Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T11:32:58.788Z Has data issue: false hasContentIssue false
  • English
  • Français

Bistability between a stationary and an oscillatory dynamo in a turbulent flow of liquid sodium

Published online by Cambridge University Press:  16 November 2009

M. BERHANU ,
B. GALLET ,
R. MONCHAUX ,
M. BOURGOIN ,
PH. ODIER ,
J.-F. PINTON ,
N. PLIHON ,
R. VOLK ,
S. FAUVE  and
N. MORDANT
...Show all authors
M. BERHANU
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
B. GALLET
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
R. MONCHAUX
Affiliation:
Service de Physique de l'État Condensé, Direction des Sciences de la Matière CNRS URA 2464, CEA-Saclay, F-91191 Gif-sur-Yvette, France
M. BOURGOIN
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR5672, 46 allée d'Italie, F-69364 Lyon, France
PH. ODIER
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR5672, 46 allée d'Italie, F-69364 Lyon, France
J.-F. PINTON
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR5672, 46 allée d'Italie, F-69364 Lyon, France
N. PLIHON
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR5672, 46 allée d'Italie, F-69364 Lyon, France
R. VOLK
Affiliation:
Laboratoire de Physique, École Normale Supérieure de Lyon, CNRS UMR5672, 46 allée d'Italie, F-69364 Lyon, France
S. FAUVE*
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
N. MORDANT
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
F. PÉTRÉLIS
Affiliation:
Laboratoire de Physique Statistique, École Normale Supérieure CNRS UMR8550, 24 rue Lhomond, F-75005 Paris, France
S. AUMAÎTRE
Affiliation:
Service de Physique de l'État Condensé, Direction des Sciences de la Matière CNRS URA 2464, CEA-Saclay, F-91191 Gif-sur-Yvette, France
A. CHIFFAUDEL
Affiliation:
Service de Physique de l'État Condensé, Direction des Sciences de la Matière CNRS URA 2464, CEA-Saclay, F-91191 Gif-sur-Yvette, France
F. DAVIAUD
Affiliation:
Service de Physique de l'État Condensé, Direction des Sciences de la Matière CNRS URA 2464, CEA-Saclay, F-91191 Gif-sur-Yvette, France
B. DUBRULLE
Affiliation:
Service de Physique de l'État Condensé, Direction des Sciences de la Matière CNRS URA 2464, CEA-Saclay, F-91191 Gif-sur-Yvette, France
F. RAVELET
Affiliation:
Service de Physique de l'État Condensé, Direction des Sciences de la Matière CNRS URA 2464, CEA-Saclay, F-91191 Gif-sur-Yvette, France
*
Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We report the first experimental observation of a bistable dynamo regime. A turbulent flow of liquid sodium is generated between two disks in the von Kármán geometry (VKS experiment). When one disk is kept at rest, bistability is observed between a stationary and an oscillatory magnetic field. The stationary and oscillatory branches occur in the vicinity of a codimension-two bifurcation that results from the coupling between two modes of magnetic field. We present an experimental study of the two regimes and study in detail the region of bistability that we understand in terms of dynamical system theory. Despite the very turbulent nature of the flow, the bifurcations of the magnetic field are correctly described by a low-dimensional model. In addition, the different regimes are robust; i.e. turbulent fluctuations do not drive any transition between the oscillatory and stationary states in the region of bistability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 217 - 226
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Present address: ENSTA-UME, chemin de la Hunière, 91761 Palaiseau Cedex, France

