The structure of Taylor's constraint in three dimensions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 464, Issue 2100, 2008, Pages 3149-3174

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

^a UNIVERSITY OF CALIFORNIA   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Magnetostrophic balance; Taylor state; Taylor's constraint

Indexed keywords

ELECTRIC GENERATORS; ELECTROMAGNETIC FIELD EFFECTS; HARMONIC ANALYSIS; HELIUM; MAGNETIC FIELD EFFECTS; MAGNETIC FIELDS; PROGRAMMABLE LOGIC CONTROLLERS; ROTATION;

ANALYTIC; AZIMUTHAL COMPONENTS; COAXIAL; CONDUCTING FLUIDS; DYNAMICAL BALANCES; DYNAMO ACTIONS; EARTH'S CORES; GEODYNAMO; GEOSTROPHIC CONTOURS; INFINITE NUMBERS; INNER CORES; MAGNETOSTROPHIC BALANCE; SPECTRAL EXPANSIONS; SPHERICAL HARMONIC BASES; TAYLOR STATE; TAYLOR'S CONSTRAINT; THREE DIMENSIONS;

LORENTZ FORCE;

EID: 54849405932     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0091     Document Type: Article

References (29)

1. Backus, G., Parker, R. & Constable, C. 1996 Foundations of geomagnetism. Cambridge, UK: Cambridge University Press.
2. Boyd, J. P. 2001 Chebyshev and Fourier spectral methods. New York, NY: Dover.
3. Braginsky, S. I. 1970 Torsiorial magnetohydrodynamic vibrations in the earth's core and variations in the length of day. Geomag. Aeron. 10, 1-10.
4. Bullard, E. C. & Gellman, H. 1954 Homogeneous dynamos and terrestrial magnetism. Phil. Trans. R. Soc. A 247, 213-278. (doi:10.1098/rsta.1954.0018)
5. Dumberry, M. & Bloxham, J. 2003 Torque balance, Taylor's constraint and torsiorial oscillations in a numerical model of the geodynamo. Phys. Earth Planet. Int. 140, 29-51. (doi:10.1016/ j.popi.2003.07.012)
6. Fearn, D. 1994 Nonlinear planetary dynamos. In Lectures on solar and planetary dynamos (eds M. R. E. Proctor & A. D. Gilbert), pp. 219-244. Cambridge, UK: Cambridge University Press.
7. Fearn, D. 1998 Hydromagnetic flow in planetary cores. Rep. Prog. Phys. 61, 175-235. (doi:10.1088/ 0034-4885/61/3/001)
8. Fearn, D. & Proctor, M. R. E. 1987 Dynamically consistent magnetic fields produced by differential rotation. J. Fluid Mech. 178, 521-534. (doi:10.1017/S0022112087001356)
9. Gubbins, D. & Zhang, K. 1993 Symmetry properties of the dynamo equations for paleomagnctism and geomagnetism. Phys. Earth Planet. Int. 75, 225-241. (doi:10.1016/0031-9201(93)90003-R)
10. Hollerbach, R. 1990 α-effect dynamos and Taylor's constraint in the asymptotic limit of small viscosity. PhD thesis, University of California San Diego, USA.
11. Hollerbach, R. 2000 A spectral solution of the magneto-convection equations in spherical geometry. Int. J. Numer. Methods Fluids 32, 773 797. (doi:10.1002/(SICI)1097-0363(20000415)32:7〈 773::AID- FLD988〉3.0.CO;2-P)
12. 2-dynamo in the limit of asymptotically small viscosity. Geophys. Astrophys. Fluid Dyn. 56, 133-158. (doi:10.1080/03091929108219515)
13. Hollerbach, R. & Jones, C. A. 1993 Influence of the Earth's inner core on geomagnetic fluctuations and reversals. Nature 365, 541-543. (doi:10.1038/365541a0)
14. 2 dynamos. Geophys. Astrophys. Fluid Dyn. 34, 143-173. (doi:10.1080/03091928508245441)
15. Jackson, A. 1997 Time-dependency of tarigeritially geostrophic core surface motions. Phys. Earth Planet. Int. 103, 293-311. (doi:10.1016/S0031-9201(97)00039-3)
16. Jault, D. 1995 Model Z by computation and Taylor's condition. Geophys. Astrophys. Fluid Dyn. 79, 99-124. (doi: 10.1080/03091929508228993)
17. Jault, D. & Cardin, P. 1999 On dynamic geodynamo models with imposed velocity as energy source. Phys. Earth Planet. Int. 111, 75-81. (doi:10.1016/S0031-9201(98)00147-2)
18. 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. (doi:10.1038/333353a0)
19. Kono, M. & Roberts, P. H. 2002 Recent geodynamo simulations and observations of the geomagnetic field. Rev. Geophys. 40, 1013. (doi:10.1029/2000RG00102)
20. Lewis, H. R. & Bellan, P. M. 1990 Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates. J. Math. Phys. 31, 2592-2596. (doi:10.1063/1.529009)
21. Livermore, P. In preparation. Generalized exponentially convergent orthogonal polynomials.
22. Malkus, W. V. R. & Proctor, M. R. E. 1975 The macrodynamics of α-effect dynamos in rotating fluids. J. Fluid Mech. 67, 417-443. (doi:10.1017/S0022112075000390)
23. Olsen, N., Hulot, G. & Sabaka, T. J. 2007 The present field. In Treatise on geophysics (ed. G. Schubert). Amsterdam, The Netherlands: Elsevier.
24. Rochester, M. G. 1962 Geomagnetic core-mantle coupling. J. Geophys. Res. 67, 4833-4836. (doi:10.1029/JZ067i012p04833)
25. Rotvig, J. & Jones, C. A. 2002 Rotating convection-driven dynamos at low Ekman number. Phys. Rev. E 66, 056 308. (doi:10.1103/PhysRevE. 66.056308)
26. Smylic, D. E. & Rochester, M. G. 1984 The dynamics of the Earth's inner and outer cores. Rep. Prog. Phys. 47, 855-906. (doi:10.1088/0034-4885/47/7/002)
27. 2-dyriarnos and Taylor's constraint. Geophys. Astrophys. Fluid Dyn. 27, 87-122. (doi:10.1080/03091928308210122)
28. Taylor, J. B. 1963 The magneto-hydrodynamics of a rotating fluid and the Earth's dynamo problem. Proc. R. Soc. A 9, 274 283. (doi:10.1098/rspa.1963.0130)
29. Walker, M. R. & Barenghi, C. F. 1998 Accurate numerical computations of Taylor integrals. Geophys. Astrophys. Fluid Dyn. 87, 173-191. (doi:10.1080/03091929808221146)