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Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves

Published online by Cambridge University Press:  14 May 2008

DENYS SCHMITT ,
T. ALBOUSSIÈRE ,
D. BRITO ,
P. CARDIN ,
N. GAGNIÈRE ,
D. JAULT  and
H.-C. NATAF
DENYS SCHMITT
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
T. ALBOUSSIÈRE
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
D. BRITO
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
P. CARDIN
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
N. GAGNIÈRE
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
D. JAULT
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
H.-C. NATAF
Affiliation:
Laboratoire de Géophysique Interne et Tectonophysique, CNRS-UJF, BP 53, 38041 Grenoble Cedex 9, France
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Abstract

The magnetostrophic regime, in which Lorentz and Coriolis forces are in balance, has been investigated in a rapidly rotating spherical Couette flow experiment. The spherical shell is filled with liquid sodium and permeated by a strong imposed dipolar magnetic field. Azimuthally travelling hydromagnetic waves have been put in evidence through a detailed analysis of electric potential differences measured on the outer sphere, and their properties have been determined. Several types of wave have been identified depending on the relative rotation rates of the inner and outer spheres: they differ by their dispersion relation and by their selection of azimuthal wavenumbers. In addition, these waves constitute the largest contribution to the observed fluctuations, and all of them travel in the retrograde direction in the frame of reference bound to the fluid. We identify these waves as magneto-inertial waves by virtue of the close proximity of the magnetic and inertial characteristic time scales of relevance in our experiment.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 604 , 10 June 2008 , pp. 175 - 197
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Acheson, D. J. 1978 On the instability of toroidal magnetic fields and differential rotation in stars. Phil. Trans. R. Soc. Lond. A 289, 459–500.Google Scholar
Acheson, D. J. & Hide, R. 1973 Hydromagnetics of rotating fluids. Rep. Prog. Phys. 36, 159–221.CrossRefGoogle Scholar
Alfvén, H. 1942 Existence of electromagnetic-hydrodynamic waves. Nature 150, 405–406.CrossRefGoogle Scholar
Bloxham, J., Zatman, S. & Dumberry, M. 2002 The origin of geomagnetic jerks. Nature 420, 65–68.Google Scholar
Braginsky, S. 1970 Torsional magnetohydrodynamic vibrations in the earth's core and variations in day length. Geomag. Aeron. 10, 1–8.Google Scholar
Braginsky, S. I. 1980 Magnetic waves in the core of the earth. II. Geophys. Astrophys. Fluid Dyn. 14, 189–208.CrossRefGoogle Scholar
Cardin, P., Brito, D., Jault, D., Nataf, H.-C. & Masson, J.-P. 2002 Towards a rapidly rotating liquid sodium dynamo experiment. Magnetohydrodynamics 38, 177.Google Scholar
Dormy, E. & Mandea, M. 2005 Tracking geomagnetic impulses at the core mantle boundary. Earth Planet. Sci. Lett. 237, 300–309.CrossRefGoogle Scholar
Finlay, C. C. 2005 Hydromagnetic waves in Earth's core and their influence on geomagnetic secular variation. PhD thesis, University of Leeds.Google Scholar
Finlay, C. C. & Jackson, A. 2003 Equatorially dominated magnetic field change at the surface of Earth's core. Science 300, 2084–2086.CrossRefGoogle ScholarPubMed
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
Gailitis, A., Lielausis, O., Platacis, E., Gerbeth, G. & Stefani, F. 2003 The Riga dynamo experiment. Surveys Geophys. 24, 247–267.Google Scholar
Glatzmaier, G. A. & Roberts, P. H. 1996 Rotation and magnetism of Earth's inner core. Science 274, 1887–1891.CrossRefGoogle ScholarPubMed
Gubbins, D. & Roberts, P. 1987 Magnetohydrodynamics of the Earth's core. In Geomagnetism (ed. Jacobs, J. A.), vol. 2, pp. 1–184. Academic.Google Scholar
Hide, R. 1966 Free hydromagnetic oscillations of the earth's core and the theory of geomagnetic secular variation. Phil. Trans. R. Soc. Lond. A 259, 615–647.Google Scholar
Jameson, A. 1964 A demonstration of Alfvén waves. Part 1. Generation of standing waves. J. Fluid Mech. 19, 513–527.CrossRefGoogle Scholar
