From isotropic to rapidly rotating anisotropic alpha-squared dynamos

Abstract

Mean field α 2 -dynamos in a sphere with an insulating exterior are considered for a steady α-effect of the form α = a(I − A z z), A ≥ 0, derived by Moffatt (Dynamo action associated with random inertial waves in a rotating conducting fluid. J. Fluid Mech. 1970, 44, 705-719) for strong rotation. The unit vector z is aligned with the angular velocity Ω and as Ω → ∞, A → 1. We consider the effect on axisymmetric magnetic fields of increasing rotation rate, i.e. A → 1, so that the α-effect varies from isotropic to anisotropic, for two models. We find that both equatorially symmetric and antisymmetric critical solutions bifurcate from steady to oscillatory at some value of A ∈ (0, 1). The bifurcation is associated with the poleward migration of strong magnetic fields, leaving a region of weak field near the equator. This region increases with the rotation rate. No antidynamo action was found at the fast rotation limit A = 1. The α-effect is re-scaled to α = a((1 + A)I − A z z) for A < 0 allowing all possible solutions to be studied by restricting A to [−2, 2]. In particular, we consider the mean field axisymmetric antidynamo limit at A = −1. Our results are in complete agreement with those in Phillips (Mean dynamos. Ph.D. Thesis, University of Sydney, 1993), where A ∈ [0, 1] is considered.

Homogeneous planar and two-dimensional mean-field antidynamo theorems with zero mean flow

“…Thus, if the turbulence is homogeneous, any two-dimensional mean-field decays. However, no general antidynamo result can be expected: dynamo action occurs in the spherical case (Phillips and Ivers 2013). Neither mean-field ADT applies in rapidly-rotating turbulence with a strong magnetic field, e.g.…”