Plate tectonics provides a remarkably accurate kinematic description of the motion of the earth's crust but a fully dynamical theory requires an understanding of convection in the mantle. Thus the properties of plates and of the mantle must be related to a systematic study of convection. This paper reviews both the geophysical information and the fluid dynamics of convection in a Boussinesq fluid of infinite Prandtl number. Numerical experiments have been carried out on several simple two-dimensional models, in which convection is driven by imposed horizontal temperature gradients or else by heating either internally or from below. The results are presented and analysed in terms of simple physical models. Although the computations are highly idealized and omit variation of viscosity and other major features of mantle convection, they can be related to geophysical measurements. In particular, the external gravity field depends on changes in surface elevation; this suggests an observational means of investigating convection in the upper mantle.
The empirical relation between rotation period, spectral type, and activity cycle period is investigated for a sample of 13 slowly rotating lower main-sequence stars, including the Sun, all of which show long-term chromospheric variability like that of the solar cycle. It is found that for slowly rotating stars of similar spectral type, the cycle period P cyc and rotation period P rot are related by P cyc oc P rot n , where n & 1.25. When the stars, whose individual spectral types range from G2 to K7, are considered as a group, their cycle periods are found to be consistent with the relation P cyc ae (P rot /T c)", where t c is the convective turnover time near the bottom of the convection zone appropriate to each spectral type, and n is the same as before. These relations are interpreted in terms of simple nonlinear dynamo models. The increase of P cyc with increasing P rot disagrees with models in which the magnetic field is limited by quenching of the a effect or of differential rotation; however, it is consistent with models in which dynamo action is limited by losses due to magnetic buoyancy.
Measurements of 10 Be concentration in the Dye 3 ice core show that magnetic cycles persisted throughout the Maunder Minimum, although the Sun's overall activity was drastically reduced and sunspots virtually disappeared. Thus the dates of maxima and minima can now be reliably estimated. Similar behaviour is shown by a nonlinear dynamo model, which predicts that, after a grand minimum, the Sun's toroidal field may switch from being antisymmetric to being symmetric about the equator. The presence of cyclic activity during the Maunder Minimum limits estimates of the solar contribution to climatic change.
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