X10.1103/ PhysRevE.60.2949 60, 2949 (1999).
40. R. Avalos-Zuniga and F. Plunian, "Influence of electromagnetic boundary conditions onto the onset of dynamo action in laboratory experiments," Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.68.066307 68, 066307 (2003).
41. E.N. Parker, "Hydromagnetic dynamo models," Astrophys. J.ASJOAB0004-637X10.1086/146087 122, 293 (1955).
42. N. Leprovost, "Influence des petites échelles sur la dynamique à grande échelle en turbulence magnétohydrodynamique," Ph.D. thesis, Université Paris VI (2004).
43. S. Childress and A. D. Gilbert, Stretch, Twist, Fold: The Fast Dynamo (Springer, New York, 1995).
44. V. Archontis, S. B. F. Dorch, and A. Nordlund, "Numerical simulations of kinematic dynamo action," Astron. Astrophys. AAEJAF0004-636110.1051/0004-6361:20021568 397, 393 (2003).
45. M. Bourgoin, P. Odier, J.-F. Pinton, and Y. Ricard, "An iterative study of time independent induction effects in magnetohydrodynamics," Phys. Fluids PHFLE61070-663110.1063/ 1.1739401 16, 2529 (2004).