Magnetoconvection in a rapidly rotating sphere: The weak-field case

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

Volumn 459, Issue 2031, 2003, Pages 773-797

  Jones, C A ^a   Mussa, A I ^a,b   Worland, S J ^a  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b KING ABDULAZIZ CITY FOR SCIENCE AND TECHNOLOGY   (Saudi Arabia)

Author keywords

Columnar rolls; Magnetoconvection; Rotating sphere

Indexed keywords

ARTICLE; MAGNETIC FIELD; MAGNETISM; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICS; PHYSICS; ROTATION; THERMODYNAMICS;

EID: 1542327527     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2002.1048     Document Type: Article

References (26)

1. Brito, D., Nataf, H.-C., Cardin, P., Aubert, J. & Masson, J.-P. 2001 Ultrasonic Doppler velocimetry in liquid gallium. Expts Fluids 31, 653-663.
2. Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441-460.
3. Cardin, P. & Olson, P. 1995 The influence of toroidal magnetic field on thermal convection in the core. Earth Planet. Sci. Lett. 132, 167-181.
4. Eltayeb, I. A. 1972 Hydromagnetic convection in a rapidly rotating fluid layer. Proc. R. Soc. Lond. A 326, 229-254.
5. Eltayeb, I. A. 1992 The propagation and stability of linear wave motions in rapidly rotating spherical shells: weak magnetic fields. Geophys. Astrophys. Fluid Dynam. 67, 211-239.
6. Eltayeb, I. A. & Kumar, S. 1977 Hydromagnetic convection instability of a rotating, self-gravitating fluid sphere containing a uniform distribution of heat sources. Proc. R. Soc. Lond. A 353, 145-162.
7. Fearn, D. R. 1979a Thermally driven hydromagnetic convection in a rapidly rotating sphere. Proc. R. Soc. Lond. A 369, 227-242.
8. Fearn, D. R. 1979b Thermal and magnetic instabilities in a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dynam. 14, 103-126.
9. 2Ω-dynamo waves in stellar shells. Geophys. Astrophys. Fluid Dynam. 94, 85-133.
10. Gubbins, D. & Zhang, K. 1993 Symmetry properties of the dynamo equations for paleomagnetism and geomagnetism. Phys. Earth Planet. Inter. 75, 225-241.
11. Hollerbach, R. 2000 A spectral solution of the magnetoconvection equations in spherical geometry. Int. J. Numer. Meth. Fluids 32, 773-797.
12. Jones, C. A., Soward, A. M. & Mussa, A. I. 2000 The onset of thermal convection in a rapidly rotating sphere. J. Fluid Mech. 405, 157-179.
13. Malkus, W. V. R. 1967 Hydromagnetic planetary waves. J. Fluid Mech. 28, 793-802.
14. Proctor, M. R. E. 1994 Convection and magnetoconvection in a rapidly rotating sphere. Lectures on solar and planetary dynamos (ed. M. R. E. Proctor & A. D. Gilbert), pp. 97-115. Cambridge University Press.
15. Roberts, P. H. 1968 On the thermal instability of a rotating fluid sphere containing heat sources. Phil Trans. R. Soc. Lond. A 263, 93-117.
16. Soward, A. M. 1979 Thermal and magnetically driven convection in a rapidly rotating fluid layer. Geophys. Astrophys. Fluid Dynam. 90, 669-684.
17. Soward, A. M. & Jones, C. A. 1983 The linear stability of the flow in the narrow gap between two concentric rotating spheres. Q. J. Mech. Appl. Math. 36, 19-42.
18. Zhang, K. 1992 Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech. 236, 535-556.
19. Zhang, K. 1993 On equatorially trapped boundary inertial waves. J. Fluid Mech. 248, 203-217.
20. Zhang, K. 1994 On coupling between the Poincaré equation and the heat equation. J. Fluid Mech. 268, 211-229.
21. Zhang, K. 1995 Spherical shell rotating convection in the presence of a toroidal magnetic field. Proc. R. Soc. Lond. A 448, 245-268.
22. Zhang, K. & Busse, F. H. 1995 On the hydrodynamic instabilities driven by the Hartmann boundary layer in a rapidly rotating sphere. J. Fluid Mech. 304, 263-283.
23. Zhang, K. & Fearn, D. R. 1994 Hydromagnetic waves in rapidly rotating spherical shells generated by magnetic toroidal decay rates. Geophys. Astrophys. Fluid Dynam. 77, 133-157.
24. Zhang, K. & Jones, C. A. 1993 The influence of Ekman boundary layers on rotating convection. Geophys. Astrophys. Fluid Dynam. 71, 145-163.
25. Zhang, K. & Jones, C. A. 1996 On small Roberts number magnetoconvection in rapidly rotating systems. Proc. R. Soc. Lond. A 452, 981-995.
26. Zhang, K. & Schubert, G. 2000 Magnetohydrodynamics in rapidly rotating spherical systems. A. Rev. Fluid Mech. 32, 409-443.