‡

Present address: LEGI, CNRS UMR 5519, BP53, F-38041 Grenoble, France

‖

Present address: LEMFI, ENSAM, 151 bld de l'Hôpital, 75013 Paris, France

References

REFERENCES

Arnold, V. 1982 Geometrical Methods in the Theory of Ordinary Differential Equations. Springer.Google Scholar
Berhanu, M. 2008. Magnétohydrodynamique turbulente dans les métaux liquides. PhD thesis, Université Pierre et Marie Curie, Paris, p. 105.Google Scholar
Berhanu, M., Monchaux, R., Fauve, S., Mordant, N., Pétrélis, F., Chiffaudel, A., Daviaud, F., Dubrulle, B., Marié, L., Ravelet, F., Bourgoin, M., Odier, Ph., Pinton, J.-F. & Volk, R. 2007 Magnetic field reversals in an experimental turbulent dynamo. Europhys. Lett. 77, 59001.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.Google Scholar
Chiffaudel, A. & Fauve, S. 1987 Strong resonance in forced oscillatory convection. Phys. Rev. A 35, 4004–4007.CrossRefGoogle ScholarPubMed
Christensen, U. R., Olson, P. & Glatzmaier, G. A. 1999 Numerical modelling of the geodynamo: a systematic parameter study. Geophys. J. Intl 138, 393–409.CrossRefGoogle Scholar
Cortet, P.-P., Diribarne, P., Monchaux, R., Chiffaudel, A., Daviaud, F. & Dubrulle, B. 2009 Normalized kinetic energy as a hydrodynamical global quantity for inhomogeneous anisotropic turbulence. Phys. Fluids 21, 025104.CrossRefGoogle Scholar
Coullet, P. 1986 Commensurate-incommensurate transition in nonequilibrium systems. Phys. Rev. Lett. 56, 724–727.CrossRefGoogle ScholarPubMed
Fuchs, H., Rädler, K.-H. & Rheinhardt, M. 2001 Suicidal and parthenogenetic dynamos. In Dynamo and Dynamics, a Mathematical Challenge (ed. Chossat, P., Armbuster, D. & Oprea, I.), pp. 339–347. Kluwer Academic.CrossRefGoogle Scholar
Gailitis, A., Lielausis, O., Platacis, E., Dement'ev, S., Cifersons, A., Gerbeth, G., Gundrum, T., Stefani, F., Christen, M. & Will, G. 2001 Magnetic field saturation in the Riga dynamo experiment. Phys. Rev. Lett. 86, 3024–3027.CrossRefGoogle ScholarPubMed
Gambaudo, J. M. 1985 Perturbation of a Hopf bifurcation by an external time-periodic forcing. J. Diff. Eq. 57, 172–199.CrossRefGoogle Scholar
Giesecke, A., Nore, C., Plunian, F., Laguerre, R., Ribeiro, A., Stefani, F., Gerbeth, G., Léorat, J. & Guermond, J.-L. 2009 a Generation of axisymmetric modes in cylindrical kinematic mean-field dynamos of VKS type. Geophys. Astrophys. Fluid Dyn. In press.CrossRefGoogle Scholar
Giesecke, A., Stefani, F. & Gerbeth, G. 2009 b Role of soft-iron impellers on the mode selection in the VKS dynamo experiment. Phys. Rev. Lett. Submitted.CrossRefGoogle Scholar
Gissinger, C. 2009 A numerical model of the VKS experiment. Europhys. Lett. 87, 39002.CrossRefGoogle Scholar
Guckenheimer, J. & Holmes, P. 1986 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer.Google Scholar
Laguerre, R., Nore, C., Ribeiro, A., Léorat, J., Guermond, J.-L. & Plunian, F. 2008 Impact of impellers on the axisymmetric magnetic mode in the VKS2 dynamo experiment. Phys. Rev. Lett. 101, 104501, 219902.CrossRefGoogle ScholarPubMed
Monchaux, R., Berhanu, M., Aumaître, S., Chiffaudel, A., Daviaud, F., Dubrulle, B., Ravelet, F., Fauve, S., Mordant, N., Pétrélis, F., Bourgoin, M., Odier, Ph., Pinton, J.-F., Plihon, N. & Volk, R. 2009 The von Kármán sodium experiment: turbulent dynamical dynamos. Phys. Fluids 21, 035108.CrossRefGoogle Scholar
Monchaux, R., Berhanu, M., Bourgoin, M., Moulin, M., Odier, Ph., Pinton, J.-F., Volk, R., Fauve, S., Mordant, N., Pétrélis, F., Chiffaudel, A., Daviaud, F., Dubrulle, B., Gasquet, C. & Marié, L. 2007 Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. Phys. Rev. Lett. 98, 044502.CrossRefGoogle Scholar
Morin, V. 2005 Instabilités et bifurcations associées à la modélisation de la Géodynamo. PhD thesis, Université Pierre et Marie Curie. Paris.Google Scholar
Morin, V. & Dormy, E. 2009 Weak and strong field dynamos. Phys. Rev. Lett. Submitted.Google Scholar
Pétrélis, F. & Fauve, S. 2008. Chaotic dynamics of the magnetic field generated by dynamo action in a turbulent flow. J. Phys. Condens. Matt. 20, 494203.CrossRefGoogle Scholar
Pétrélis, F., Fauve, S., Dormy, E. & Valet, J.-P. 2009 A simple mechanism for the reversals of Earth's magnetic field. Phys. Rev. Lett. 102, 144503.CrossRefGoogle ScholarPubMed
Pétrélis, F., Mordant, N. & Fauve, S. 2007 On the magnetic fields generated by experimental dynamos. Geophys. Astrophys. Fluid Dyn. 101, 289–323.CrossRefGoogle Scholar
Ponty, Y., Laval, J.-P., Dubrulle, B., Daviaud, F. & Pinton, J.-F. 2007 Subcritical dynamo bifurcation in the Taylor–Green flow. Phys. Rev. Lett. 99, 224501.CrossRefGoogle ScholarPubMed
Ravelet, F., Berhanu, M., Monchaux, R., Bourgoin, M., Odier, Ph., Pinton, J.-F., Plihon, N., Volk, R., Fauve, S., Mordant, N., Pétrélis, F., Aumaître, S., Chiffaudel, A., Daviaud, F., Dubrulle, B. & Marié, L. 2008 Chaotic dynamos generated by a turbulent flow of liquid sodium. Phys. Rev. Lett. 101, 074502.CrossRefGoogle ScholarPubMed
Ravelet, F., Marié, L., Chiffaudel, A. & Daviaud, F. 2004 Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation. Phys. Rev. Lett. 93, 164501.CrossRefGoogle Scholar
Rincon, F., Ogilvie, G. I. & Proctor, M. R. E. 2007 Self-sustaining nonlinear dynamo process in Keplerian shear flows. Phys. Rev. Lett. 98, 254502.CrossRefGoogle ScholarPubMed
Roberts, P. H., 1978 Magneto-convection in a rapidly rotating fluid. In Rotating Fluids in Geophysics (ed. Roberts, P. H. & Soward, A. M.), pp. 421–435. Academic.Google Scholar
Stieglitz, R. & Müller, U. 2001 Experimental demonstration of a homogeneous two-scale dynamo. Phys. Fluids 13, 561–564.CrossRefGoogle Scholar