The integral equation approach to kinematic dynamo theory and its application to dynamo experiments in cylindrical geometry

Journal of Computational Physics

Volumn 227, Issue 17, 2008, Pages 8130-8144

  Xu, M ^a   Stefani, F ^a   Gerbeth, G ^a  

^a INSTITUTE OF ION BEAM PHYSICS AND MATERIALS RESEARCH   (Germany)

Author keywords

Dynamo; Integral equation; Magnetohydrodynamics

Indexed keywords

COMPUTATION THEORY; CYLINDERS (SHAPES); INTEGRAL EQUATIONS; INTERACTIVE DEVICES; KINEMATICS;

COMPUTATIONAL DOMAINS; CYLINDRICAL GEOMETRY; DYNAMO ACTION; DYNAMO THEORIES; INTEGRAL EQUATION APPROACHES; INTEGRAL EQUATION SYSTEM; ITS APPLICATIONS; KINEMATIC DYNAMO; MAGNETIC INDUCTION EQUATIONS; THEORY APPLICATIONS;

MAGNETOHYDRODYNAMICS;

EID: 47049106012     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.05.009     Document Type: Article

References (42)

1. Rüdiger G., and Hollerbach R. The Magnetic Universe (2004), Wiley-VCH, Weinheim
2. Gailitis A., Lielausis O., Platacis E., Gerbeth G., and Stefani F. Laboratory experiments on hydromagnetic dynamos. Rev. Mod. Phys. 74 (2002) 973-990
3. Brandenburg A., Nordlund A., Stein R.F., and Torkelsson U. Dynamo-generated turbulence and large scale magnetic fields in a Keplerian shear flow. Astrophys. J. 446 (1995) 741-754
4. Kenjereš S., and Hanjalić K. Numerical simulation of a turbulent magnetic dynamo. Phys. Rev. Lett. 98 (2007) 104501
5. Rädler K.-H., Apstein E., Rheinhardt M., and Schüler M. The Karlsruhe dynamo experiment - a mean-field approach. Stud. Geophys. Geod. 42 (1998) 224-231
6. Rädler K.-H., Rheinhardt M., Apstein E., and Fuchs H. On the mean-field theory of the Karsruhe dynamo experiment. Nonl. Proc. Geophys. 9 (2002) 171-178
7. Stefani F., Gerbeth G., and Gailitis A. Velocity profile optimization for the Riga dynamo experiment. In: Alemany A., Marty Ph., and Thibault J.-P. (Eds). Transfer Phenomena in Magnetohydrodynamics and Electroconducting Flows (1999), Kluwer, Dordrecht 31-44
8. Guermond J.-L., Léorat J., and Nore C. A new finite element method for magneto-dynamical problems: two-dimensional results. Eur. J. Mech. B/Fluids 22 (2003) 555-579
9. Laguerre R., Nore C., L'eorat J., and Guermond J.-L. Effects of conductivity jumps in the envelope of a kinematic dynamo flow. Comptes Rendus Mecanique 334 (2006) 593-598
10. Iskakov A.B., Descombes S., and Dormy E. An integro-differential formulation for magnetic induction in bounded domains: boundary element-finite volume method. J. Comp. Phys. 197 (2004) 540-554
11. Iskakov A.B., and Dormy E. On magnetic boundary conditions for non-spectral dynamo simulations. Geophys. Astrophys. Fluid Dyn. 99 (2005) 481-492
12. Gailitis A. Self-excitation of a magnetic field by a pair of annular vortices. Magnetohydrodynamics 6 1 (1970) 14-17
13. Gailitis A., and Freibergs Ya. Self-excitation of a magnetic field by a pair of annular eddies. Magnetohydrodynamics 10 1 (1974) 26-30
14. Freibergs Ya. Optimization of the shape of the toroidal model of an MHD dynamo. Magnetohydrodynamics 11 3 (1975) 269-272
15. Dobler W., and Rädler K.-H. An integral equation approach to kinematic dynamo models. Geophys. Astrophys. Fluid Dyn. 89 (1998) 45-74
16. Stefani F., Gerbeth G., and Rädler K.-H. Steady dynamos in finite domains: an integral equation approach. Astron. Nachr. 321 (2000) 65-73
17. Xu M., Stefani F., and Gerbeth G. The integral equation method for a steady kinematic dynamo problem. J. Comp. Phys. 196 (2004) 102-125
