Simulation study of the symmetry-breaking instability and the dipole field reversal in a rotating spherical shell dynamo

Abstract

The reversal mechanism of a dipole magnetic field generated by dynamo action in a rotating spherical shell is investigated by a three-dimensional nonlinear magnetohydrodynamic simulation as well as a linear stability analysis. The emphasis of the study is on understanding the relationship between dipole reversal and the symmetry properties of the dynamo solution. As a result, first, it is found that there is a threshold of the magnetic Prandtl number, below which the dipole field is never reversed, and above which the reversal occurs at irregular intervals like the paleomagnetic evolution of the geodynamo. Second, it is shown that the dynamo process responsible for the generation of a dipole field (called “a-dynamo” in this paper) consists only of the antimirror symmetric magnetic field and the mirror symmetric velocity field with respect to the equatorial plane. Third, it is found that the components of the opposite symmetry to the a-dynamo grow only during the polarity reversal events and quickly decay afterwards. This indicates that the dipole field reversal and the loss of equatorial symmetry are tightly connected. In fact, it is clearly demonstrated by numerical analyses that the a-dynamo process is linearly unstable for the perturbation of opposite symmetry when the magnetic Prandtl number exceeds the threshold for dipole reversal. Mode coupling between the longitudinal Fourier components plays a crucial role in creating the instability. Based on the above results, it is proposed that symmetry-breaking instability could be the mechanism for dipole field reversal in the geodynamo process. The energy conversion between components of different symmetry is also analyzed in the quasistable polarity phase and in the polarity reversal phase, respectively.

Theory and Modeling of Planetary Dynamos

“…Several authors have observed that numerical reversal processes correlate with an increased equatorially symmetric magnetic field component (Li et al 2002;Takahashi et al 2005, Nishikawa and Kusano 2008. This is typically accompanied by an increase of the equatorially asymmetric kinetic field which is required to convert equatorially asymmetric magnetic field into its symmetric counterpart.…”

“…In magnetic upwellings, the north/south coherence is obviously violated and inverse field is produced predominantly on one side of the equator (Aubert et al 2008b;Wicht and Olson 2004). This corresponds to the loss of equatorial asymmetry in the magnetic field and of equatorial symmetry in the flow field described by some authors (Li et al 2002;Takahashi et al 2007;Nishikawa and Kusano 2008).…”

“…5.2 that the scaling based on the heat flux out of Earth core places the geodynamo at Ro = 0.09 and thus into the regime E where Earth like reversals are found in many simulations (Christensen and Aubert 2006;Olson and Christensen 2006). Should the weakly compressible models that seem to model reversals at smaller local Rossby numbers provide a vital alternative here (Li et al 2002;Nishikawa and Kusano 2008;McMillan and Sarson 2003)?…”

“…Li et al (2002) and Nishikawa and Kusano (2008) present Kageyama type models where magnetic field reversals set in at relatively low Rayleigh numbers when the magnetic Prandtl number is increased (see also McMillan and Sarson 2003). This is at odds with the minor influence illustrated in Fig.…”

“…The Kageyama type model describes the dynamo medium as an ideal gas and retains weak compressibility effects Sato 1995, 1997;Kageyama et al , 2008Li et al 2002;Kageyama and Yoshida 2005;Nishikawa and Kusano 2008).…”