Bypassing Cowling's theorem in axisymmetric fluid dynamos

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.

4 pages, 6 figures

References in corpus (4)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• On the magnetic fields generated by experimental dynamos
• Numerical simulations of current generation and dynamo excitation in a mechanically-forced, turbulent flow
• Intermittent magnetic field excitation by a turbulent flow of liquid sodium

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• Wave-driven dynamo action in spherical MHD systems
• Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid
• Numerical simulation of laminar plasma dynamos in a cylindrical von Kármán flow
• Self-consistent simulations of a von Kármán type dynamo in a spherical domain with metallic walls
• Effect of metallic walls on dynamos generated by laminar boundary-driven flow in a spherical domain
• Energy Fluxes during Dynamo Reversals