18. Xu M., Stefani F., and Gerbeth G. Integral equation approach to time-dependent kinematic dynamos in finite domains. Phys. Rev. E 70 (2004) 056305
19. Stefani F., Xu M., Gerbeth G., Ravelet F., Chiffaudel A., Daviaud F., and Léorat J. Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment. Eur. J. Mech./B Fluids 25 (2006) 894-908
20. Monchaux R., et al. Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. Phys. Rev. Lett. 98 (2007) (Art. No. 04450)
21. Berhanu M., et al. Magnetic field reversals in an experimental turbulent dynamo. Europhys. Lett. 77 (2007) 59001
22. Bourgoin M., et al. Magnetohydrodynamics measurements in the von Kármán sodium experiment. Phys. Fluids 14 (2002) 3046-3058
23. Pétrélis F., et al. Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow. Phys. Rev. Lett. 90 (2003) 174501
24. Gailitis A., et al. Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility. Phys. Rev. Lett. 84 (2000) 4365-4368
25. Gailitis A., et al. Magnetic field saturation in the Riga dynamo experiment. Phys. Rev. Lett. 86 (2001) 3024-3027
26. Gailitis A., Lielausis O., Platacis E., Gerbeth G., and Stefani F. The Riga dynamo experiment. Surv. Geophys. 24 (2003) 247-267
27. Gailitis A., Lielausis O., Platacis E., Gerbeth G., and Stefani F. Riga dynamo experiment and its theoretical background. Phys. Plasmas 11 (2004) 2838-2843
28. Moler C., and Stewart G.W. An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10 (1973) 241-256
29. Ivers D.J., and Phillips C.G. A vector spherical harmonic spectral code for linearised magnetodydrodynamics. ANZIAM J. 44 E (2003) C423-C442
30. Beltrami E. Considerazione idrodinamiche. Rend. Inst. Lobardo Acad. Sci. Lett. 22 (1889) 122-131
31. Chandrasekhar S., and Kendall P.C. On force-free magnetic fields. Astrophys. J. 126 (1957) 457-460
32. Montgomery D., Turner L., and Vahala G. Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry. Phys. Fluids 21 (1978) 757-764
33. Yoshida Z. Eigenfunction expansion associated with the curl derivatives in cylindrical geometries: completeness of Chandrasekhar-Kendall eigenfunctions. J. Math. Phys. 33 (1992) 1252-1256
34. J. Léorat, personal communication.
35. Wang Z., Pariev V.I., Barnes C.W., and Barnes D.C. Laminar plasma dynamos. Phys. Plasmas 9 (2002) 1491-1494
36. Spence E.J., Nornberg M.D., Jacobson C.M., Kendrick R.D., and Forest C.B. Observation of a turbulence-induced large scale magnetic field. Phys. Rev. Lett. 96 (2006) 055002
37. Nornberg M.D., Spence E.J., Kendrick R.D., Jacobson C.M., and Forest C.B. Intermittent magnetic field excitation by a turbulent flow of liquid sodium. Phys. Rev. Lett. 97 (2006) 044503
38. Ponty Y., Mininni P.D., Montgomery D.C., Pinton J.-F., Politano H., and Pouquet A. Numerical study of dynamo action at low magnetic Prandtl numbers. Phys. Rev. Lett. 94 (2005) 164502
39. Laval J.-P., Blaineau P., Leprovost N., Dubrulle B., and Daviaud F. Influence of turbulence on the dynamo threshold. Phys. Rev. Lett. 96 (2006) 204503
40. Marié L., Burguete J., Daviaud F., and Leéorat J. Numerical study of homogeneous dynamo based on experimental von Kármán type flows. Eur. Phys. J. B 33 (2003) 469-485
41. Ravelet F., Chiffaudel A., Daviaud F., and Léorat J. Towards an experimental von Kármán dynamo: numerical studies for an optimized design. Phys. Fluids 17 (2005) 117104
42. F. Ravelet, Bifurcations globales hydrodynamiques et magnétohydrodynamiques dans un écoulement de von Kármán turbulent, Ph.D. Thesis, CEA Saclay, 2005.