1 | Equation (2) is written here in a frame of reference rotating with angular velocity , so that a Coriolis force term appears explicitly, while the centrifugal force has been subsumed into the gravitational term. | |

2 | Note, however, that an axisymmetric flow can sustain a non-axisymmetric magnetic field against resistive decay. | |

3 | Helioseismology has also revealed the existence of a significant radial shear in the outermost layers of the solar convective envelope. Even if the storage problem could be somehow bypassed, it does not appear possible to construct a viable solar dynamo model relying exclusively on this angular velocity gradient (see, e.g., Dikpati et al., 2002; Brandenburg, 2005, for illustrative calculations). | |

4 | Models retaining both -terms are dubbed dynamos, and may be relevant to the solar case even in the regime, if the latter operates in a very thin layer, e.g. the tachocline (see, e.g., DeLuca and Gilman, 1988; Gilman et al., 1989; Choudhuri, 1990); this is because the -effect gets curled in Equation (25) for the mean toroidal field. Models relying only on the -terms are said to be dynamos. Such models are relevant to dynamo action in planetary cores and convective stars with vanishing differential rotation (if such a thing exists). | |

5 | These are not “waves” in usual sense of the word, although they are described by modal solutions of the form . | |

6 | Although some turbulence model predict such higher-order latitudinal dependencies, the functional forms adopted here are largely ad hoc, and are made for strictly illustrative purposes. | |

7 | Mea culpa on this one... | |

8 | For this particular choice of , , and profiles, solutions with negative are non-oscillatory in most of the parameter space. This is in agreement with the results of Markiel and Thomas (1999). | |

9 | We largely exclude from the foregoing discussion mathematical toy-models that aim exclusively at reproducing the shape of the sunspot number time series. For recent entry points in this literature, see, e.g., Mininni et al. (2002). | |

10 | Dynamo saturation can also occur by magnetically-mediated changes in the “topological” properties of a turbulent flow, without significant decrease in the turbulent flow amplitudes; see Cattaneo et al. (1996) for a nice, simple example. | |

11 | This effect has been found to be the dominant dynamo quenching mechanism in some numerical simulations of dynamo action in a rotating, thermally-driven turbulent spherical shell (see, e.g., Gilman, 1983), as well as in models confined to thin shells (DeLuca and Gilman, 1988). |

Living Rev. Solar Phys. 7, (2010), 3
http://www.livingreviews.org/lrsp-2010-3 |
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