Nonlinear generation of large-scale magnetic fields in forced spherical shell dynamos

Abstract

In an earlier paper [P. W. LivermoreD. W. HughesS. M. Tobias"The role of helicity stretching in forced kinematic dynamos in a spherical shell," Phys. Fluids19057101 (2007)]we considered the kinematic dynamo action resulting from a forced helical flow in a spherical shell. Although mean field electrodynamics suggests that the resulting magnetic field should have a significant mean (axisymmetric) componentwe found no evidence for this; the dynamo action was distinctly small scale. Here we extend our investigation into the nonlinear regime in which the magnetic field reacts back on the velocity via the Lorentz force. Our main result is somewhat surprisingnamelythat nonlinear effects lead to a considerable change in the structure of the magnetic fieldits final state having a significant mean component. By investigating the dominant flow-field interactionswe isolate the dynamo mechanism show schematically how the generation process differs between the kinematic nonlinear regimes. In additionwe are able to calculate some components of the transport coefficient α thus discuss our results within the context of mean field electrodynamics. © 2010 American Institute of Physics.