Acta Mechanica

, Volume 215, Issue 1–4, pp 1–8 | Cite as

Magnetic spherical Couette flow in linear combinations of axial and dipolar fields

Article

Abstract

We present axisymmetric numerical calculations of the fluid flow induced in a spherical shell with inner sphere rotating and outer sphere stationary. A magnetic field is also imposed, consisting of particular linear combinations of axial and dipolar fields, chosen to make Br = 0 at either the outer sphere, or the inner, or in between. This leads to the formation of Shercliff shear layers at these particular locations. We then consider the effect of increasingly large inertial effects and show that an outer Shercliff layer is eventually destabilized, an inner Shercliff layer appears to remain stable, and an in-between Shercliff layer is almost completely disrupted even before the onset of time-dependence, which does eventually occur though.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hollerbach R.: Magnetohydrodynamic Ekman and Stewartson layers in a rotating spherical shell. Proc. R. Soc. Lond. A 444, 333–346 (1994)MATHCrossRefGoogle Scholar
  2. 2.
    Sisan D.R., Mujica N., Tillotson W.A., Huang Y.M., Dorland W., Hassam A.B., Antonsen T.M., Lathrop D.P.: Experimental observation and characterization of the magnetorotational instability. Phys. Rev. Lett. 93, 0114502 (2004)CrossRefGoogle Scholar
  3. 3.
    Nataf H.-C., Alboussiere T., Brito D., Cardin P., Gagniere N., Jault D., Masson J.-P., Schmitt D.: Experimental study of super-rotation in a magnetostrophic spherical Couette flow. Geophys. Astrophys. Fluid Dyn. 100, 281–298 (2006)CrossRefGoogle Scholar
  4. 4.
    Schmitt D., Alboussiere T., Brito D., Cardin P., Gagniere N., Jault D., Nataf H.-C.: Rotating spherical Couette flow in a dipolar magnetic field: experimental study of magneto-inertial waves. J. Fluid Mech. 604, 175–197 (2008)MATHCrossRefGoogle Scholar
  5. 5.
    Starchenko S.V.: Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field. J. Exp. Theor. Phys. 85, 1125–1137 (1997)CrossRefGoogle Scholar
  6. 6.
    Starchenko S.V.: Magnetohydrodynamic flow between insulating shells rotating in strong potential field. Phys. Fluids 10, 2412–2420 (1998)CrossRefGoogle Scholar
  7. 7.
    Dormy E., Cardin P., Jault D.: MHD flow in a slightly differentially rotating spherical shell with conducting inner core in a dipolar magnetic field. Earth Planet. Sci. Lett. 160, 15–30 (1998)CrossRefGoogle Scholar
  8. 8.
    Dormy E., Jault D., Soward A.M.: A super-rotating shear layer in magnetohydrodynamic spherical Couette flow. J. Fluid Mech. 452, 263–291 (2002)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Mizerski K.A., Bajer K.: On the effect of mantle conductivity on the super-rotating jets near the liquid core surface. Phys. Earth Planet. Inter. 160, 245–268 (2007)CrossRefGoogle Scholar
  10. 10.
    Hollerbach R.: Magnetohydrodynamic flows in spherical shells. In: Egbers, C., Pfister, G. (eds) Physics of rotating fluids. Lecture notes in physics, Vol. 549, pp. 295–316. Springer, Dordrecht (2000)Google Scholar
  11. 11.
    Buhler L.: On the origin of super-rotating layers in magnetohydrodynamic flows. Theor. Comp. Fluid Dyn. 23, 491–507 (2009)CrossRefGoogle Scholar
  12. 12.
    Hollerbach R., Skinner S.: Instabilities of magnetically induced shear layers and jets. Proc. R. Soc. Lond. A 457, 785–802 (2001)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hollerbach R.: Super- and counter-rotating jets and vortices in strongly magnetic spherical Couette flow. In: Chossat, P., Armbruster, D., Oprea, J. (eds) Dynamo and dynamics, a mathematical challenge. NATO science series II, Vol. 26, pp. 189–197. Springer, Dordrecht (2001)Google Scholar
  14. 14.
    Roberts P.H.: Singularities of Hartmann layers. Proc. R. Soc. Lond. A 300, 94–107 (1967)MATHCrossRefGoogle Scholar
  15. 15.
    Loper D.E.: General solution for the linearised Ekman–Hartmann layer on a spherical boundary. Phys. Fluids 12, 2995–2998 (1970)CrossRefGoogle Scholar
  16. 16.
    Wei X., Hollerbach R.: Instabilities of Shercliff and Stewartson layers in spherical Couette flow. Phys. Rev. E 78, 026309 (2008)CrossRefGoogle Scholar
  17. 17.
    Hollerbach R.: Non-axisymmetric instabilities in magnetic spherical Couette flow. Proc. R. Soc. Lond. A 465, 2003–2013 (2009)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Hollerbach R., Canet E., Fournier A.: Spherical Couette flow in a dipolar magnetic field. Eur. J. Mech. B 26, 729–737 (2007)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Hollerbach R.: A spectral solution of the magneto-convection equations in spherical geometry. Int. J. Numer. Methods Fluids 32, 773–797 (2000)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Cowling T.G.: Magnetohydrodynamics. Interscience, New York (1957)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institute of Geophysics, ETHZürichSwitzerland
  2. 2.Department of Applied MathematicsUniversity of LeedsLeedsUK

Personalised recommendations