Jault, D. & Légaut, G. 2005 Alfvén waves within the Earth's core. In Fluid Dynamics and Dynamos in Astrophysics and Geophysics (ed. Soward, A. M., Jones, C. A., Hughes, D. W. & Weiss, N. O.), pp. 277–293. CRC Press, Boca Raton.Google Scholar
Jault, D., Gire, C. & Le Mouel, J. L. 1988 Westward drift, core motions and exchanges of angular momentum between core and mantle. Nature 333, 353–356.CrossRefGoogle Scholar
Kelley, D. H., Triana, S. A., Zimmerman, D. S., Brawn, B., Lathrop, D. P. & Martin, D. H. 2006 Driven inertial waves in spherical Couette flow. Chaos 16, 1105.CrossRefGoogle ScholarPubMed
Kelley, D. H., Triana, S. A., Zimmerman, D. S., Tilgner, A. & Lathrop, D. P. 2007 Inertial waves driven by differential rotation in a planetary geometry. Geophys. Astrophys. Fluid Dyn. 101, 469–487.CrossRefGoogle Scholar
Kitchatinov, L. L. & Ruediger, G. 1997 Global magnetic shear instability in spherical geometry. Mon. Not. R. Astr. Soc. 286, 757–764.CrossRefGoogle Scholar
Lehnert, B. 1954 a Magneto-hydrodynamic waves in liquid sodium. Phys. Rev. 94, 815–824.CrossRefGoogle Scholar
Lehnert, B. 1954 b Magnetohydrodynamic waves under the action of the Coriolis force. Astrophys. J. 119, 647.CrossRefGoogle Scholar
Lundquist, S. 1949 Experimental investigations of magneto-hydrodynamic waves. Phys. Rev. 76, 1805–1809.CrossRefGoogle Scholar
Malkus, W. V. R. 1967 Hydromagnetic planetary waves. J. Fluid Mech. 28, 793–802.Google Scholar
Monchaux, R., Berhanu, M., Bourgoin, M., Moulin, M., Odier, P., Pinton, J.-F., Volk, R., Fauve, S., Mordant, N., Pétrélis, F., Chiffaudel, A., Daviaud, F., Dubrulle, B., Gasquet, C., Marié, L. & Ravelet, F. 2007 Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. Phys. Rev. Lett. 98, 044502.CrossRefGoogle Scholar
Motz, R. O. 1966 Alfvén wave generation in a spherical system. Phys. Fluids 9, 411–412.CrossRefGoogle Scholar
Mueller, U., Stieglitz, R. & Horanyi, S. 2004 A two-scale hydromagnetic dynamo experiment. J. Fluid Mech. 498, 31–71.CrossRefGoogle Scholar
Nataf, H.-C., Alboussière, T., Brito, D., Cardin, P., Gagnière, N., Jault, D., Masson, J.-P. & Schmitt, D. 2006 Experimental study of super-rotation in a magnetostrophic spherical Couette flow. Geophys. Astrophys. Fluid Dyn. 100, 281–298.CrossRefGoogle Scholar
Nataf, H.-C., Alboussière, T., Brito, D., Cardin, P., Gagnière, N., Jault, D. & Schmitt, D. 2008 Rotating spherical Couette flow in a dipolar magnetic field: an experimental study of the mean axisymmetric flow. Phys. Earth Planet. Interi. (under revision).CrossRefGoogle Scholar
Reese, D., Rincon, F. & Rieutord, M. 2004 Oscillations of magnetic stars. II. Axisymmetric toroidal and non-axisymmetric shear Alfvén modes in a spherical shell. Astron. Astrophys. 427, 279–292.CrossRefGoogle Scholar
Roberts, P. 1967 An Introduction to Magnetohydrodynamics. Elsevier.Google Scholar
Roberts, P. H. & Soward, A. M. 1972 Magnetohydrodynamics of the Earth's core. Annu. Rev. Fluid Mech. 4, 117–154.CrossRefGoogle Scholar
Rüdiger, G., Hollerbach, R., Schultz, M. & Elstner, D. 2007 Destabilization of hydrodynamically stable rotation laws by azimuthal magnetic fields. Mon. Not. R. Astron. Soc. 377, 1481–1487.Google Scholar
Simitev, R. & Busse, F. H. 2005 Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells. J. Fluid Mech. 532, 365–388.CrossRefGoogle Scholar
Sisan, D. R., Shew, W. L. & Lathrop, D. P. 2003 Lorentz force effects in magneto-turbulence. Phys. Earth Planet. Inter. 135, 137–159.Google Scholar
Sisan, D. R., Mujica, N., Tillotson, W. A., Huang, Y.-M., Dorland, W., Hassam, A. B., Antonsen, T. M. & Lathrop, D. P. 2004 Experimental observation and characterization of the magnetorotational instability. Phys. Rev. Lett. 93, 114502.CrossRefGoogle ScholarPubMed
Spruit, H. C. 1999 Differential rotation and magnetic fields in stellar interiors. Astron. Astrophys. 349, 189–202.Google Scholar
Stefani, F., Gundrum, T., Gerbeth, G., Rüdiger, G., Schultz, M., Szklarski, J. & Hollerbach, R. 2006 Experimental evidence for magnetorotational instability in a Taylor–Couette flow under the influence of a helical magnetic field. Phys. Rev. Lett. 97, 184502.CrossRefGoogle Scholar
Stieglitz, R. & Mueller, U. 2001 Experimental demonstration of a homogeneous two-scale dynamo. Phys. Fluids 13, 561–564.Google Scholar
Zhang, K., Liao, X. & Schubert, G. 2003 Nonaxisymmetric instabilities of a toroidal magnetic field in a rotating sphere. Astrophys. J. 585, 1124–1137.Google Scholar