Bypassing Cowling's theorem in axisymmetric fluid dynamos

TL;DR

This paper demonstrates how an axisymmetric fluid dynamo can generate an axial dipole magnetic field, bypassing Cowling's theorem through secondary bifurcations and mode interactions, supported by numerical simulations and symmetry-based models.

Contribution

It reveals a new mechanism for axial dipole generation in axisymmetric flows, bypassing Cowling's theorem, via secondary bifurcations at low Reynolds numbers.

Findings

Axial dipole can be generated at low Re through secondary bifurcation.

Magnetic field structures can switch from equatorial to axial dipoles.

System always finds a way to bypass Cowling's theorem constraints.

Abstract

We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. At small enough Reynolds number, Re, the flow is axisymmetric and generates an equatorial dipole above a critical magnetic Reynolds number Rmc . The magnetic field thus breaks axisymmetry, in agreement with Cowling's theorem. This structure of the magnetic field is however replaced by a dominant axial dipole when Re is larger and allows non axisymmetric fluctuations in the flow. We show here that even in the absence of such fluctuations, an axial dipole can also be generated, at low Re, through a secondary bifurcation, when Rm is increased above the dynamo threshold. The system therefore always find a way to bypass the constraint imposed by Cowling's theorem. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.