The construction of exact Taylor states. II: The influence of an inner core

Physics of the Earth and Planetary Interiors

Volumn 178, Issue 1-2, 2010, Pages 16-26

  Livermore, Philip W ^a   Ierley, Glenn R ^a   Jackson, Andrew ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Inner core; Taylor's constraint

Indexed keywords

AXISYMMETRIC; AXISYMMETRIC MODELS; CHARACTERISATION; EARTH'S CORE; EARTH'S MAGNETIC FIELD; GEODYNAMO; INNER CORE; LENGTH SCALE; MAGNETIC TORQUES; RADIAL BASIS; ROTATIONAL AXIS; SHELL GEOMETRY; SOLID ANGLE; SPHERICAL HARMONICS; TAYLOR STATE; TAYLOR'S CONSTRAINT; THEORETICAL DEVELOPMENT; TWO STAGE; UNDER-DETERMINED;

CYLINDERS (SHAPES); ELECTRIC GENERATORS; HARMONIC ANALYSIS; MAGNETIC FIELDS; MAGNETIC MATERIALS; SHELLS (STRUCTURES);

SPHERES;

GEODYNAMO; INNER CORE; MAGNETIC FIELD; MANTLE CONVECTION; NUMERICAL METHOD; SPHERICAL HARMONICS;

EID: 72049113844     PISSN: 00319201     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pepi.2009.07.015     Document Type: Article

References (29)

1. Aubert J., and Wicht J. Axial vs. equatorial dipolar dynamo models with implications for planetary magnetic fields. Earth Planet. Sci. Lett. 221 (2004) 409-419
2. Aurnou J., Andreadis S., Zhu L., and Olson P. Experiments on convection in Earth's core tangent cylinder. Earth Planet. Sci. Lett. 212 (2003) 119-134
3. Backus G., Parker R., and Constable C. Foundations of Geomagnetism (1996), CUP
4. Boyd J.P. Chebyshev and Fourier Spectral Methods (2001), Dover
5. Buffett B.A. The Thermal State of Earth's Core. Science 299 5613 (2003) 1675-1677
6. Christensen U., and Aubert J. Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Int. 166 (2006) 97-114
7. Fearn D. Hydromagnetic flow in planetary cores. Rep. Prog. Phys. 61 (1998) 175-235
8. Gropp, W., Moré, J., 1997. Optimization environments and the NEOS server, in: M.D. Buhmann, A. Iserles (Eds.), Approximation Theory and Optimization, pp. 167-182.
9. Gubbins D. The distinction between geomagnetic excursions and reversals. Geophys. J. Int. 137 (1999) F1-F3
10. Hollerbach R. Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell. Phys. Fluids 6 7 (1994) 2540-2544
11. Hollerbach R. A spectral solution of the magneto-convection equations in spherical geometry. Int. J. Numer. Methods Fluids 32 (2000) 773-797
12. 2-dynamo in the limit of asymptotically small viscosity. Geophys. Astrophys. Fluid Dyn. 56 (1991) 133-158
13. Hollerbach R., and Jones C.A. Influence of the Earth's inner core on geomagnetic fluctuations and reversals. Nature 365 (1993) 541-543
14. Hulot G., Eymin C., Langlais B., Mandea M., and Olsen N. Small-scale structure of the geodynamo inferred from ørsted and magsat data. Nature 416 (2002) 620-623
15. Jackson A., Jonkers A.R.T., and Walker M.R. Four centuries of geomagnetic secular variation from historical records. Philos. Trans. R. Soc. Lond. A 358 (2000) 957-990
16. Kageyama A., Miyagoshi T., and Sato T. Formation of current coils in geodynamo simulations. Nature 454 7208 (2008) 1106-1109
17. Kono M., and Roberts P.H. Recent geodynamo simulations and observations of the geomagnetic field. Rev. Geophys. 40 4 (2002) 1013
18. Livermore, P., 2009. A compendium of generalized orthogonal polynomials. Tech. rep., Scripps Institute of Oceanography, Available at http://repositories.cdlib.org/sio/techreport/98/.
19. Livermore, P., Ierley, G., in press. A new hypergeometric identity linking coefficients of a certain class of homogeneous polynomials motivated from magnetohydrodynamics. Adv. App. Math.
20. Livermore P., Ierley G., and Jackson A. The structure of Taylor's constraint in three dimensions. Proc. R. Soc. A 464 (2008) 3149-3174
21. Livermore, P., Ierley, G., Jackson, A., in press. The construction of exact Taylor states. I: The full sphere. Geophys. J. Int.
22. Olsen N., and Mandea M. Rapidly changing flows in the Earth's core. Nature Geoscience 1 (2008) 390-394
23. Rotvig J., and Jones C.A. Rotating convection-driven dynamos at low Ekman number. Phys. Rev. E 66 (2002) 056308-1-05630815-05630815
24. 2-Dynamos and Taylor's Constraint. Geophys. Astrophys. Fluid Dyn. 27 (1983) 87-122
25. Sreenivasan B., and Jones C.A. Structure and dynamics of the polar vortex in the earth's core. Geophys. Res. Lett. 32 (2005) 20301
26. Sreenivasan B., and Jones C.A. The role of inertia in the evolution of spherical dynamos. Geophys. J. Int. 164 (2006) 467-476
27. Takahashi F., Matsushima M., and Honkura Y. Simulations of a Quasi-Taylor state geomagnetic field including polarity reversals on the Earth simulator. Science 309 (2005) 459-461
28. Takahashi F., Matsushima M., and Honkura Y. Scale variability in convection-driven MHD dynamos at low Ekman number. Phys. Earth Planet. Int. 167 3-4 (2008) 168-178
29. Taylor J.B. The magneto-hydrodynamics of a rotating fluid and the Earth's dynamo problem. Proc. R. Soc. A 9 (1963) 274-283