20
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

The influence of deferential rotation on magnetic instability, and nonlinear magnetic instability in the magnetostrophic limit

, , &
Pages 173-200 | Received 09 Sep 1996, Accepted 07 Mar 1997, Published online: 01 Dec 2006

References

  • Abramowitz , M. and Stegun , I. A. 1965 . Handbook of Mathematical Functions , New York : Dover .
  • Acheson , D. J. 1972 . “On the hydromagnetic stability of a rotating fluid annulus,” . J. Fluid Mech. , 52 : 529 – 541 .
  • Acheson , D. J. 1973 . “Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid,” . J. Fluid Mech. , 61 : 609 – 624 .
  • Acheson , D. J. 1983 . “Local analysis of thermal and magnetic instabilities in a rapidly rotating fluid,” . Geophys. Astrophys. Fluid Dynam. , 27 : 123 – 136 .
  • Bloxham , J. and Jackson , A. 1992 . “Time-dependent mapping of the magnetic field at the core-mantle boundary,” . J. Geophys. Res. , 97 : 19537 – 19563 .
  • Courtillot , V. and Le Mouël , J.-L. 1988 . “Time variations of the Earth's magnetic field: from daily to secular,” . Ann. Rev. Earth Planet. Sci. , 16 : 389 – 476 .
  • Fearn , D. R. 1983a . “Boundary conditions for a rapidly rotating hydromagnetic system in a cylindrical container,” . Geophys. Astrophys. Fluid Dynam. , 25 : 65 – 75 .
  • Fearn , D. R. 1983b . “Hydromagnetic waves in a differentially rotating annulus L A test of local stability analysis,” . Geophys. Astrophys. Fluid Dynam. , 27 : 137 – 162 .
  • Fearn , D. R. 1984 . “Hydromagnetic waves in a differentially rotating annulus II. Resistive instabilities,” . Geophys. Astrophys. Fluid Dynam. , 30 : 227 – 239 .
  • Fearn , D. R. 1985 . “Hydromagnetic waves in a differentially rotating annulus III. The effect of an axial field.” . Geophys. Astrophys. Fluid Dynam. , 33 : 185 – 197 .
  • Fearn , D. R. 1988 . “Hydromagnetic waves in a differentially rotating annulus IV. Insulating boundaries,” . Geophys. Astrophys. Fluid Dynam. , 44 : 55 – 15 .
  • Fearn , D. R. 1993 . “Magnetic instabilities in rapidly rotating systems,” . In Solar and Planetary Dynamos , Edited by: Proctor , M. R. E. , Matthews , P. C. and Rucklidge , A. M. 59 – 68 . CUP .
  • Fearn , D. R. 1994 . “Nonlinear planetary dynamos,” . In Lectures on Solar and Planetary Dynamos , Edited by: Proctor , MS. M. R. E. and Gilbert , A. D. 219 – 244 . CUP . Chapter 7
  • Fearn , D. R. 1997 . “The geodynamo,” . In Earth's Deep Interior. , Edited by: Crosscley , D. 79 – 114 . Gordon and Breach .
  • Fearn , D. R. and Proctor , M. R. E. 1983a . “Hydromagnetic waves in a differentially rotating sphere,” . J. Fluid Mech. , 128 : 1 – 20 .
  • Fearn , D. R. and Proctor , M. R. E. 1983b . “The stabilising role of differential rotation on hydromagnetic waves,” . J. Fluid Mech. , 128 : 21 – 36 .
  • Fearn , D. K. and Weiglhofer , W. S. 1992 . “Magnetic instabilities in rapidly rotating spherical geometries III. The effect of differential rotation,” . Geophys. Astrophys. Fluid Dynam. , 67 : 163 – 184 .
  • Fearn , D. R. , Proctor , M. R. E. and Sellar , C. C. 1994 . “Nonlinear magnetoconvection in a rapidly rotating sphere and Taylor's constraint” . Geophys. Astrophys. Fluid Dynam. , 77 : 111 – 132 .
  • Glatzmaier , G. A. and Roberts , P. H. 1995a . “A three-dimensional self-consistent computer simulation of a geomagnetic field reversal,” . Nature , 377 : 203 – 209 .
  • Glatzmaier , G. A. and Roberts , P. H. 1995b . “A three-dimensional convective dynamo solution with rotating and finitely conducting inner core and mantle,” . Phys. Earth Planet. Inter. , 91 : 63 – 75 .
