The α-effect in 2D fast dynamos

References

• Cattaneo , F and Hughes , DW . 2006 . Dynamo action in a convective rotating layer . J. Fluid Mech. , 553 : 401 – 418 .
   Web of Science ®Google Scholar
• Cattaneo , F and Tobias , SM . 2005 . Interactions between dynamos at different scales . Phys. Fluids , 17 : 127105
   Web of Science ®Google Scholar
• Childress , S . 1979 . Alpha-effect in flux ropes and sheets . Phys. Earth Planet Int. , 20 : 172 – 180 .
   Web of Science ®Google Scholar
• Childress , S and Gilbert , AD . 1995 . Stretch, twist, fold, the fast dynamo , Berlin, , Germany : Springer .
   Google Scholar
• Childress , S and Soward , AM . 1989 . Scalar transport and alpha-effect for a family of cat's-eye flows . J. Fluid Mech. , 205 : 99 – 133 .
   Web of Science ®Google Scholar
• Courvoisier , A . 2006 . Dynamo action and the generation of large-scale magnetic fields in Astrophysics. PhD thesis , Leeds, , England : University of Leeds .
   Google Scholar
• Courvoisier , A , Gilbert , AD and Ponty , Y . 2005 . Dynamo action in flows with cat's-eyes . Geophys. Astrophys. Fluid Dyn. , 99 : 413 – 429 .
   Web of Science ®Google Scholar
• Courvoisier , A , Hughes , DW and Tobias , SM . 2006 . α − effect in a family of chaotic flows . Phys. Rev. Lett. , 96 : 034503
   PubMedGoogle Scholar
• Galloway , DJ and Proctor , MRE . 1992 . Numerical calculations of fast dynamos for smooth velocity fields with realistic diffusion . Nature , 356 : 691 – 693 .
   Web of Science ®Google Scholar
• Gilbert , AD and Bayly , BJ . 1992 . Magnetic field intermittency and fast dynamo action in random helical flows . Phil. Trans. R. Soc. Lon. A , 241 : 199 – 214 .
   Google Scholar
• Gilbert , AD , Soward , AM and Childress , S . 1996 . A fast dynamo of αω-type . Geophys. Astrophys. Fluid Dyn. , 85 : 279 – 314 .
   Google Scholar
• Hughes , DW , Cattaneo , F and Kim , E-J . 1998 . Nonlinear multi-cellular fast dynamos . Studia geoph. et. geod. , 42 : 328 – 334 .
   Google Scholar
• Klapper , I and Young , LS . 1995 . Bounds on the fast dynamo growth rate involving topological entropy . Comm. Math. Phys. , 173 : 623 – 646 .
   Web of Science ®Google Scholar
• Krause , F and Rädler , K-H . 1980 . Mean field magnetohydrodynamics and dynamo theory , Oxford, , England : Pergamon Press .
   Google Scholar
• Moffatt , HK . 1974 . The mean electromotive force generated by turbulence in the limit of perfect conductivity . J. Fluid Mech. , 65 : 1 – 10 .
   Google Scholar
• Moffatt , HK . 1978 . Magnetic field generation in electrically conducting fluids , Cambridge, , England : Cambridge University Press .
   Google Scholar
• Ossendrijver , M , Stix , M and Brandenburg , A . 2001 . Magnetoconvection and dynamo coefficients I: Dependence of the α-effect on rotation and magnetic field . Astron. Astrophys. , 376 : 713 – 726 .
   Web of Science ®Google Scholar
• Otani , NF . 1993 . A fast kinematic dynamo in time-dependent two-dimensional flows . J. Fluid Mech. , 253 : 327 – 340 .
   Web of Science ®Google Scholar
• Parker , EN . 1955 . Hydromagnetic dynamo models . Astrophys. J. , 122 : 293 – 314 .
   Web of Science ®Google Scholar
• Plunian , F , Marty , G and Alemani , A . 1999 . Kinematic dynamo action in a network of screw motions: application to the core of a fast breeder reactor . J. Fluid Mech. , 382 : 137 – 154 .
   Web of Science ®Google Scholar
• Plunian , F and Rädler , K-H . 2002 . Harmonic and subharmonic solutions of the Roberts dynamo problem. Application to the Karlsruhe experiment . Magnetohydrodynamics , 38 : 92 – 103 .
   Google Scholar
• Ponty , Y , Pouquet , A and Sulem , P-L . 1995 . Dynamos in weakly chaotic two-dimensional flows . Geophys. Astrophys. Fluid Dyn. , 79 : 239 – 257 .
   Web of Science ®Google Scholar
• Press , WH , Teukolsky , SA , Vetterling , WT and Flannery , BP . 1992 . Numerical Recipes in Fortran 77, Second Edition , Cambridge, , England : Cambridge University Press .
   Google Scholar
• Rädler , K-H . 1969a . A new turbulent dynamo [English translation by Roberts and Stix (1971)] . Monats Dt Akad Wiss , 11 : 272 – 279 .
   Google Scholar
• Rädler , K-H . 1969b . On the electrodynamics of turbulent fluids under the influence of Coriolis forces [English translation by Roberts and Stix (1971)] . Monats Dt. Akad. Wiss. , 11 : 194 – 201 .
   Google Scholar
• Rädler , K-H and Brandenburg , A . 2003 . Contributions to the theory of a two-scale homogeneous dynamo experiment . Phys. Rev. E. , 67 : 2 – 026401 .
   Google Scholar
• Rädler , K-H , Rheinhardt , M , Apstein , E and Fuchs , H . 2002 . On the mean-field theory of the Karlsruhe dynamo experiment . Nonlinear Processes in Geophysics , 9 : 171 – 187 .
   Web of Science ®Google Scholar
• Rhines , PB and Young , WR . 1983 . How rapidly is a passive scalar mixed within closed streamlines . J. Fluid Mech. , 133 : 133 – 145 .
   Web of Science ®Google Scholar
• Roberts , GO . 1970 . Spatially periodic dynamos . Phil. Trans. R. Soc. Lon. A , 266 : 535 – 558 .
   Web of Science ®Google Scholar
• Roberts , GO . 1972 . Dynamo action of fluid motions with two-dimensional periodicity . Phil. Trans. R. Soc. Lon. A , 271 : 411 – 454 .
   Web of Science ®Google Scholar
• Roberts , PH and Stix , M . 1971 . The turbulent dynamo: a translation of a series of papers by Krause F., Rädler K.-H., Steenbeck M. Tech. Note 60, NCAR, Boulder, Colorado
   Google Scholar
• Soward , AM . 1987 . Fast dynamo action in a steady flow . J. Fluid Mech. , 180 : 267 – 295 .
   Web of Science ®Google Scholar
• Soward , AM . 1994 . “ Fast dynamos ” . In Lectures on Solar and Planetary Dynamos , Edited by: Proctor , MRE and Gilbert , AD . 181 – 217 . Cambridge, , England : Cambridge University Press .
   Google Scholar
• Vainshtein , SI and Zel'dovich , YB . 1972 . Origin of magnetic fields in astrophysics . Sov. Phys. Usp. , 15 : 159 – 172 .
   Google Scholar
• Weiss , NO . 1966 . The expulsion of magnetic flux by eddies . Proc. R. Soc. Lon. A , 293 : 310 – 328 .
   Web of Science ®Google Scholar