Statistical properties of reversals and chrons in numerical dynamos and implications for the geodynamo

We analyse a series of very long runs (equivalent to up to 50 Myr) produced by chemically-driven dynamos. All runs assume homogeneous boundary conditions, an electrically conducting inner-core (except for one run) and only differ by the choice of the Rayleigh number Ra ★ . Introducing dynamo-based definitions of reversals, chrons and related concepts, such as “failed reversals” and “segments” (bounded by reversals or failed reversals), we investigate the distributions of chron and segment lengths, those of reversal and failed reversal durations, the way dipole field behaves through reversals and failed reversals, and the possible links between the axial dipole intensity and chron or segment lengths. We show that chron and segment lengths are very well described in terms of a Poisson process (with no occurrence of superchrons), while distributions of reversal and failed reversal durations are better fitted by log-normal distributions. We found that reversal rates generally increase in proportion to Rm - Rm c , Rm being the magnetic Reynolds number and Rm c a critical value. In contrast, reversal and failed reversal durations appear to be mainly controlled by the core’s magnetic diffusion timescale. More generally, we show that much of the reversing behaviour of these dynamos can be understood by examining their signature in a ( g 1 0 , g 1 1 , h 1 1 ) phase-space plot. This reveals that the run with an insulating inner-core is very different and has only two distinct modes of opposite polarity, which we argue is the reason it displays less reversals and failed reversals, and has a clear tendency to produce an intensity “overshoot” and some systematic pattern in the dipole pole behaviour through reversals and failed reversals. This contrasts with conducting inner-core runs, which display an additional central unstable mode, the importance of which increases with Rm, and which is responsible for the more complex reversing behaviour of these dynamos. Available paleomagnetic data suggest that the current geodynamo could have such a (small) central mode, which would thus imply a strong sensitivity of the frequency and complexity of reversals and of the likelihood of failed reversals, to changes in the geodynamo’s driving parameters through geological times.