  • Hoffman , K. A. 1992 . “Dipolar reversal states of the geomagnetic field and core mantle dynamics,” . Nature , 359 : 189 – 794 .
  • Hutchecon , K. A. and Fearn , D. R. 1995a . “The nonlinear evolution of magnetic instabilities in a rapidly rotating annulus,” . J. Fluid Mech. , 291 : 343 – 368 .
  • Hutcheson , K. A. and Fearn , D. R. 1995b . “Nonlinear stability of the geomagnetic field,” . Geophys. Res. Lett. , 22 : 1637 – 1640 .
  • Hutcheson , K. A. and Fearn , D. R. 1996 . “The stability of toroidal magnetic fields with equztorial symmetry: implication for the Earth's magnetic field,” . Phys. Earth Planet. Inter. , 97 : 43 – 54 .
  • Hutcheson , K. A. and Fearn , D. R. 1997 . “The stability of toroidal magnetic fields with equatorial symmetry: evolution of instabilities.” . Phys. Earth Planet. Inter. , 99 : 19 – 32 .
  • Jault , D. 1995 . “Model Z by computation and Taylor's condition,” . Geophys. Astrophys. Fluid Dynam. , 79 : 99 – 124 .
  • Jones , C. A. 1991 . “Dynamo models and Taylor's constraint,” . In Advances in Solar System Magnetohydrodynamics , Edited by: Priest , E. R. and Hood , A. W. 25 – 50 . CUP .
  • Jones , C. A. and Roberts , P. H. 1990 . “Magnetoconvection in rapidly rotating Boussinesq and compressible fluids,” . Geophys. Astrophys. Fluid Dynm. , 55 : 263 – 308 .
  • Lan , S. , Kuang , W. and Roberts , P. H. 1993 . “Ideal instabilities in rapidly rotating MHD systems that have critical layers,” . Geophys. Astrophys. Fluid Dym. , 69 : 133 – 160 .
  • Lanzerotti , L. J. , Chave , A. D. , Sayres , C. H. , Medford , L. V. and Maclennan , C. G. 1993 . “Large-scale electric field measurements on the Earth's surface: A review,” . J. Geophys. Res. , 98 : 23525 – 23534 .
  • Levy , E. H. and Pearce , S. J. 1991 . “Steady state toroidal magnetic field at the Earth's coremantle boundary,” . J. Geophys. Res. , 96 : 3935 – 3942 .
  • McFadden , P. L. and Merrill , R. T. 1993 . “Inhibition and geomagnetic field reversals,” . J. Geophys. Res. , 98 : 6189 – 6199 .
  • McLean , D. R. and Fcarn , D. R. 1996 . “Classification of magnetic instabilities” . Geophys. Astrophys. Fluid Dynam. , 82 : 221 – 236 .
  • Malkus , W. V. R. 1967 . “Hydromagnetic planetary waves,” . J. Fluid Mech. , 28 : 793 – 802 .
  • Michael , D. H. 1954 . “The stability of an incompressible electrically conducting fluid rotating about an axis when cumnt flows parallel to the axis,” . Mathemath. , 1 : 45 – 50 .
  • Ogden , R. R. and Fearn , D. R. 1995 . “The destabilising role of differential rotation,” . Geophys. Astrophys. Fluid Dynam. , 81 : 215 – 232 .
  • Skinner , P. H. and Soward , A. M. 1988 . “Convection in a rotating magnetic system and Taylor's constraint,” . Geophys. Astrophys. Fluid Dynam. , 44 : 91 – 116 .
  • Skinner , P. H. and Soward , A. M. 1990 . “Convection in a rotating magnetic system and Taylor's constraint II,” . Geophys. Astrophys. Fluid Dynam. , 60 : 335 – 356 .
  • Soward , A. M. 1991 . “The Earth's dynamo,” . Geophys. Astrophys. Fluid Dynam. , 62 : 191 – 209 .
  • Taylor , J. B. 1963 . “The magnetohydrodynamics of a rotating fluid and the Earth's dynamo problem,” . Proc R. Soc. Lond. , A274 : 274 – 283 .
  • Zhang , K. and Fearn , D. R. 1994 . “Hydromagnetic waves in rapidly rotating spherical shells, generated by toroidal decay modes,” . Geophys. Astrophys. Fluid Dynom. , 77 : 133 – 157 .
  • Zhang , K. and Fearn , D. R. 1995 . “Hydromagnetic waves in rapidly rotating spherical shells, generated by poloidal decay modes,” . Geophys. Astrophys. Fluid Dynam. , 81 : 193 – 209 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.