Abstract.
To study the onset of a stationary dynamo in the presence of inner or outer walls of various electromagnetic properties, we propose a simple 1D-model in which the flow is replaced by an alpha effect. The equation of dispersion of the problem is derived analytically. It is solved numerically for walls of different thicknesses and of electric conductivity and magnetic permeability different from those of the fluid in motion. We also consider walls in the limit of infinite conductivity or permeability.
Similar content being viewed by others
References
A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, F. Stefani, Rev. Mod. Phys. 74, 973 (2002)
K.-H Rädler, A. Cebers, Special issue on MHD Dynamo Experiments, Magnetohydrodynamics 28, 5–218 (2002)
R. Avalos-Zuñiga, F. Plunian, A. Gailitis, Phys. Rev. E 68, 066307 (2003)
R. Stieglitz, U. Müller, Phys. Fluids 13, 561 (2001)
U. Müller, R. Stieglitz, S. Horanyi, J. Fluid Mech. 498, 31 (2004)
A. Gailitis, O. Lielausis, S. Dementiev, E. Platacis, A. Cifersons, G. Gerbeth, Th. Gundrum, F. Stefani, M. Christen, H. Hänel, G. Will, Phys. Rev. Lett. 84, 4365 (2000)
A. Gailitis, O. Lielausis, E. Platacis, S. Dementiev, A. Cifersons, G. Gerbeth, Th. Gundrum, F. Stefani, M. Christen, G. Will, Phys. Rev. Lett. 86, 3024 (2001)
F. Ravelet, A. Chiffaudel, F. Daviaud, J. Léorat, Phys. Fluids, submitted
G.R. Sarson, D. Gubbins, J. Fluid Mech. 306, 223 (1996)
R. Kaiser, A. Tilgner, Phys. Rev. E 60, 2949 (1999)
P. Frick, V. Noskov, S. Denisov, S. Khripchenko, D. Sokoloff, R. Stepanov, A. Sukhanovsky, Magnetohydrodynamics 38, 143 (2002)
G. Schubert, K. Zhang, Astrophys. J. 557, 930 (2001)
R. Hollerbach, C.A. Jones, Phys. Earth Planet. In. 87, 171 (1995)
J. Wicht, Phys. Earth Planet. In. 132, 281 (2002)
J.-C. Thelen, F. Cattaneo, Mon. Not. R. Astron. Soc. 315, 13 (2000)
F. Plunian, P. Marty, A. Alemany, J. Fluid Mech. 382, 137 (1999)
J. Soto, Ph.D. thesis, I.N.P.G., 1999
F. Plunian, K.-H. Rädler, Geophys. Astro. Fluid Dyn. 96 2, 115 (2002)
K.-H. Rädler, M. Rheinhardt, E. Apstein, H. Fuchs, Nonlin. Proc. Geoph. 9, 171 (2002)
F. Krause, K.-H. Rädler, Mean-Field Magnetohydrodyna- mics and Dynamo Theory (Akademie-Verlag, Berlin, 1980)
S. Fauve, F. Pétrélis, in Peyresp lectures on nonlinear phenomena, edited by J. Sepulchre (World Scientific, 2003), pp. 1–64
A. Martin, P. Odier, J.-F. Pinton, S. Fauve, Eur. Phys. J. B 18, 337 (2000)
P. Frick, S. Khripchenko, S. Denisov, J.-F. Pinton, D. Sokoloff, Eur. Phys. J. B 25, 399 (2002)
L. Landau, E. Lifchitz, Electrodynamique des milieux continus (Ed. MIR, Moscou, 1969)
W.V.R. Malkus, M.R.E. Proctor, J. Fluid Mech. 67, 417 (1975)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Avalos-Zuñiga, R., Plunian, F. Influence of inner and outer walls electromagnetic properties on the onset of a stationary dynamo. Eur. Phys. J. B 47, 127–135 (2005). https://doi.org/10.1140/epjb/e2005-00294-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2005-00294-0