Kinematic dynamo action in a sphere: Effects of periodic time-dependent flows on solutions with axial dipole symmetry

Geophysical and Astrophysical Fluid Dynamics

Volumn 98, Issue 6, 2004, Pages 537-554

  Willis, Ashley P ^a   Gubbins, David ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Eigenvalue problems; Floquet theory; Geomagnetism; Kinematic dynamos; Time dependent stability

Indexed keywords

EARTH (PLANET); GEOMAGNETISM; KINEMATICS; MAGNETIC FIELD EFFECTS; MAGNETIC FLUX; OSCILLATIONS; STEADY FLOW;

DYNAMO ACTION; FLUX CONCENTRATION; OSCILLATORY FIELDS;

FLOW OF FLUIDS;

FLUID DYNAMICS; KINEMATICS; SPHERE;

EID: 10244222253     PISSN: 03091929     EISSN: None     Source Type: Journal    
DOI: 10.1080/03091920412331312402     Document Type: Article

References (20)

1. Arnoldi, W.E., "The principle of minimised iterations in the solution of the matrix eigenvalue problem", Q. J. Appl. Math. 9, 17-29 (1951).
2. Backus, G., "A class of self-sustaining dissipative spherical dynamos", Ann. Phys. 4, 372-447 (1958).
3. Braginsky, S.I., "Kinematic models of the Earth's hydrodynamic dynamo", Geomag. Aeron. 4, 572-583 (1964).
4. Brummell, N.H., Cattaneo, F. and Tobias, S.M., "Linear and nonlinear dynamo action", Phys. Lett. 249, 437-442 (1998).
5. Bullard, G.E. and Gellman, H., "Homogeneous dynamos and terrestrial magnetism", Phil. Trans. R. Soc. Lond. A250, 543-585 (1954).
6. Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wicht, J. and Zhang, K., "A numerical dynamo benchmark", Phys. Earth Planet. Inter. 128, 25-34 (2001).
7. Edwards, W.S., Tuckerman, L.S. Friesner, R.A. and Sorensen, D.C., "Krylov methods for the incompressible Navier-Stokes equations" , J. Comput. Phys. 110, 82-102 (1994).
8. Gog, J.R., Oprea, I., Proctor, M.R.E. and Rucklidge, A.M., "Destabilisation by noise of transverse perturbations to hetroclinic cycles: a simple model and an example from dynamo theory", Proc. R. Soc. Lond. A455, 4205-4222 (1999).
9. Gubbins, D. and Gibbons, S., "Three-dimensional dynamo waves in a sphere", Geophys. Astrophys. Fluid Dynam. 96, 481-498 (2002).
10. Gubbins, D. and Kelly, P., "Persistent patterns in the geomagnetic field over the past 2.5 Myr", Nature 365, 829-832 (1993).
11. Gubbins, D. and Sarson, G.R., "Geomagnetic field morphologies from a kinematic dynamo model", Nature 368, 51-55 (1994).
12. Gubbins, D., Barber, C.N., Gibbons, S. and Love, J.J., "Kinematic dynamo action in a sphere. I - Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry", Proc. R. Soc. Lond. A456, 1333-1353 (2000).
13. Gubbins, D., Barber, C.N., Gibbons, S. and Love, J.J., "Kinematic dynamo action in a sphere. II - Symmetry selection", Proc. R. Soc. Lond. A456, 1669-1683 (2000).
14. Kumar, S. and Roberts, P.H., A three-dimensional kinematic dynamo", Proc. R. Soc. Lond. A244, 235-258 (1975).
15. Lehoucq, R.B., Sorensen, D.C. and Yang, C., Arpack Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, Philadelphia, PA: SIAM (1998).
16. Livermore, P.W. and Jackson, A., "On magnetic energy instability in spherical stationary flows", Proc. R. Soc. Lond. A460, 1453-1476 (2004).
17. Sarson, G.R. and Gubbins, D., "Three-dimensional kinematic dynamos dominated by strong differential rotation", J. Fluid Mech. 306 223-265 (1996).
18. Sarson, G.R. and Jones, C.A., "A convection driven geodynamo reversal model", Phys. Earth Planet. Inter. 111, 3-20 (1999).
19. Verhulst, F., Nonlinear Differential Equations and Dynamical Systems Springer, Berlin (1996).
20. Wicht, J. and Olsen, P., "A detailed study of the polarity reversal mechanism in a numerical dynamo model", Geochem. Geophys. Geosyst. 5, No. 3, Q03H10 (2004).