Non-linear marginal convection in a rotating magnetic system

References

• Abramowitz , M. and Stegun , I. A. , eds. 1965 . Handbook of Mathematical Functions , New York : Dover Publications, Inc. .
   Google Scholar
• Acheson , D. J. 1983 . Local analysis of thermal and magnetic instabilities in a rapidly rotating fluid . Geophys. & Astrophys. Fluid Dyn. , 27 : 123 – 136 .
   Web of Science ®Google Scholar
• Braginsky , S. I. 1964a . Self-excitation of a magnetic field during the motion of a highly conducting fluid . JETP , 47 : 1084 – 1098 . English transl. Sov. Phys. JETP 20, 726–735 (1965)
   Google Scholar
• Braginsky , S. I. 1964b . Theory of the hydromagnetic dynamo . JETP , 47 : 2178 – 2193 . English transl. Sov. Phys, JETP 20, 1462–1471 (1965)
   Google Scholar
• Braginsky , S. I. 1975 . Nearly axially symmetric model of the hydromagnetic dynamo of the Earth. I . Goemagn. & Aeron. , 15 : 149 English transl. pp. 122–128
   Google Scholar
• Braginsky , S. I. 1976 . On the nearly axially-symmetrical model of the hydromagnetic dynamo of the Earth . Phys. Earth & Plant. Inter. , 11 : 191 – 199 .
   Web of Science ®Google Scholar
• Braginsky , S. I. 1978 . A nearly axially symmetric model of the hydromagnetic dynamo of the Earth . Geomagn. & Aeron. , 18 : 340 – 351 . English transl. pp. 225–231
   Google Scholar
• Busse , F. H. 1970 . Thermal instabilities in rapidly rotating systems . J. Fluid Mech. , 44 : 441 – 460 .
   Web of Science ®Google Scholar
• Busse , F. H. 1975 . A model of the geodynamo . Geophys. J. R. Astron. Soc. , 42 : 437 – 459 .
   Web of Science ®Google Scholar
• Eltayeb , I. A. and Kumar , S. 1977 . Hydromagnetic convective instability of a rotating self-gravitating fluid sphere containing a uniform distirubiton of heat sources . Proc. R. Soc. London , A353 : 145 – 162 .
   Google Scholar
• Eltayeb , I. A. and Roberts , P. H. 1970 . On the hydromagnetics of rotating fluids . Astrophys. J. , 162 : 699 – 701 .
   Web of Science ®Google Scholar
• Fearn , D. R. 1979a . Thermally driven hydromagnetic convection in a rapidly rotating sphere . Proc. R. Soc. London , A369 : 227 – 242 .
   Web of Science ®Google Scholar
• Fearn , D. R. 1979b . Thermal and magnetic instabilities in a rapidly rotating fluid sphere . Geophys. & Astrophys. Fluid Dyn. , 14 : 103 – 126 .
   Google Scholar
• Fearn , D. R. 1983 . Boundary conditions for a rapidly rotating magnetic system in a cylindrical container . Geophys. & Astrophys. Fluid Dyn. , 25 : 65 – 75 .
   Web of Science ®Google Scholar
• Fearn , D. R. 1985 . Hydromagnetic waves in a differentially rotating annulus III. The effect of an axial field . Geophys. & Astrophys. Fluid Dyn. , 33 : 185 – 197 .
   Web of Science ®Google Scholar
• Fearn , D. R. and Proctor , M. R. E. 1984 . Self-consistent dynamo models driven by hydromagnetic instabilities . Phys. Earth & Planet. Inter. , 36 : 78 – 84 .
   Web of Science ®Google Scholar
• Ierley , G. R. 1985 . Macrodynamics of α2-dynamos . Geophys. & Astrophys. Fluid Dyn. , 34 : 143 – 173 .
   Web of Science ®Google Scholar
• Malkus , W. V. R. and Proctor , M. R. E. 1975 . The macrodynamics of α-effect dynamos in rotating fluids . J. Fluid Mech. , 67 : 417 – 443 .
   Web of Science ®Google Scholar
• Roberts , P. H. 1968 . On the thermal instability of a rotating fluid sphere containing heat sources . Philos. Trans. R. Soc. London , A263 : 93 – 117 .
   Web of Science ®Google Scholar
• Roberts , P. H. and Stewartson , K. 1974 . On finite amplitude convection in a rotating magnetic system . Philos. Trans. R. Soc. London , A277 : 287 – 315 .
   Web of Science ®Google Scholar
• Roberts , P. H. and Stewartson , K. 1975 . Double roll convection in a rotating magnetic system . J. Fluid Mech. , 68 : 447 – 466 .
   Web of Science ®Google Scholar
• Soward , A. M. 1979a . Convection driven dynamos . Phys. Earth & Planet. Inter. , 20 : 134 – 151 .
   Web of Science ®Google Scholar
• Soward , A. M. 1979b . Thermal and magnetically driven convection in a rapidly rotating fluid layer . J. Fluid Mech. , 90 : 669 – 684 .
   Web of Science ®Google Scholar
• Soward , A. M. 1980 . Finite-amplitude thermal convection and geostrophic flow in a rotating magnetic system . J. Fluid Mech. , 98 : 449 – 471 .
   Web of Science ®Google Scholar
• Soward , A. M. 1983 . “ Convection-driven dynamos ” . In Stellar and Planetary Magnetism Edited by: Soward , A. M. 237 – 244 . in The Fluid Mechanics of Astrophysics and Geophysics, Vol. 2 (series ed. P. H. Roberts)
   Google Scholar
• Soward , A. M. and Jones , C. A. 1983 . α2-dynamos and Taylor's constraint . Geophys. & Astrophys. Fluid Dyn. , 27 : 87 – 122 .
   Web of Science ®Google Scholar
• Stevenson , D. J. 1984 . The energy flux number and three types of planetary dynamo . Astron. Nachr. , 305 : 257 – 264 .
   Google Scholar
• Taylor , J. B. 1963 . The magnetohydrodynamics of a rotating fluid and the Earth's dynamo problem . Proc. R. Soc. London , A274 : 274 – 283 .
   Web of Science ®Google Scholar
• Tough , J. G. and Roberts , P. H. 1968 . Nearly symmetric hydromagnetic dynamos . Phys. Earth & Planet. Inter. , 1 : 288 – 296 .
   Google Scholar