Abstract
The present understanding of convection in rotating spherical fluid shells is reviewed and some recent results on coherent structures and magnetic field generation are considered in detail. The constraints exerted by the Coriolis force leads to unusual properties not found in nonrotating systems, such as vacillations, localized convection, and chaotic relaxation oscillations. The central role played by the differential rotation generated by the Reynolds stress of convection in the case of Prandtl numbers of the order unity or less is emphasized. Magnetic fields generated through the dynamo process offer new degrees of freedom. Through the braking of the differential rotation the Lorentz force contributes to an enhanced heat transport.
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