The nonlinear solar dynamo and differential rotation: A Taylor number puzzle?

Abstract

We consider dynamically consistent mean-field dynamos in a spherical shell of incompressible fluid. The generation of magnetic field and differential rotation is parameterized by the α- and Λ-effects, respectively. Extending previous investigations, we include now the cases of moderate and rapid rotation in the sense that the inverse Rossby number can approach or exceed unity: This can lead to disk-shaped Ω-contours, which are in better accordance with recent results of helioseismology than cylindrical Ω-contours. On the other hand, in order to obtain αω-dynamo cycles the Taylor number has to be so large, that eventually cylindrical Ω-contours become unavoidable (cf. Taylor-Proudman theorem). We discuss the different possibilities in a state diagram, where the inverse Rossby number and the relative correlation length are taken as the elementary parameters for mean-field dynamos.