Hysteresis cycle in a turbulent, spherically bounded MHD dynamo model

We report direct numerical magnetohydrodynamic simulations at low magnetic Prandtl numbers of a turbulent two-cell flow in a bounded, spherical geometry, driven by a constant body force. The flow amplifies infinitesimal magnetic perturbations if the magnetic Reynolds number Rm is larger than a threshold Rmc, resulting in a self-excited equatorial magnetic dipole. However, finite amplitude perturbations to the magnetic field can trigger dynamo action below Rmc: a hysteresis cycle has been found that can sustain dynamo action in an interval Rm0 < Rm < Rmc. The instability is therefore governed by a subcritical bifurcation. This hysteretic behaviour is associated with changes in the turbulent velocity field caused by the finite amplitude magnetic field. It is then shown that the dynamo state can be accessed by transiently applying a magnetic field from an external source. Finally, a dynamo state with characteristics different from the self-excited case is found in the vicinity of Rm0. 3 Author to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 013027 1367-2630/09/013027+21$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft