Nonlinear planetary dynamos in a rotating spherical shell

Abstract

Results are presented of an investigation of nonlinear planetary dynamo models in the rapid rotation limit for the geometry of a spherical shell. The magnetic induction equation for axisymmetric fields is solved with a prescribed differential rotation and α-effect. The nonlinearity comes from the azimuthal geostrophic flow, whose magnitude is linked to Taylor's constraint as modified by core-mantle viscous coupling in the Ekman boundary layer. The objectives of this work are to determine whether Taylor's constraint is met when the magnetic field is strong and to solve the special numerical stability problems associated with the term which describes the modified Taylor's condition. A stable numerical method based on spectral approximations is presented to solve the general α²ω-dynamo equations. Evidence of the existence of Taylor's states in the geometry of a spherical shell is demonstrated in both the α²- and the αω-limits.